Managerial incentives to increase firm volatility provided by debt stock and options

Joshua D Anderson jdandersmitedu

(617) 253-7974

John E Core jcoremitedu (617) 715-4819

Abstract We measure a managerrsquos risk-taking incentives as the total sensitivity of the managerrsquos debt stock and option holdings to firm volatility We compare this measure to the option vega and to relative measures used by the prior literature Vega does not capture risk incentives from managersrsquo stock and debt holdings and does not reflect the fact that employee options are warrants The relative measures do not incorporate the sensitivity of options to volatility The new measure explains risk choices better than vega and the relative measures Our measure should be useful for future research on managersrsquo risk choices

First draft October 2011 This draft May 30 2013

_______________ Corresponding author We gratefully acknowledge comments from Ana Albuquerque (discussant) Wayne Guay Mitchell Petersen Eric So Daniel Taylor Anand Venkateswaran Jerry Zimmerman and seminar participants at the American Accounting Association 2012 Annual Meeting Columbia University MIT Sloan School of Management Northeastern University Pennsylvania State University Temple University and the University of Technology Sydney We thank Ingolf Dittmann for his estimates of CEO non-firm wealth We appreciate the financial support of the MIT Sloan School of Management

1

1 Introduction

A large literature uses the sensitivity of stock options to an increase in stock volatility

(ldquovegardquo) to study whether managersrsquo equity portfolios provide incentives to increase risk

Studies on early samples show a strong positive association between vega and risk-taking (Guay

1999 Coles et al 2006) whereas studies on later samples show mixed results (eg Hayes et al

2012) We re-examine vega and show that it has two shortcomings (1) it does not capture

potential risk incentives from managersrsquo stock and inside debt (unsecured pensions and deferred

compensation) and (2) it does not reflect the fact that employee options are warrants We derive

and calculate an overall measure of a managerrsquos risk-taking incentives using the total sensitivity

of the managerrsquos debt stock and option holdings to firm volatility

Limited liability implies that equity is an option on firm value with a strike price equal to

the face value of debt Consequently an increase in firm volatility increases equity value by

reducing debt value (Black and Scholes 1973 Merton 1974) When a firm has options this

increase in equity value is shared between the stock and options This implies that the option

sensitivity to volatility is larger than vega Because options are warrants an increase in volatility

that increases option value comes in part from a decrease in stock value If the firm has no debt

all of the increase in option value comes from a decrease in stock value This implies a stock

sensitivity to volatility that goes from being negative to positive as leverage increases A

managerrsquos attitude toward risk will be affected by the sensitivities of the managersrsquo holdings of

debt stock and options to firm volatility

2

To estimate these sensitivities we follow Merton (1974) and value total firm equity

(stock and stock options) as an option on the value of firm assets The model gives an estimate of

the decrease in debt value for an increase in firm volatility This decrease in debt value implies

an equal increase in equity value In turn the increase in equity value is shared between the stock

and stock options We estimate the CEOrsquos sensitivities by applying the CEOrsquos ownership of debt

stock and options to the firmrsquos sensitivities

We estimate these sensitivities for a sample of 5967 Execucomp CEO-years from 2006

to 2010 The typical CEO in our sample owns roughly 2 of the debt 2 of the stock and 16

of the options In terms of incentives to increase volatility this CEO has small negative

incentives from debt small positive incentives from stock and large positive incentives from

options A one standard deviation increase in firm volatility increases the average CEOrsquos wealth

by $3 million or 7 of total wealth

The total sensitivity increases as leverage increases but the vega roughly remains

constant with leverage As leverage increases the debt sensitivity becomes more negative

(making the CEO averse to risk increases) but the equity sensitivity (the sum of stock and option

sensitivities) increases more rapidly This occurs because the stock sensitivity changes from

being negative to strongly positive

Because vega ignores the debt and stock sensitivities it can be a noisy and biased

measure of risk-taking incentives If the total sensitivity better reflects CEO incentives we

expect it to be more highly associated with CEOsrsquo risk-taking choices To test this conjecture we

examine the association between the total sensitivity and vega and three proxies for future firm

3

risk stock volatility research and development expense and leverage We specify regression

models following Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

Theory suggests that incentives relative to wealth determine risk-taking For this reason

we examine modified specifications in which we scale the CEOrsquos risk-taking incentives with a

proxy for the CEOrsquos total wealth We also scale the CEOrsquos incentives to increase stock price

(ldquodeltardquo) by total wealth Prior research (eg Coles et al 2006) controls for wealth effects by

using tenure and cash compensation as proxies for CEO wealth We find that the scaled measures

explain firm risk better than the unscaled measures and that the scaled total sensitivity explains

firm risk better than the scaled vega

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

unscaled measures1

1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample

4

A concern about regressions of incentives on risk-taking is reverse causality (that is

when risk is expected to be high firms use high risk-taking incentives) To explore the

robustness of our results we follow Hayes et al (2012) and use the introduction of option

expensing in 2005 as an exogenous change to incentives Consistent with Hayes et al we find

no significant association between changes in vega and changes in firm risk for our sample

However the change in scaled equity sensitivity is significantly positively associated with both

the change in stock volatility and the change in leverage We find no association however with

the change in RampD expense

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures used in the recent literature (eg Cassell et al 2012 Sundaram and

Yermack 2007 Wei and Yermack 2011) are noisy and can be biased These measures do not

correctly incorporate the sensitivity of option value to firm volatility We calculate a measure

that correctly weights the managerrsquos debt stock and option sensitivities The prior measures

suggest that CEOs on average are highly aligned with debt holders the average CEO has debt

incentives to reduce volatility that are three times his or her equity incentives to increase

volatility By contrast the corrected measure which explicitly takes into account the incentives

to increase firm volatility from options is an order of magnitude smaller suggesting that CEOs

have little alignment with debt holders the average CEO has incentives to reduce volatility that

are equal to 04 times his or her equity incentives to increase volatility Consistent with prior

literature we find that these ratios are negatively associated with risk choices However our

5

scaled total sensitivity measure is more highly associated with risk-taking choices than the

relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

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of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

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inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

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Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

1

1 Introduction

A large literature uses the sensitivity of stock options to an increase in stock volatility

(ldquovegardquo) to study whether managersrsquo equity portfolios provide incentives to increase risk

Studies on early samples show a strong positive association between vega and risk-taking (Guay

1999 Coles et al 2006) whereas studies on later samples show mixed results (eg Hayes et al

2012) We re-examine vega and show that it has two shortcomings (1) it does not capture

potential risk incentives from managersrsquo stock and inside debt (unsecured pensions and deferred

compensation) and (2) it does not reflect the fact that employee options are warrants We derive

and calculate an overall measure of a managerrsquos risk-taking incentives using the total sensitivity

of the managerrsquos debt stock and option holdings to firm volatility

Limited liability implies that equity is an option on firm value with a strike price equal to

the face value of debt Consequently an increase in firm volatility increases equity value by

reducing debt value (Black and Scholes 1973 Merton 1974) When a firm has options this

increase in equity value is shared between the stock and options This implies that the option

sensitivity to volatility is larger than vega Because options are warrants an increase in volatility

that increases option value comes in part from a decrease in stock value If the firm has no debt

all of the increase in option value comes from a decrease in stock value This implies a stock

sensitivity to volatility that goes from being negative to positive as leverage increases A

managerrsquos attitude toward risk will be affected by the sensitivities of the managersrsquo holdings of

debt stock and options to firm volatility

2

To estimate these sensitivities we follow Merton (1974) and value total firm equity

(stock and stock options) as an option on the value of firm assets The model gives an estimate of

the decrease in debt value for an increase in firm volatility This decrease in debt value implies

an equal increase in equity value In turn the increase in equity value is shared between the stock

and stock options We estimate the CEOrsquos sensitivities by applying the CEOrsquos ownership of debt

stock and options to the firmrsquos sensitivities

We estimate these sensitivities for a sample of 5967 Execucomp CEO-years from 2006

to 2010 The typical CEO in our sample owns roughly 2 of the debt 2 of the stock and 16

of the options In terms of incentives to increase volatility this CEO has small negative

incentives from debt small positive incentives from stock and large positive incentives from

options A one standard deviation increase in firm volatility increases the average CEOrsquos wealth

by $3 million or 7 of total wealth

The total sensitivity increases as leverage increases but the vega roughly remains

constant with leverage As leverage increases the debt sensitivity becomes more negative

(making the CEO averse to risk increases) but the equity sensitivity (the sum of stock and option

sensitivities) increases more rapidly This occurs because the stock sensitivity changes from

being negative to strongly positive

Because vega ignores the debt and stock sensitivities it can be a noisy and biased

measure of risk-taking incentives If the total sensitivity better reflects CEO incentives we

expect it to be more highly associated with CEOsrsquo risk-taking choices To test this conjecture we

examine the association between the total sensitivity and vega and three proxies for future firm

3

risk stock volatility research and development expense and leverage We specify regression

models following Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

Theory suggests that incentives relative to wealth determine risk-taking For this reason

we examine modified specifications in which we scale the CEOrsquos risk-taking incentives with a

proxy for the CEOrsquos total wealth We also scale the CEOrsquos incentives to increase stock price

(ldquodeltardquo) by total wealth Prior research (eg Coles et al 2006) controls for wealth effects by

using tenure and cash compensation as proxies for CEO wealth We find that the scaled measures

explain firm risk better than the unscaled measures and that the scaled total sensitivity explains

firm risk better than the scaled vega

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

unscaled measures1

1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample

4

A concern about regressions of incentives on risk-taking is reverse causality (that is

when risk is expected to be high firms use high risk-taking incentives) To explore the

robustness of our results we follow Hayes et al (2012) and use the introduction of option

expensing in 2005 as an exogenous change to incentives Consistent with Hayes et al we find

no significant association between changes in vega and changes in firm risk for our sample

However the change in scaled equity sensitivity is significantly positively associated with both

the change in stock volatility and the change in leverage We find no association however with

the change in RampD expense

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures used in the recent literature (eg Cassell et al 2012 Sundaram and

Yermack 2007 Wei and Yermack 2011) are noisy and can be biased These measures do not

correctly incorporate the sensitivity of option value to firm volatility We calculate a measure

that correctly weights the managerrsquos debt stock and option sensitivities The prior measures

suggest that CEOs on average are highly aligned with debt holders the average CEO has debt

incentives to reduce volatility that are three times his or her equity incentives to increase

volatility By contrast the corrected measure which explicitly takes into account the incentives

to increase firm volatility from options is an order of magnitude smaller suggesting that CEOs

have little alignment with debt holders the average CEO has incentives to reduce volatility that

are equal to 04 times his or her equity incentives to increase volatility Consistent with prior

literature we find that these ratios are negatively associated with risk choices However our

5

scaled total sensitivity measure is more highly associated with risk-taking choices than the

relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

2

To estimate these sensitivities we follow Merton (1974) and value total firm equity

(stock and stock options) as an option on the value of firm assets The model gives an estimate of

the decrease in debt value for an increase in firm volatility This decrease in debt value implies

an equal increase in equity value In turn the increase in equity value is shared between the stock

and stock options We estimate the CEOrsquos sensitivities by applying the CEOrsquos ownership of debt

stock and options to the firmrsquos sensitivities

We estimate these sensitivities for a sample of 5967 Execucomp CEO-years from 2006

to 2010 The typical CEO in our sample owns roughly 2 of the debt 2 of the stock and 16

of the options In terms of incentives to increase volatility this CEO has small negative

incentives from debt small positive incentives from stock and large positive incentives from

options A one standard deviation increase in firm volatility increases the average CEOrsquos wealth

by $3 million or 7 of total wealth

The total sensitivity increases as leverage increases but the vega roughly remains

constant with leverage As leverage increases the debt sensitivity becomes more negative

(making the CEO averse to risk increases) but the equity sensitivity (the sum of stock and option

sensitivities) increases more rapidly This occurs because the stock sensitivity changes from

being negative to strongly positive

Because vega ignores the debt and stock sensitivities it can be a noisy and biased

measure of risk-taking incentives If the total sensitivity better reflects CEO incentives we

expect it to be more highly associated with CEOsrsquo risk-taking choices To test this conjecture we

examine the association between the total sensitivity and vega and three proxies for future firm

3

risk stock volatility research and development expense and leverage We specify regression

models following Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

Theory suggests that incentives relative to wealth determine risk-taking For this reason

we examine modified specifications in which we scale the CEOrsquos risk-taking incentives with a

proxy for the CEOrsquos total wealth We also scale the CEOrsquos incentives to increase stock price

(ldquodeltardquo) by total wealth Prior research (eg Coles et al 2006) controls for wealth effects by

using tenure and cash compensation as proxies for CEO wealth We find that the scaled measures

explain firm risk better than the unscaled measures and that the scaled total sensitivity explains

firm risk better than the scaled vega

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

unscaled measures1

1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample

4

A concern about regressions of incentives on risk-taking is reverse causality (that is

when risk is expected to be high firms use high risk-taking incentives) To explore the

robustness of our results we follow Hayes et al (2012) and use the introduction of option

expensing in 2005 as an exogenous change to incentives Consistent with Hayes et al we find

no significant association between changes in vega and changes in firm risk for our sample

However the change in scaled equity sensitivity is significantly positively associated with both

the change in stock volatility and the change in leverage We find no association however with

the change in RampD expense

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures used in the recent literature (eg Cassell et al 2012 Sundaram and

Yermack 2007 Wei and Yermack 2011) are noisy and can be biased These measures do not

correctly incorporate the sensitivity of option value to firm volatility We calculate a measure

that correctly weights the managerrsquos debt stock and option sensitivities The prior measures

suggest that CEOs on average are highly aligned with debt holders the average CEO has debt

incentives to reduce volatility that are three times his or her equity incentives to increase

volatility By contrast the corrected measure which explicitly takes into account the incentives

to increase firm volatility from options is an order of magnitude smaller suggesting that CEOs

have little alignment with debt holders the average CEO has incentives to reduce volatility that

are equal to 04 times his or her equity incentives to increase volatility Consistent with prior

literature we find that these ratios are negatively associated with risk choices However our

5

scaled total sensitivity measure is more highly associated with risk-taking choices than the

relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

3

risk stock volatility research and development expense and leverage We specify regression

models following Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

Theory suggests that incentives relative to wealth determine risk-taking For this reason

we examine modified specifications in which we scale the CEOrsquos risk-taking incentives with a

proxy for the CEOrsquos total wealth We also scale the CEOrsquos incentives to increase stock price

(ldquodeltardquo) by total wealth Prior research (eg Coles et al 2006) controls for wealth effects by

using tenure and cash compensation as proxies for CEO wealth We find that the scaled measures

explain firm risk better than the unscaled measures and that the scaled total sensitivity explains

firm risk better than the scaled vega

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

unscaled measures1

1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample

4

A concern about regressions of incentives on risk-taking is reverse causality (that is

when risk is expected to be high firms use high risk-taking incentives) To explore the

robustness of our results we follow Hayes et al (2012) and use the introduction of option

expensing in 2005 as an exogenous change to incentives Consistent with Hayes et al we find

no significant association between changes in vega and changes in firm risk for our sample

However the change in scaled equity sensitivity is significantly positively associated with both

the change in stock volatility and the change in leverage We find no association however with

the change in RampD expense

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures used in the recent literature (eg Cassell et al 2012 Sundaram and

Yermack 2007 Wei and Yermack 2011) are noisy and can be biased These measures do not

correctly incorporate the sensitivity of option value to firm volatility We calculate a measure

that correctly weights the managerrsquos debt stock and option sensitivities The prior measures

suggest that CEOs on average are highly aligned with debt holders the average CEO has debt

incentives to reduce volatility that are three times his or her equity incentives to increase

volatility By contrast the corrected measure which explicitly takes into account the incentives

to increase firm volatility from options is an order of magnitude smaller suggesting that CEOs

have little alignment with debt holders the average CEO has incentives to reduce volatility that

are equal to 04 times his or her equity incentives to increase volatility Consistent with prior

literature we find that these ratios are negatively associated with risk choices However our

5

scaled total sensitivity measure is more highly associated with risk-taking choices than the

relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

4

A concern about regressions of incentives on risk-taking is reverse causality (that is

when risk is expected to be high firms use high risk-taking incentives) To explore the

robustness of our results we follow Hayes et al (2012) and use the introduction of option

expensing in 2005 as an exogenous change to incentives Consistent with Hayes et al we find

no significant association between changes in vega and changes in firm risk for our sample

However the change in scaled equity sensitivity is significantly positively associated with both

the change in stock volatility and the change in leverage We find no association however with

the change in RampD expense

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures used in the recent literature (eg Cassell et al 2012 Sundaram and

Yermack 2007 Wei and Yermack 2011) are noisy and can be biased These measures do not

correctly incorporate the sensitivity of option value to firm volatility We calculate a measure

that correctly weights the managerrsquos debt stock and option sensitivities The prior measures

suggest that CEOs on average are highly aligned with debt holders the average CEO has debt

incentives to reduce volatility that are three times his or her equity incentives to increase

volatility By contrast the corrected measure which explicitly takes into account the incentives

to increase firm volatility from options is an order of magnitude smaller suggesting that CEOs

have little alignment with debt holders the average CEO has incentives to reduce volatility that

are equal to 04 times his or her equity incentives to increase volatility Consistent with prior

literature we find that these ratios are negatively associated with risk choices However our

5

scaled total sensitivity measure is more highly associated with risk-taking choices than the

relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

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Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

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Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

5

scaled total sensitivity measure is more highly associated with risk-taking choices than the

relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

6

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

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Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

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Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

7

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted This result for options on

stock is similar to the result when stock is an option on the value of the levered firm Increases in

volatility do not change the value of the firm Therefore any gains to the options are offset by

losses to the stock

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have purchased a call on the assets and they

have ldquosoldrdquo a call on the equity to employees They are in a position with respect to the equity

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the

call on the equity Since the change in stockholdersrsquo value is a combination of these two

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

8

opposing effects whether stockholders prefer more volatility depends on the number of options

outstanding and firm leverage as we illustrate next

211 Estimation of firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the face value of debt

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

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Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

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Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

9

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 change in the standard deviation of the assets at various levels of leverage An increase in

volatility reduces debt value and this reduction is greater for greater leverage This reduction in

debt value is shared between the stock and options Options always benefit from increases in

volatility When leverage is low the sensitivity of debt to firm volatility is very low Since there

is little debt to transfer value from option holders gain at the expense of stockholders when

volatility increases As leverage increases the sensitivity of debt to firm volatility decreases As

this happens the stock sensitivity becomes positive as the stock offsets losses to options with

gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

10

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses the vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) The vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing the vega with the

total sensitivity in (8) one can see that the vega is a subset of total risk-taking incentives In

particular it does not include incentives from debt and stock and does not account for the fact

that employee stock options are warrants Inspection of the difference between (8) and (9)

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

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Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

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Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

11

reveals that for the vega to be similar to total risk-taking incentives the firm must have low or no

leverage (so that the volatility increase causes little re-distribution from debt value to equity

value) and the firm must have low amounts of options (so that the volatility increase causes little

re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

(10a)

From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has

options but little leverage In this case the ratio of risk-reducing to risk-increasing incentives is

(10b)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

12

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes

(11)

The first expression follows from (4) and the sensitivity of total debt value to

volatility divides off The second equality follows from the definition of β and α as the

managerrsquos fractional holdings of debt and stock An advantage of this ratio is that if in fact the

firm has no employee options one does not have to estimate the sensitivity of debt to volatility to

compute the ratio Much prior literature (eg Anantharaman et al 2011 Cassell et al 2012

Sundaram and Yermack 2007 Tung and Wang 2011 Wang et al 2010 2011) uses this

measure and terms it the ldquorelative leverage ratiordquo as it compares the managerrsquos leverage to the

firmrsquos leverage Since most firms have options in their capital structure to operationalize the

relative leverage ratio researchers make an ad hoc adjustment by adding the Black-Scholes value

of the options (O for the firm and for the CEO) to the value of the firmrsquos stock and CEOrsquos

stock

(12)

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

13

Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for options by

converting the options into equivalent units of stock by multiplying the options by their Black-

Scholes delta forthe irmand fortheCEO

(13)

That these adjustments for options are not correct may be seen by comparing the measures to the

correct relative sensitivity measure shown in (10) which uses the option sensitivity to firm

volatility Equations (12) and (13) which instead use the option value and delta implicitly

assume that options are less sensitive to firm volatility then stock or debt Only when the firm

has no employee options are the relative leverage and incentive ratios equal to the relative

sensitivity ratio

However it is important to note that scaling away the levels information contained in

(8) can lead to incorrect inference even when calculated correctly For example imagine

two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 09

Although they are otherwise identical CEO A has risk-reducing incentives of -$900 and has

risk-increasing incentives of $1000 while CEO B has risk-reducing incentives of -$90000 and

has risk-increasing incentives of $100000 The relative measure (09) scales away the

sensitivities and suggests that both CEOs make the same risk choices However CEO B is much

more likely to take risks his wealth increases by $10000 (1 of wealth) for each 1 increase in

firm volatility while CEO Arsquos increases by only $100 (001 of wealth)

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

14

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 and re-calculate the value

The sensitivity is the difference in these values Prior literature (eg Guay 1999) calculates vega

using a 001 increase in stock volatility The disadvantage of using a 001 increase in stock

volatility for our calculations is that it implies an increase in firm volatility that grows smaller

than 001 as firm leverage increases So that the measures are directly comparable we therefore

use a 1 increase in stock volatility to compute vega The 1 vega is highly correlated (091)

with the 001 increase vega used in the prior literature and all of our inferences in Tables 4 6 7

and 8 below with the 1 vega are identical to those with the 001 increase vega

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

15

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows the vega for the example CEO In contrast to the equity sensitivity and

the total sensitivity which both increase in leverage the vega first increases and then decreases

with leverage in this example Part of the reason is that the vega does not capture the debt and

stock sensitivities Holding this aside the vega does not measure well the sensitivity of the

option to firm volatility It captures the fact that the option price is sensitive to stock volatility

but it misses the fact that equity value benefits from decreases in debt value As leverage

increases the sensitivity of stock price to firm volatility increases dramatically (as shown by the

increasingly negative debt sensitivity) but this effect is omitted from the vega calculations

Consequently the vega is likely to be a good approximation of the CEOrsquos incentives to increase

risk when leverage is very low but the approximation is much noisier as leverage increases

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

16

The final Columns (8) to (10) illustrate the various relative incentive measures The

relative sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the

sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are -$6

for the low-leverage firms and -$57 for the high-leverage firms The risk-increasing incentives

are $46 for the low-leverage firms and $115 for the high-leverage firms Accordingly as

leverage increases the relative sensitivity measure increases from 013 (= 646) to 050 (=

57115) indicating that the CEO is more identified with debt holders (has fewer relative risk-

taking incentives) This inference that risk-taking incentives decline is the opposite of the

increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even

when the relative ratio is calculated correctly

In columns (9) and (10) of the final rows we illustrate how the relative leverage and

relative incentive ratios for our example CEO The relative leverage ratio is computed by

dividing the CEOrsquos percentage debt ownership (2) by the CEOrsquos ownership of total stock and

option value (roughly 24) Because these value ratios do not change much with leverage the

relative leverage ratio stays about 08 suggesting that the CEO is highly identified with debt

holders The relative incentive ratio which is similarly computed by dividing the CEOrsquos

percentage debt ownership (2) by the CEOrsquos ownership of total stock and option delta (roughly

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

17

28) also shows high identification with debt holders and little change with leverage Again

this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)

for the total sensitivity As noted above these ratios only measure relative incentives correctly

when the firm has little or no options and even a correctly calculated relative risk-taking ratio

can lead to incorrect inference The incentive ratios are not informative about the magnitude of

the sensitivity of the managerrsquos wealth to an increase in firm volatility

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt only beginning in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

18

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 Panel A shows descriptive statistics for volatility the market value of firm debt

stock and options and leverage for the firms in our sample We describe in Appendix A3 how

we estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 14 and the mean is 19 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles2

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

2 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

19

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth The vega is smaller than the total sensitivity and has

strictly positive values as compared to the total sensitivity which has about 8 negative values3

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

will respond less to the same incentives if wealthier CEOs are less risk-averse4 In this case a

direct way to generate a measure of the strength of incentives across CEOs is to scale the level of

incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of the value of the

CEOrsquos debt stock and option portfolio and wealth outside the firm5 We use the measure of

CEO outside wealth developed by Dittmann and Maug (2007)67 The average scaled total

sensitivity is 014 of wealth The value is low because the sensitivities are calculated with

3 This vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity 4 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 5 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 6 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 7 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

20

respect to a 1 increase in firm volatility If the average CEO increases firm volatility by one

standard deviation (199) that CEOrsquos wealth increases by 7 While some CEOs have net

incentives to decrease risk these incentives are small For the CEO at the first percentile of the

distribution who has large risk-reducing incentives a one standard deviation decrease in firm

volatility increases the CEOrsquos wealth by 2

We present sample descriptive statistics sorted by leverage in Table 3 Panel B We rank

the sample by leverage and divide it into five groups of 1193 firm-years The first set of rows

shows the sensitivity of the value of CEOrsquos debt stock and options for a 1 increase in firm

volatility at various levels of leverage

The second set of rows show the mean sensitivity of the CEOrsquos debt stock and options

as a percentage of the CEOrsquos wealth Since CEO wealth varies greatly the percentage values are

more interpretable and we concentrate our discussion on the values in these rows Column (2)

shows that as leverage increases the mean of the CEOsrsquo debt sensitivity to firm volatility

decreases Intuitively the sensitivity of the firmrsquos debt decreases in leverage so the sensitivity of

the CEOrsquos inside debt also decreases holding percentage ownership constant The mean stock

and option sensitivities in Columns (3) and (4) both increase with leverage While the CEOrsquos

stock sensitivity is negative for low levels of leverage the mean incentives from stock are very

small as a fraction of wealth When leverage is high the magnitude of the stock sensitivity is

much larger CEOsrsquo option sensitivity also increases with leverage Given the large increase in

equity sensitivity shown in Column (5) the CEOsrsquo total sensitivity to firm volatility in Column

(6) increases across leverage bins By contrast the vega in Column (7) has no relation with

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

21

leverage The vega excludes one of the two channels that affect option sensitivity to firm

volatility the stock-sensitivity channel When leverage is high the stock price responds strongly

to increases in firm volatility changing the value of the stock options Since the vega excludes

this channel it is biased downwards when leverage is high

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)

all decrease in leverage consistent with the increase in the total sensitivity in Column (6) The

mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins This is

consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase

risk For the 40 of firms with the lowest leverage the relative leverage and incentive ratios are

much greater than one These measures suggest that low leverage firms choose to strongly

identify their CEOs with their debt holders However these are the firms that have few agency

problems from debt so there is little need to provide strong identification with debt holders This

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

22

puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOsrsquo

options to firm volatility

35 Correlations ndash CEO incentive measures

Panel C of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (14)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

23

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 7) argue that ldquovega provides managers with an unambiguous incentive

to adopt risky projectsrdquo and that this relation should manifest empirically so long as the

regression adequately controls for differences in the risk premiums Delta (incentives to increase

stock price) is an important determinant of the managerrsquos risk premium When a managerrsquos

wealth is more concentrated in firm stock he or she is less diversified and requires a greater risk

premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) We also control for cash compensation and CEO

tenure which prior literature (Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos

outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatilityt+1) measured using

daily stock volatility over year t+1 (2) RampD Expenset+1 measured as the ratio of RampD expense

to total assets and (3) Book Leveraget+1 measured as the book value of long-term debt to the

book value of assets Like the prior literature we consider ln(Stock Volatility) to be a summary

measure of the outcome of firm risk choices RampD Expense to be a major input to increased risk

through investment risk and Book Leverage to be a major input to increased risk through capital

structure risk We measure all control variables at t and all risk choice variables at t+1 By doing

this we hope to mitigate concerns about reverse causality

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

24

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatilityt+1) we also control for risk from past RampD

Expense and CAPEX and Book Leverage In the regression with RampD Expense we also control

for ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of CEOrsquos attitudes

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking Incentiveswealth

Deltawealth + wealth + Control

(15)

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

25

To enable comparison across the models we include the same control variables in (15) as in (14)

above

42 Association of level and scaled incentive measures with firm risk choices

Table 4 Panel A contains the Stock Volatility regressions Vega in Column (1) has an

unexpected significant negative coefficient This result is inconsistent with findings in Coles at al

(2006) for 1992-2001 When we examine data from 1994-2005 in Section 44 below however

we find a positive coefficient on vega This finding and findings in Hayes et al (2012) are

consistent with changes in the cross-sectional relation between vega and risk-taking over time

The coefficient on total sensitivity in Column (2) is positive but not significant As noted above

scaling the level of incentives by total wealth can provide a better cross-sectional measure of

CEOsrsquo incentives The coefficients on both the scaled vega in Column (3) and the total

sensitivity in Column (4) are both positive and the coefficient on scaled total sensitivity is

significant

To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better

explains stock volatility than the scaled vega in Column (3) we test whether the adjusted R2 is

significantly greater using a Vuong test This test compares the explanatory power of the

regressions (Vuong 1989)8 We cluster the standard errors by firm and year (Barth Gow and

Taylor 2012) This test (labeled Col 3 = Col 4 at the bottom of Panel A) rejects the scaled vega

8 The J-test is another widely-used test of nonnested hypotheses In contrast to the J-test the Vuong test is preferable because it compares the specifications directly without embedding one model in the other (Greene 2008 p 139)

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

26

in favor of the scaled total sensitivity (p-value lt 001) A similar test (labeled Col 2 = Col 4)

rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value lt 001)

In contrast in Panel B all four measures have positive and significant relations with RampD

Expense consistent with the prediction that greater risk-taking incentives lead to more RampD In

this instance vega has significantly higher explanatory power than the total sensitivity (p-values

lt 001) Again the scaled measures do a better job of explaining RampD Expense than the level

measures (p-values lt 002)

In Panel C vega is unexpectedly negatively related to Book Leverage The total

sensitivity however is positively related to leverage We note that the total sensitivity is a noisy

measure of incentives to increase leverage An increase in leverage does not affect asset

volatility but does increase stock volatility The total sensitivity therefore is only correlated with

a leverage increase through components sensitive to stock volatility (options and the warrant

effect of options on stock) but not through components sensitive to asset volatility (debt and the

debt effect on equity)9 The scaled measures are both positively and significantly associated with

leverage Consistent with Panel A using the scaled total sensitivity rather than the scaled vega

improves the explanatory power (p-value lt 001)

9 Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

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Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

27

Based on Table 4 the total sensitivity scaled by wealth is positively related to each of the

risk variables The specification that includes scaled total sensitivity also provides the most

explanatory power for most of the firm risk variables In summary scaling the incentive

variables and including wealth significantly improves the specification and using the scaled total

sensitivity rather than the scaled vega improves the explanatory power further

43 Association of relative ratios with firm risk choices

The preceding section compares the total sensitivity to vega In this section we compare

the scaled total sensitivity to the relative leverage ratio10 The regression specifications are

identical to Table 4 These specifications are similar to but not identical to those of Cassell et al

(2012)11 Because our main interest is the incentive variables the only controls we tabulate are

wealth and delta scaled by wealth

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 5 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

10 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 11 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio They find inconsistent signs and little significance with the variable

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

28

the ratio at the 90th percentile12 We present results for the subsample where the relative leverage

ratio is defined in Columns (1) and (2) of each panel As another way of addressing this problem

Cassell et al (2012) use the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 We

present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)

of each panel Note that the total sensitivity measure is defined more often than the relative

leverage ratio or its natural logarithm The total sensitivity measure could be used to study

managerrsquos incentives in a broader sample of firms than the relative ratios

In Panel A the relative leverage ratio is negatively related to stock volatility which is

consistent with CEOs talking less risk when they are more identified with debt holders but the

relation is not significant Scaled total sensitivity is significantly related to stock volatility in this

subsample In addition this regression has a higher adjusted R2 (p-value 001) In this subsample

both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly

related to stock volatility However in the restricted subsample the explanatory power of the

logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly

different

In Panel B when RampD expense is the dependent variable the relative leverage ratio is

again insignificant in Column (1) while the scaled total sensitivity is significantly related to

RampD expense in the larger subsample in Column (2) In addition this regression has a higher

12 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

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43

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Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

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Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

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and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

29

adjusted R2 (p-value 002) In the smaller subsample the coefficient of the logarithm of the

relative leverage ratio has the expected negative sign but the adjusted R2 is significantly lower

than that of the model using the scaled total sensitivity (p-value 002)

All of the incentive measures are significantly related to leverage in the expected

direction (Panel C) In the larger subsample the scaled sensitivity measure has significantly

higher explanatory power than the relative leverage ratio In the smaller subsample the

specification using the natural logarithm of the relative leverage ratio has an insignificantly

higher adjusted R2 than that using the scaled total sensitivity

Overall the results in Table 5 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio However there is only weak

evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of

the relative leverage ratio for the smaller subsample where the latter is defined

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time unusual of shocks to returns and to return volatility which may have

affected both incentives and risk-taking

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

30

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 6 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Column (1) compares the explanatory power of vega to

that our sensitivity measure in Column (2) Vega has a positive sign but is insignificant while

the equity sensitivity is positive and significant The equity sensitivity provides a small but

statistically significant increase in explanatory power Similarly the scaled vega provides less

explanatory power than the scaled equity sensitivity (p-value lt 001)

When RampD expense is the dependent variable the results are similar to those in Table 4

for our main sample While the equity sensitivity and scaled equity sensitivity both have positive

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

31

and significant coefficients they explain RampD expense less well than vega and scaled vega

However most of these differences are not significant

As in Table 4 Panel C vega has a significantly negative relation with book leverage in

this sample These regressions include controls based on Hayes et al (2012) and the results

therefore are not directly comparable to the Coles et al (2006) findings The adjusted R2 is

higher using equity sensitivity (p-value 002) which has a positive and significant coefficient

The scaled equity sensitivity has a positive and significant coefficient and has higher

explanatory power for book leverage than either scaled vega (p-value lt 001) of the unscaled

equity sensitivity (p-value lt 001) The results in Table 6 suggest that our inferences from our

later sample hold in the earlier period 1994-2005 as well

45 Changes in vega and equity sensitivity and changes in firm risk choices

A concern about our prior results is that incentives are endogenous and the results may

reflect reverse causality rather than incentives influencing risk choices Instrumental variables

approaches can mitigate endogeneity concerns but it is difficult to identify variables that affect

incentives but do not affect policy choices (eg Gormley et al 2013) An alternative is to

identify an environmental change that affects incentives but not risk-taking Hayes et al (2012)

use a change in accounting standards which required firms to recognize compensation expense

for employee stock options beginning in December 2005 Firms responded to this accounting

expense by granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock

options cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

They do not find evidence that the change in incentives led to a reduction in firm risk-taking

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

32

This finding is interesting and could lead to the conclusion that changes in convexity do not lead

to changes in risk-taking Within the context of our study however an alternative explanation is

that vega is a noisy measure of risk-taking incentives and that changes in vega may not detect a

relation between convexity and risk-taking We briefly examine this alternative in this section

We follow Hayes et al (2012) and estimate Eq (15) using changes in the mean value of

the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008 (For

dependent variables we use changes in the mean value of the variables from 2003 to 2005 and

2006 to 2009) We use all available firm-years to calculate the mean and require at least one

observation per firm in both the 2002-2004 and 2005-2008 periods

Table 7 shows the results of these regressions Similar to Hayes et al (2012) in Column

(1) we find that the change in vega is negatively but not significantly related to the change in

stock volatility (Panel A) The change in equity sensitivity also has a negative and insignificant

coefficient When we examine instead the scaled measures the scaled vega is negatively but not

significantly related to the change in stock volatility In contrast the change in scaled equity

sensitivity in Column (4) is significantly positively related to the change in stock volatility

None of the incentive measures however is associated with the change in RampD expense

in Panel B

In Panel C the change in vega is negatively but not significantly related to the change in

stock volatility (Hayes et al find a significant negative relation) Both the equity sensitivity and

the scaled equity sensitivity is significantly positively related to the change in book leverage and

have higher explanatory power than the corresponding vega measures (p-values lt 004) Overall

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

33

we find some evidence that changes in the scaled equity sensitivity are related to changes in firm

risk

46 Robustness tests

Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt

sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt sensitivity

can be difficult in a sample where most firms are not financially distressed and therefore

estimates of small quantities may contain substantial measurement error To address this concern

we attempt to reduce measurement error in the estimates by using the mean estimate for a group

of similar firms To do this we note that leverage and stock volatility are the primary observable

determinants of the debt sensitivity We therefore sort firms each year into ten groups based on

leverage and then sort each leverage group into ten groups based on stock volatility For each

leverage-volatility-year group we calculate the mean sensitivity as a percentage of the book

value of debt We then calculate the debt sensitivity for each firm-year as the product of the

mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book

value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt stock and

options We then re-estimate our results in Tables 4 5 and 6 Our inferences are the same after

attempting to mitigate measurement error in this way

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

34

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument inside debt should include future cash pay as well as pensions and deferred

compensation13 To evaluate the sensitivity of our results we estimate the present value of the

CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected number of

years before the CEO terminates Our calculations follow those detailed in Cassell et al (2012)

We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives however remain small in comparison to risk-increasing incentives our

inferences remain unchanged

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 5 and 6 are unchanged

13 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

35

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the incentives from debt and stock and values

options as warrants We examine the relation between our measure of incentives and firm risk

choices and compare the results using our measure and those obtained with vega and the relative

leverage ratio used in the prior literature Our measure explains risk choices better than the

measures used in the prior literature When we scale the incentive measure by a proxy for total

wealth we find that using the scaled measure better explains firm risk We also calculate an

equity sensitivity that ignores debt incentives and find that it is 99 correlated with the total

sensitivity While we can only calculate the total sensitivity beginning in 2006 when we

examine the equity sensitivity over an earlier 1994-2005 period we find consistent results Our

measure should be useful for future research on managersrsquo risk choices

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

36

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield (dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm of the risk-free interest rate

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

37

A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey)

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

38

We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´ The new equity value is the old equity value ( lowast) plus the change in debt value ( ´) Using this equity value and we solve (A2) and (A3) for a new P and lowast The stock sensitivity is

´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

39

lowast ´ (A9)

A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

lowast (A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A11)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A12) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A13a)

If the sensitivity of stock price to volatility is negative the ratio is

(A13b)

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

40

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A14)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A15)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A12) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A12) above using the firm parameters from Appendix A3

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

41

Appendix B Measurement of Other Variables The measurement of other variables with the exception of No State Tax is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over

the fiscal year RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total

assets (at) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt)

divided by sales in year t-1 (revtt-1) CEO Tenure The tenure of the executive as CEO through year t CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Liquidity Constraint An indicator variable set to one if the firm generates negative cash

flow from operations and zero otherwise Return The stock return over the fiscal year Cash Surplus The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ROA The ratio of operating income before depreciation (oibdp) to total assets (at)

PPE The ratio of net property plant and equipment (ppent) to total assets (at)

Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score 33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at

Rating An indicator variable set to one when the firm has a long-term issuer credit rating from SampP

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

42

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate

bankruptcy Journal of Finance 23 589-609 Anantharaman D Fang V Gong G 2011 Inside debt and the design of corporate debt

contracts Working paper Rutgers University Available at SSRN httpssrncomabstract=1743634

Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity

incentives and misreporting The role of risk-taking incentives Journal of Financial Economics Forthcoming httpdxdoiorg101016jjfineco201302019

Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives

and firm value Journal of Financial Economics 104 70-88 Barth M Gow I Taylor D 2012 Why do pro forma and Street earnings not reflect changes

in GAAP Evidence from SFAS 123R Review of Accounting Studies 17 526-562 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of

Financial Economics 84 667-712 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political

Economy 81 637-654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal

of Financial Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The

Dynamic Response of Executive Compensation to Firm Performance Journal of Business 68 577-608

Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63

2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO

inside debt holdings and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

43

Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79 431-468

Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences

from risk-adjusted pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial

Economics 61 253-287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their

sensitivities to price and volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of

the firm The case of issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of

Executive Pay Journal of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation

to the use of book values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of Finance 15 75-102 Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance

33 1333-1342 Gormley T Matsa D Milbourn T 2013 CEO compensation and corporate risk Evidence

from a natural experiment Working Paper Kellogg School of Management Northwestern University Available at SSRN httpssrncomabstract=1718125

Greene W 2008 Econometric Analysis 6th Ed Pearson Prentice Hall Upper Saddle River NJ Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and

determinants Journal of Financial Economics 53 43-71 Hall B Murphy K 2002 Stock options for undiversified executives Journal of Accounting

and Economics 33 3-42

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

44

Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from FAS 123R Journal of Financial Economics 105 174-190

Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and

ownership structure Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of

Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial

Economics 82 551-589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management

Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of

Finance 29 449-470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of

Banking and Finance 18 841-859 Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial

compensation Journal of Finance 62 1551-1588 Tung F Wang X 2011 Bank CEOs inside debt compensation and the global financial crisis

Working paper Boston University School of Law Available at SSRN httpssrncomabstract=1570161

Vuong Q 1989 Likelihood ratio tests for model selection and non-nested hypotheses

Econometrica 57 307-333 Wang C Xie F Xin X 2010 Managerial ownership of debt and accounting conservatism

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703478

Wang C Xie F Xin X 2011 Managerial ownership of debt and bank loan contracting

Working paper Chinese University of Hong Kong Available at SSRN httpssrncomabstract=1703473

Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of

Financial Studies 24 3813-3840

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

45

Table 1 Panel A Entire firm -- Sensitivity of debt stock and options to firm volatility holding the firm constant ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 25 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

46

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

47

Table 2 Sample description This table provides firm descriptive statistics (Panel A) and sample distribution by leverage (Panel B) The primary sample consists of 5967firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails Panel A Sample descriptive statistics

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

48

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

49

Panel B Descriptive statistics for incentive variables -- sorted by firm leverage The firms are ranked by leverage and divided into five groups of 1193 firm-years Values shown are means within each leverage group

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

CEO Wealth

(1) (2) (3) (4) (5) (6) (7) (8)

00-02 ($ 0) ($ 4) $ 31 $ 28 $ 27 $ 34 $ 93950 02-87 ($ 1) ($ 2) $ 52 $ 50 $ 49 $ 54 $ 133911 87-186 ($ 5) $ 4 $ 65 $ 70 $ 64 $ 62 $ 111195

187-330 ($ 9) $ 14 $ 65 $ 86 $ 75 $ 53 $ 95209 330-874 ($11) $ 40 $ 76 $ 126 $ 111 $ 42 $ 75850

Leverage Debt Sens Tot Wealth

Stock Sens Tot Wealth

Opt Sens Tot Wealth

Eq Sens Tot Wealth

Tot Sens Tot Wealth

Vega Tot Wealth

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

00-02 000 -001 011 010 010 012 059 2707 1995 02-87 000 000 010 010 010 010 038 485 368 87-186 -001 001 011 012 011 011 022 150 110

187-330 -002 002 015 017 015 012 020 092 069 330-874 -003 008 020 028 025 011 018 040 032

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

50

Panel C Correlation between Incentive Measures This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

51

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

CEO Tenure -0004 -0005 -0006 -0004

(-227) (-278) (-237) (-161) Cash Compensation -0022 -0038 -0039 -0036

(-124) (-269) (-265) (-268) ln(Sales) -0200 -0218 -0211 -0204

(-1000) (-1187) (-1246) (-1176) Market-to-Book -0116 -0119 -0085 -0057

(-270) (-265) (-203) (-144) Book Leverage 0584 0579 0565 0254

(582) (477) (571) (193) RampD Expense 0971 0718 0653 0410

(286) (206) (154) (100) CAPEX 0633 0667 0772 0810

(155) (156) (194) (205) Delta 0003 -0004

(023) (-036) Delta Tot Wealth -56166 -71389

(-807) (-1202) Total Wealth 0088 0144

(123) (185) Vega -0803

(-204) Total Sensitivity 0111

(060) Vega Tot Wealth 43514

(159) Tot Sens Tot Wealth 108063

(492)

Observations 5967 5967 5967 5967 Adjusted R-squared 0464 0462 0484 0497 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 0013 p value of Vuong test 0334 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0020 0035 p value of Vuong test 0000 0000

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

52

Panel B RampD Expense (1) (2) (3) (4)

CEO Tenure -0001 -0001 0000 -0000

(-393) (-382) (088) (-097) Cash Compensation 0003 0004 0005 0006

(163) (207) (272) (296) ln(Sales) -0014 -0013 -0011 -0011

(-813) (-764) (-718) (-703) Market-to-Book 0002 0003 0005 0005

(084) (125) (259) (227) Book Leverage 0014 0006 0008 -0011

(130) (057) (078) (-095) Cash Surplus 0185 0192 0183 0194

(820) (867) (924) (923) ln(Sales Growth) 0002 0001 0006 0003

(027) (013) (070) (031) Return 0000 -0001 0002 0001

(000) (-013) (069) (015) Delta 0001 0001

(145) (137) Delta Tot Wealth -2502 -1338

(-495) (-299) Total Wealth 0019 0015

(416) (376) Vega 0135

(595) Total Sensitivity 0053

(463) Vega Tot Wealth 15751

(752) Tot Sens Tot Wealth 7996

(470)

Observations 5585 5585 5585 5585 Adjusted R-squared 0404 0396 0424 0406 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0008 0018 p value of Vuong test 0000 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0001 0021

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

53

Panel C Book Leverage (1) (2) (3) (4)

CEO Tenure 0001 -0000 0001 0002

(108) (-014) (157) (361) Cash Compensation 0002 -0007 -0002 0001

(035) (-108) (-028) (022) ln(Sales) -0000 -0009 -0005 -0003

(-008) (-258) (-149) (-104) Market-to-Book 0023 0021 0025 0035

(119) (112) (125) (189) RampD Expense -0320 -0405 -0443 -0478

(-281) (-349) (-346) (-395) ROA 0099 0097 0107 0130

(048) (046) (052) (068) PPE 0053 0057 0062 0044

(152) (163) (173) (133) Quartile Mod Z-score -0057 -0052 -0055 -0043

(-1081) (-1006) (-1020) (-880) Rated Debt 0127 0124 0127 0110

(1209) (1242) (1261) (1272) Delta -0008 -0012

(-253) (-285) Delta Tot Wealth -4226 -11811

(-236) (-499) Total Wealth -0033 0003

(-219) (017) Vega -0194

(-351) Total Sensitivity 0221

(496) Vega Tot Wealth 18359

(252) Tot Sens Tot Wealth 51544

(715)

Observations 5538 5538 5538 5538 Adjusted R-squared 0274 0281 0275 0343 Test Vega vs Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0007 -0068 p value of Vuong test 0193 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0001 -0062 p value of Vuong test 0764 0000

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

54

Table 5 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta Tot Wealth -51545 -80856 -69900 -86576

(-611) (-1370) (-800) (-1187) Total Wealth 0077 0192 -0078 0192

(100) (215) (-104) (228) Relative Leverage Ratio -0001

(-123) Tot Sens Tot Wealth 131029 144079

(502) (538) ln(Rel Lev Ratio) -0063

(-508)

Observations 4994 4994 3329 3329 Adjusted R-squared 0496 0517 0532 0543 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0021 -0011 p value of Vuong test 0011 0194

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

55

Panel B RampD Expense (1) (2) (3) (4) Delta Tot Wealth 0207 -1545 -0646 -1270 (059) (-270) (-170) (-305) Total Wealth 0008 0014 -0001 0005 (230) (341) (-026) (221) Relative Leverage Ratio -0000 (-123) Tot Sens Tot Wealth 7685 4094 (433) (352) ln(Rel Lev Ratio) -0001 (-222) Observations 4703 4703 3180 3180 Adjusted R-squared 0363 0383 0403 0413 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0020 -0010 p value of Vuong test 0002 0018

Panel C Book Leverage (1) (2) (3) (4) Delta Tot Wealth -2216 -13062 -6348 -10069 (-142) (-438) (-537) (-612) Total Wealth -0053 0005 -0101 0003 (-257) (026) (-501) (023) Relative Leverage Ratio -0001 (-305) Tot Sens Tot Wealth 52866 46585 (685) (903) ln(Rel Lev Ratio) -0029 (-929) Observations 4647 4647 3120 3120 Adjusted R-squared 0245 0315 0408 0400 Test Rel Lev Ratio vs Scaled Tot Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0070 0008 p value of Vuong test 0000 0558

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

56

Table 6 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A ln(Stock Volatility) (1) (2) (3) (4)

Delta 0019 0013

(240) (173) Delta Tot Wealth -70336 -74736

(-1241) (-1318) Total Wealth 0225 0250

(332) (381) Vega 0328

(128) Equity Sensitivity 0300 (269) Vega Tot Wealth 79536

(551) Equity Sens Tot Wealth 96888 (1347)

Observations 10048 10048 10048 10048 Adjusted R-squared 0550 0552 0579 0594 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0002 -0015 p value of Vuong test 0065 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0029 -0042 p value of Vuong test 0000 0000

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

57

Panel B RampD Expense (1) (2) (3) (4) Delta -0001 -0001 (-221) (-256) Delta Tot Wealth -1672 -0517 (-410) (-154) Total Wealth 0004 -0001 (099) (-014) Vega 0068 (485) Equity Sensitivity 0031 (605) Vega Tot Wealth 8459 (613) Equity Sens Tot Wealth 2411 (325) Observations 9548 9548 9548 9548 Adjusted R-squared 0343 0342 0347 0340 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 0001 0007 p value of Vuong test 0315 0002 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0004 0002 p value of Vuong test 0139 0236

Panel C Book Leverage (1) (2) (3) (4) Delta -0004 -0010 (-185) (-468) Delta Tot Wealth 0349 -6083 (027) (-527) Total Wealth -0046 -0010 (-295) (-059) Vega -0131 (-370) Equity Sensitivity 0169 (517) Vega Tot Wealth -2699 (-074) Equity Sens Tot Wealth 29172 (1104) Observations 9351 9351 9351 9351 Adjusted R-squared 0317 0330 0315 0363 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0013 -0048 p value of Vuong test 0012 0000 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0002 -0033 p value of Vuong test 0292 0000

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

58

Table 7 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A) RampD Expense (Panel B) and Book Leverage (Panel C) as the dependent variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Δ ln(Stock Volatility) (1) (2) (3) (4)

Δ Delta 0034 0033

(181) (181) Δ Delta Tot Wealth -77518 -81884

(-878) (-908) Δ Total Wealth 0330 0356

(243) (253) Δ Vega -0425

(-127) Δ Equity Sensitivity -0241 (-113) Δ Vega Tot Wealth 21002

(096) Δ Equity Sens Tot Wealth 33322 (191)

Observations 1168 1168 1168 1168 Adjusted R-squared 00587 00587 0138 0140 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared 00000 -0002 p value of Vuong test 09675 0306 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared -0079 -0081 p value of Vuong test 0000 0000

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088

59

Panel B Δ RampD Expense (1) (2) (3) (4) Δ Delta -0002 -0002 (-260) (-272) Δ Delta Tot Wealth -0127 -0049 (-044) (-018) Δ Total Wealth -0007 -0008 (-222) (-232) Δ Vega -0001 (-012) Δ Equity Sensitivity 0003 (067) Δ Vega Tot Wealth 0234 (031) Δ Equity Sens Tot Wealth -0066 (-012) Observations 1131 1131 1131 1131 Adjusted R-squared 00359 00361 00321 00320 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -00002 00001 p value of Vuong test 0808 0918 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 00038 00041 p value of Vuong test 0244 0263

Panel C Δ Book Leverage (1) (2) (3) (4) Δ Delta -0006 -0010 (-218) (-280) Δ Delta Tot Wealth 1072 -4613 (062) (-295) Δ Total Wealth -0051 -0009 (-237) (-041) Δ Vega -0049 (-085) Δ Equity Sensitivity 0165 (481) Δ Vega Tot Wealth -1367 (-032) Δ Equity Sens Tot Wealth 18994 (639) Observations 1098 1098 1098 1098 Adjusted R-squared 0115 0131 0114 0148 Test Vega vs Equity Sens Col 1 = Col 2 Col 3 = Col 4 Difference in Adj R-squared -0016 -0034 p value of Vuong test 0039 0003 Test Level vs Scaled Col 1 = Col 3 Col 2 = Col 4 Difference in Adj R-squared 0001 -0017 p value of Vuong test 0942 0088