1

The Momentum Effect on Estimating the Cost of Equity Capital

for Property-Liability Insurers

Joseph J. Tien

Tamkang University

Jennifer L. Wang

National Chengchi University

Abstract

The purpose of this paper is to test whether the momentum effect has the significant

impacts on the estimation of the cost of equity capital for property-liability insurers.

Our empirical results show that the cost of equity capital for property-liability insurers

may be underestimated by using traditional CAPM model. First, it is important to

consider infrequent trading factor in estimating cost of equity capital and the

property-liability insurers‘ stock returns are often sensitive to the financial distress.

Second, momentum factors have significant impacts on beta estimations. Especially,

adding the momentum factor in the model will enhance the magnitude of beta for

financial distress. Finally, different business lines of the property-liability have

different costs of equity capitals. If the insurance supervisors use the same criterions

to regulate these business lines, it could mislead the future development of

property-liability market. We find that the costs of equity capital for some business

lines increase more significantly than the others after using FF3F and momentum

models. Therefore, the government may need to set up a more strict regulation on

particular lines when the property-liability insurers are facing a dangerous financial

distress.

Keyword: Momentum, Cost of Equity

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1. Introduction

How to estimate the cost of equity capital correctly is an important issue for the

insurance companies. The use of an incorrect cost of capital can have very serious

impacts on the value of the firms and their profits. Many recent studies of insurance

pricing, reserving and asset-liability management (ALM) have discussed the

important issues and problems of estimating the cost of capital over the past two

decades. The financial models can be served as a useful tool to provide more reliable

methods to remedy the deficiencies of traditional actuarial pricing because they not

only consider the risk of firms but also contemplate other important factors such as

market risks. Thus, the financial model (such as Capital Asset Pricing Model (CAPM))

can help property-liability insurers to estimate the cost of equity more accurately.

Based on the portfolio theory of Markowitz (1952), Sharpe (1964) and Lintner

(1965) develop Capital Asset Pricing Model (CAPM)1. However, in the late 1970‘s,

some empirical studies argued that there exist other factors such as earnings-price

(E/P) ratios, market capitalization, book-to-market equity (B/M) ratio and debt-equity

ratios can also explain stock returns (Basu, 1977 and 1981; Rosenberg, Reid and

Lanstein 1985; Bhandari, 1988). Fama-French(1992) use a Fama-French Three Factor

(FF3F) model to conduct the empirical test on the cross-sectional data. They find that

the systematic market risk (beta), size and book-to-market ratio are related to the

stock returns. However, FF3F is hardly a panacea. It‘s hard to explain the momentum

effect2, which is a strategy that buy winners and sell losers in the past generate

1 Black (1972) develops another version of CAPM but gets similar results with Sharpe (1964) and

Lintner (1965) by relaxing the assumptions. Black, Jensen and Scholes (1972) use yearly data from

1926 to 1965 to test CAPM and find that beta can explain stock returns. Fama and Macbeth (1973)

remedy the deficiency of BJS(1972) by time-series regression. Their results also support the CAPM.

2 Jagadeesh and Titman (1993) suggest the strategy to buy winners and sell losers in the past generates

significant positive returns over 3 to 12 holding periods in the U.S. market. Rouwenhorst (1998) and

Chui, Titman and Wei (2000) also finds the momentum profits in the European market and in the Asian

markets such as Japan and Korea. Therefore, the momentum effect can be supported by the global

stock market.

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significant positive returns over certain holding periods. Many recent empirical

studies had proven that the momentum factors definitely play a critical role in

estimating the cost of equity capital (e.g., Barberis, Shleifer and Vishny(1998);

Cornad and Kaul(1998); Hong and Stein(1999); Jegadeesh and Titman(2001)).

Fama and French (1997) suggest that there is a significant industry factor in

estimating cost of capital for insurers and that insurance is a diverse enterprise,

encompassing numerous lines of business with different risk characters. Some

specific characters and issues (such as accounting principal, regulations, reserve and

lines of business) of property-liability insurers are indeed different from other

industries. Over the past four decades, a considerable number of research studies have

investigated the asset pricing issue, but only few attempts to apply the cost of equity

capital to property-liability insurers. Cummins and Harrington (1985) use quarterly

data to estimate the cost of capital and show that beta estimations were somewhat

unstable and conformed to the CAPM in the 1980‘s but not in the 1970‘s3. Cummins

and Lamm-Tennant (1994) develop theoretical and empirical models showing that

insurers‘ costs of capital are related to both insurance leverage and financial

leverage.4 Lee and Cummins (1998) use the CAPM, the arbitrage pricing theory

(APT) model, and a unified CAPM-APT model5 to estimate the cost of equity for

property-liability insurers during 1988-1992. They discover that APT and the

CAPM-APT model perform better than the CAPM in forecasting the cost of equity

capital for insurers. Cummins and Phillips (2005) estimate the cost of equity for

property-liability insurers by CAPM model and Fama-French three factors model

during 1992-2000. They find that the cost of equity capital for insurers by using the

3 The study has small sample size. There are only fourteen property-liability insurers in the sample.

4 Insurance leverage is the ratio of policy reserves to asset. Financial leverage is the ratio of financial

debt to asset. 5 The CAPM-APT model is developed by Wei (1998).

4

Fama-French model is significantly higher than those are estimated based on the

CAPM. Their evidence also suggests that it exist great differences in the cost of equity

capital across lines, indicating that the use of a single company-wide cost of capital is

not appropriate. Wen et al. (2008) use the Rubinstein-Leland (RL) model to adjust

cost of equity capital for property-liability insurers due to the insurance claim process

is highly skewed and heavy-tail distribution. They find cost of equity capital

estimated by RL model is better than by CAPM when the insurer is small or its

returns are not symmetrical.

These previous papers have provided ingenious empirical methodologies and

generated important empirical findings. However, there still exist some problems in

the estimation of the cost of equity capital for the property-liability insurance firms.

Firstly, the liquidity problem arises in estimating the cost of equity because many

insurance companies are not publicly trading. The liquidity premium could be

contemplated in the model for estimating the cost of equity capital for insurers.

However, it has not yet been a fair estimator. Secondly, previous literature does not

consider the momentum effect. If the momentum factor is an important factor for the

insurers, the equity cost will be underestimated without considering this factor into

the model. The purpose of this paper is to test whether the momentum effect has the

significant impacts on the estimation of the cost of equity capital for property-liability

insurers.

The remainder of the paper is organized as follows: Section 2 proposes the

sample selection and the empirical model to estimate the cost of equity for

property-liability insurers. The empirical results are given in section 3. Section 4

makes conclusions.

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2. Sample and Methodology

2.1 Sample Selection

We obtained the stock return data from the University of Chicago‘s Center for

Research on Securities Pricing (CRSP). Data were collected for the period from 1993

through 2001. We use monthly return data from CRSP to calculate cost of equity

capital for the period 1999-2001. We also obtain other factors such as excess return

for market systematic risk, size, and financial distress and relevant data about the

momentum factor from Kenneth French‘s website6. In order to estimate the cost of

equity capital by CAPM, FF3F and momentum model, we further sort data, stock

returns and insurer revenues, by lines of business. As for the revenue information

about lines of business, we use the data from National Association of Insurance

Commissioner (NAIC) annual statement.

2.2 Estimating the Cost of Capital for Property-liability Insurers

We use three different models to estimate the cost of equity capital for

property-liability insurers: CAPM, FF3F and momentum model. In addition to

estimate the aggregate cost of equity capital for insurers, we also predict costs of

equity capital by different lines of business. In order to estimate the cost of equity

capital for different lines more accurately, we add firms‘ characteristics into

Full-Information Industry Beta (FIB) approach. (Kaplan and Peterson, 1998)

We use the two-stage approach to estimate cost of equity capital for

property-liability insurers. In the first stage, the stocks returns are regressed on factors

such as the market risk, size, book-to-market and momentum factors. In the second

stage, the estimated beta coefficients from the first-stage are added into regression

6 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french.

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equations7 along with expected risk premium for factors to obtained cost of equity

capital.

2.2.1 Capital Asset Pricing Model (CAPM)

The CAPM examines the relationship between stock returns and market beta.

The first stage regression is described as follows:

titftmmiitfti rrrr ,,,,, )( (1)

where tir , = the return on stock i in period t,

tfr , = the risk-free rate in period t (Yield on 30-day Treasury bill),

tmr , = the return on the market portfolio in period t,

mi =the beta-coefficient for market systematic for firm i,

ti , =the random error term for stock i,

The market excess factor ( fm rr ) is defined as the value-weighted

NYSE/AMEX/Nasdaq return minus the risk-free rate. We estimate the parameters i

and mi from equation (1).

The regression sample periods consist of previous 72-months of return ending on

June 30 of each year before calculating cost of equity capital period from 1999 to

2001. The cost of equity capital of CAPM is given by the following formula:

fmmifi rrErrE )()( (2)

where )( irE = the cost of equity capital of CAPM for firm i,

fr = the expected return of the risk-free asset,

)( mrE the expected return on the market portfolio,

7 The second-stage equations are described as following such as (2), (4) and (6).

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mi = the estimated beta coefficient in the first regression for firm i,

The estimated beta coefficient from equation (1) from the first-stage is then

inserted into equation (2) to get the CAPM cost of equity capital. )( mrE is

calculated as the value-weight excess return on NYSE/AMEX/Nasdaq stocks from

1926 until June of 2001. Moreover, fr is the average of one-month Treasury bill

yield at the same period.8 Then, we can get the cost of equity capital of CAPM.

2.2.2 Fama-French Three Factors (FF3F) Model

The FF3F model includes the risk premium for systematic market risk (market

risk premium beta), the risk premium of firm size and financial distress into the model.

Firm size is defined in terms of total market capitalization and financial distress is

substituted by the ratio of the book value of equity (BV) to the market value of equity

(MV). The first-stage regression of FF3F model is described as follows:

(3)

si = the beta coefficient for the size factor for firm i,

tSMB = the risk premium for firm size at period t,

hi = the beta coefficient for the financial distress factor for firm i,

tHML = the risk premium for financial distress at period t,

The stock returns, risk-free rate, market portfolio return and error term are same

as in the CAPM regression. The excess returns for firm size and financial distress are

calculated by the standard procedure in Fama and French (1992). We can estimate the

parameters i , mi , si and hi from equation (3). The sample selecting procedure

is the same as CAPM. The cost of equity capital for FF3F is given by the following

8 The market risk premium is fm rrE )( . We can use same market risk premium in estimating the

cost of capital of FF3F and Momentum model.

tithitsitftmmiitfti HMLSMBrrrr ,,,,, )(

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formula:

HMLSMBrrErrE hisifmmifi )()( (4)

where SMB = the expected excess premium for size factor,

HML =the expected excess premium for financial factor,

The estimated beta coefficients from equation (3) are then inserted into equation

(4) to get the FF3F cost of equity capital. As in the case of the market risk premium

estimation, we calculate the average risk premium SMB and HML for size and

financial distress from 1926-2001. Then, we can get the cost of equity capital of FF3F

model.

2.2.3 Momentum Model

Jagadeesh and Titman (1993) add the extra factor –momentum into FF3F model.

The first-stage regression of momentum model is described as follows:

titmonithitsitftmmiifrti MomtHMLSMBrrrr ,,,,, )(

(5)

where moni = the beta coefficient for the momentum factor for firm i,

tM o m t= the risk premium for momentum at period t,

The excess returns for momentum are calculated by the standard procedure in

Jagadeesh and Titman (1993)9. We can estimate the parameters i , mi , si , hi and

imon from equation (5). The sample selecting procedure is the same as CAPM and

FF3F model. The cost of equity capital of momentum model is given by the following

9 At the beginning of every month from June 1993 to June 2001, we rank all stocks traded on NYSE,

AMEX and the Nasdaq on the basis of past one-month returns. Based on these rankings, ten decile

portfolios are formed that equally weight the stocks contained in the top decile, the second, the third

decile and so on. Then, it can calculate the weighted return by market value of each decile portfolio.

The top decile portfolio is called the ―winners‖ and the bottom decile portfolio is called the ―losers‖. In

each month, the strategy buys the winner portfolio and sells the loser portfolio. The risk premium for

momentum factor of every month is estimated for the difference between the returns on winners and on

losers.

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formula:

MomtHMLSMBrrErrE monihisifmmifi )()(

(6)

where Momt = the expected excess premium for momentum factor,

The estimated beta coefficients from equation (5) are then inserted into equation

(6) to get the cost of equity capital of momentum model. As in the case of the market

risk premium, size and financial distress estimation, we calculate the average risk

premium Momt for momentum factor from 1926-2001. Then, we can get the cost of

equity capital of momentum model.

2.3 Adjust for Infrequent Trading

The average trading volumes for property-liability insurance industry is lower

than other industry. In order to control this biases cause by infrequent trading, we

utilize the sum-beta approach provided by Schole and Williams (1977) to adjust the

infrequent trading. The CAPM beta is adjusted as the following:

titftmmitftmmiitfti rrrrrr ,1,1,0,,1,, )()( (7)

The estimated sum-beta coefficient can be gotten by sum of the contemporaneous

and lagged beta estimations ( 01 mimimi ) from the equation (7). Moreover, FF3F

and momentum model adjust for infrequent trading as the following, respectively (8)

and (9):

titktk

tStStftmmtftmmtfti

HMLHML

SMBSMBrrrrarr

,101

1011,1,0,,1,, )()()(

(8)

titmontmontktk

tStStftmmtftmmtfti

MomMomHMLHML

SMBSMBRRRRarr

,101101

1011,1,0,,1,, )()()(

(9)

The different kind of estimated sum-beta coefficient can be gained by sum of each

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the contemporaneous term and lagged-term beta estimations (for example:

monksmjjijiji ,,,,01 ) from the above equation. By using the sum-beta

approach, we can contemplate the risk premium for the infrequent trading of

property-liability insurers.

2.4 Estimating the Cost of Equity Capital for Different Lines of Business

After obtaining the sum-beta estimators from CAPM, FF3F and momentum model,

we further calculated the betas for different lines of business by full-information beta

(FIB) method. More detail about how to estimate the cost of equity capital for

business line of property-liability insurers is described as follows.

The purpose of the full-information beta method is to estimate the cost of equity

capital that reflects the lines of business composition of the firm. The FIB method can

be widely used to estimate the cost of equity capital for non-traded stock insurers,

mutual and divisions for the firm. The fundamental of the FIB method is that the

company can be regarded as a portfolio of asset, where the assets represent different

lines of business, individual department or divisions. In this conceptualization, the

firm‘s overall market beta coefficients are the weighted average of the beta

coefficients of the separate divisions of lines of business.

There exist two steps in obtaining beta estimates for any given firm using FIB

approach. In the first step, we can obtain an estimation of the beta coefficient for each

firm in the sample. For example, we can get the sum-beta estimation mi , si , hi

and imon from equation (9) of momentum model.

10 The second step is to process the

cross-sectional regressions with each of the sum-beta estimation as a dependent

variable and the ratio of net premiums in business lines as explanatory variables.

10

Similarly, we can obtain the sum beta estimationsmi from equation (1) of CAPM

andmi ,

si andhi from equation (3) of FF3F model.

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The FIB regression is described as following:

ij

J

j

ikfjkji w 1

(10)

where ji = overall beta estimation of type j for insurer i, (j = m, s, h and mon)

fjk = full-information beta of type j for i in line of business k,

(j = m, s, h and mon)

ikw = net premium weight for insurer i in line of business k,

ij = the error term for insurer i of equation j,

3. Empirical Results

We provide the empirical results in this section. Firstly, the overall beta and

sum-beta estimation results are presented. Then, we test whether cost of equity

calculated by CAPM, FF3F and momentum model are significantly different. Finally,

we compare the cost of equity capital for three separate lines of business including

long-tail versus short-tail, personal versus commercial, and automobile versus

workers‘ compensation versus all other lines.

3.1 Beta Estimations

The beta estimations by capital asset pricing model (CAPM), FF3F and

momentum model are presented in Table 1. The table provides the average beta and

average sum-beta for each year of the estimated period.

[Insert Table 1]

The sum-beta coefficient estimations are consistently larger than the original beta

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coefficient estimations. In column (1) and (2), the average sum-beta by CAPM is

0.6952 and the average beta by CAPM is 0.5740. We also find the similar results in

FF3F and momentum model. Therefore, it is important to consider infrequent trading

factor in estimating beta and calculating cost of equity capital for property-liability

industry. Moreover, by further all samples into the quartile, empirical results do not

reveal that large insurers constantly have smaller betas than small insurers11

. It is

interesting to note that, for both beta and sum-beta, the coefficients decline sharply in

2001. It may reflect the internet bubble in 2000 and induce this phenomenon.

Column (3) and (4) summarizes the beta and sum-beta estimations based on

Fama-French Three Factor Model (FF3F). The beta coefficients for systematic market,

size and financial distress (book-to-market value) are presented in the sample period

(1999-2001). The average sum-beta estimations for market risk premium, size

premium and financial distress premium are respectively 0.8535, 0.5388 and 0.7528.

Generally speaking, the sum-beta estimations are larger than traditional beta

estimations due to the infrequently trading. The market systematic risk factor has a

higher beta coefficient than the financial distress, and the coefficient for size factor is

the lowest. Our empirical results are consistent with Cummins and Phillips (2005)12

.

11

For conserve space, we do not report the beta results of quartile group in our table. However, in

Table 2, readers can find the cost of equity capital by the quartile group. 12

The sum-beta estimations calculated by Cummins and Phillips (2005) are respectively 1.04 (market

beta), 0.503 (size beta) and 0.942 (book-to-market beta). Comparing with Cummins and Phillips (2005),

our beta estimations are somewhat lower than their estimations. It could be due to our estimated period

covers the market collapse periods in 2000.

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We also find the beta coefficients decline in 2001 due to market fluctuation. Therefore,

we suggest using the average beta estimations to calculate the cost of equity is more

reasonable and reliable than using the beta estimations of the specific year.

The market beta and size beta estimations for property-liability insurers are not

significant different from the all-industry averages for these two parameters in

Fama-French (1997). Our financial average distress beta estimation by FF3F is 0.7528

which is larger than that for all-industry. Our results provide evidence that

property-liability stock returns are more sensitive to financial distress than stock

return in other industries in general. Therefore, the financial distress plays a vital role

in estimating cost of equity capital for property-liability insurers.

The beta coefficients based on momentum model are shown in Columns (5) and

(6). The average sum-beta estimations for systematic and financial distress are 0.9732

and 1.0969 respectively. The average sum-beta estimation for momentum factor is the

smallest (0.40849) in all beta estimators.13

By using the momentum model, we also

find the sum-beta coefficients are larger than the betas without adjustment. As for

estimating the cost of equity capital in the momentum model, we find that beta

estimations for market systematic, size and financial distress are larger than these

estimations in Fama-French FF3F model and CAPM. Although the estimation of beta

13

For conserve the space, we do not report the quartile empirical results in Table 1. Similarly, by using

the momentum model, empirical results do not reveal that large insurers constantly have smaller betas

than small insurers.

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for momentum factor is the lowest in all groups, it indeed enhances the magnitude of

betas for other factors. In FF3F model, the beta estimations of financial distress are

lower than those of systematic market. However, if we consider the momentum factor

in the model, the financial distress betas are almost the same as the systematic market

betas. It may imply that the financial distress is more important and sensitive when

considering the momentum factor in the model.

3.2 Overall Cost of Equity Capital

In this section, we compare the difference of the cost of equity capital

estimations by CAPM, FF3F, and momentum models. For estimating the cost of

equity capital, we use the 30-days Treasury-bill rate as the proxy for the risk-free rate.

As for the risk premium for systematic risk, size, financial distress and momentum

factor, we utilize the long-run average historical data of NYSE/AMEX/Nasdaq stocks

from 1926 to 2001 on Fama-French website14

.

[Insert Table 2 and Table 3]

In Table 2, we find that the average cost of capital for CAPM with infrequent

adjustment is 0.10457. However, the average cost of equity capital for FF3F model

significantly enhance to 0.16355. Moreover, the cost of equity capital from FF3F

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The long-run average historical for risk-free rate is 0.0481. The risk premium for systematic risk,

size, financial distress factors are respectively 0.0811, 0.0279 and 0.0414. The risk premium for the

momentum factor is 0.0923.

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method is consistent higher than the estimations based on CAPM method. Therefore,

it seems to imply that size and financial distress both play important roles in

estimating the cost of equity capital for property-liability industry. For failing to

adjust these two factors may underestimate the cost of equity capital and mislead the

financial decision of the company.

The cost of equity capital from momentum model with infrequent adjustment is

0.22559. In other word, the cost of equity capital from momentum model is

consistently higher than estimations based on CAPM and FF3F method. Comparing

with Cummins and Phillips (2005), our cost of equity capital (22.56%) is higher than

nearly four percents than their estimation based on FF3F model (18.5%). Jagadeesh

and Titman (1993) suggest that momentum strategy may generate significant positive

returns. Table 3 shows the results of F-test for the differences of cost of equity capital

between CAPM, FF3F and momentum model. We find significant results of F-test

(33.78141, 98.09357, and 10.16608) in 1999, 2000 and 2001. It means that the cost of

equity capital estimated by FF3F is significantly higher than those estimated by

CAPM. If we fail to adjust size and financial factors, we could underestimate the cost

of equity capital. Although the value of F-test is smaller, the empirical results show

the momentum factor still plays an important role in estimating cost of equity.

The empirical results support that momentum effect has some impacts on beta

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estimations. Especially, adding the momentum factor in FF3F model will enhance the

magnitude of beta for financial distress. This result provides the evidence that

property-liability insurers with poor financial statement could reduce the value of

companies and the willingness to invest. Financial distress for property-liability

insurers plays an important role in many aspects such as insurance purchase,

regulation, and cost of capital etc. The important implication of these phenomena will

be particularly important after considering the momentum strategy because the

institutional investors intend not to invest the bad companies. Therefore, the

momentum factor may reflect the influence of financial distress and increase the cost

of equity capital for property-liability insurers. It is important for the regulators or

insurers in the property-liability industry to seriously consider the momentum effect

in estimating cost of equity capital.

3.3 Costs of Equity Capital by Business Line

In this section, we use the FIB method to compose the overall cost of equity

capital and get the cost of equity for different business line. The sum-beta cost of

equity capital estimations from different models for short-tail15

and long-tail16

lines

15

Short-tail lines of insurance includes property coverages (such as fire, allied lines, homeowner

mulperil, automobile physical damage), all accident, health coverages and all financial guaranty

business. (such as fidelity, surety, mortgage guaranty, etc) 16

Long-tail business includes all liability insurance coverages (such as other liability, product liability,

personal and commercial automobile liability) and reinsurance.

17

are presented in Table 4.

[Insert Table 4]

The results show that the costs of equity capital do not differ significantly

between short-tail and long-tail lines in CAPM and FF3F model, except in the

momentum model. In CAPM model, consistent to Cummins and Lamm-Tennant

(1994), we find that the cost of equity capital is lower for short-tail line (10.94470%)

than for long-tail lines (12.13304%), but it is not significant. However, in FF3F and

the momentum model, the results which are consistent to Cummins and Phillips (2005)

indicate that the cost of equity capital is higher for short-tail (18.47852% and

21.92094%) than for long-tail line (15.86151% and 17.76818%). Our results after

considering size, financial distress and momentum factors seem to be contrary to the

conventional thoughts that the long-tail lines are riskier than the short-lines. One

possible explanation is that asset and liability tend to move in the same direction in

response to interest rate changes, therefore the long-tail lines may have higher

discount effect against the interest rate risk. However, short-line lines are more

susceptible to hurricanes and earthquakes, providing another possible explanation to

these phenomena. Moreover, the cost of equity capital in FF3F model is higher than

CAPM and is lower than momentum model. The results confirm that adding the size,

financial distress and momentum factor in estimating the cost of equity capital are

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important for property-liability insurers.

We continuously discuss the cost of equity capital for personal lines17

and

commercial lines in Table 4. In all CAPM, FF3F and momentum models, the results

shows commercial lines have higher cost of equity capital than personal lines18

. But

there is no difference between commercial lines and personal lines while calculating

by the equal value weight. These results provide evidences to suggest that the

commercial lines have a higher cost of equity capital than the personal lines for the

market as a whole but not for insurers on average. This may imply that larger

property-liability companies such as national or international insurers have more risky

for commercial business than smaller insurers focusing on local or regional risks. It

may also indicate that larger insurers have superior ability to cover commercial lines

risk because of their better capitalization. Generally speaking, estimating the cost of

equity capital for property-liability insurers in momentum model is higher than

CAPM and FF3F model. Therefore, the results further confirm that considering the

market factors in estimating the cost of equity seems necessary for property-liability

insurers.

Finally, the empirical results about automobile insurance, workers compensation,

17

Personal lines of insurance include earthquake, personal automobile liability, homeowners,

farmowners and automobile physical damage. All other lines of insurance are considered commercial

lines. 18

We also calculate the cost of equity capital by equal value weight. For conserve the space, we do not

report the equal weight value results in Table 4. The empirical results show the difference of equal

weight estimation between personal line and commercial line is not significant.

19

and all other lines are shown in Table 4. Based on CAPM model, we find that for both

equal or market value weighted, the differences of cost of equity capital among

automobile, workers compensation and all other property-liability lines are

insignificant. We find that the market value weighted cost of equity capital for

automobile insurance (11.92098%) is lower than all other property-liability lines

(18.53244%) and for workers‘ compensation is the lowest (11.79052%). But the

difference between automobile insurance and workers‘ compensation is not

significant. However, based on the momentum model, we find that the all other

property-liability lines still have the highest cost of equity capital but the automobile

insurance become to have the lowest cost of equity capital. As the FF3F model, the

difference between automobile insurance and workers‘ compensation is not

significant. In momentum model, the cost of equity capital for all other

property-liability lines is the significantly highest in this group. The overall results

indicate that estimating the cost of equity capital based on the momentum model is

higher than CAPM and FF3F model. This result further confirm that fail to adjust

some factors in the market will mislead the cost of equity capital for different lines for

property-liability insurers. Moreover, we also suggest that insurance supervisors

should enact suitable capital criterions for different business lines of property-liability

insurers.

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4. Conclusions

How to estimate the cost of equity capital accurately plays the prominent role for

the insurers. The misunderstanding the calculation for cost of equity capital could

have very serious negative impacts on the value of the firms. However, using the

traditional aspect to look at the cost of equity may underestimate some important

factors existing in the capital market. We believe our study has provided new insights

to the insurance literature. Firstly, the empirical results show that the cost of equity

capital for property-liability insurers may be underestimated by using CAPM model.

Our results provide evidence that the property-liability insurers‘ stock returns are

sensitive to the financial distress. Thus, failure to adjust size and financial distress

factor could lead to underestimate the cost of equity capital significantly.

Secondly, we find that the cost of equity capital could be biased without

adjusting the momentum factor. Our results confirm that the momentum factor indeed

have significant impacts on beta estimations. Especially, adding the momentum factor

in FF3F model will enhance the magnitude of beta for financial distress. In the

property-liability industry, the financial distress plays an important role in many

aspects such as purchase of insurance policies, regulation requirements of capital, and

the estimation for cost of equity capital etc. The impacts of these phenomena will be

21

particularly significant after considering the momentum strategy because the

institutional investors intend not to invest the bad companies. Therefore, the

momentum factors will enlarge the influence of financial distress factor and increase

the cost of equity capital for property-liability insurers.

Then, we find it is important to consider infrequent trading factor in estimating

cost of equity capital. The average trading volumes of property-liability insurers are

smaller than the trading volumes of companies in other industries. We use the

sum-beta approach to adjust the infrequent trading and find the cost of equity capital

based on sum-beta approach is significantly larger than the cost of equity capital

without adjustment.

Finally, different business lines of the property-liability have different costs of

equity capital. If the insurance supervisors use the same criterions to regulate these

business lines, it could mislead the future development of property-liability market.

Moreover, some business lines are more sensitive to the financial distress and

momentum factors. We find that the costs of equity capital for some business lines

increase more significantly than the others after using FF3F and momentum models.

Therefore, the government may need to set up a more strict regulation on particular

lines while the property-liability insurers are facing the serious financial distress.

22

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25

Table 1 Beta Estimations by CAPM, FF3F and Momentum Model for Property-Liability Insurers

(1) Beta by

CAPM

(2) Sum-Beta by

CAPM

(3) Beta by

FF3F Model

(4) Sum-Beta by

FF3F Model

(5) Beta by

Momentum Model

(6) Sum-Beta by

Momentum Model

m (1999) 0.66753 0.77919 0.86419 0.92665 0.95023 0.99137

S (1999) - - 0.46947 0.53398 0.63971 0.68747

h (1999) - - 0.66052 0.85191 0.98514 1.17920

mon (1999) - - - - 0.45619 0.52198

m (2000) 0.59365 0.74723 0.91565 0.88808 0.98747 1.00255

S (2000) - - 0.35750 0.65791 0.41856 0.77638

h (2000) - - 0.66881 0.81513 0.88668 1.18326

mon (2000) - - - - 0.34178 0.38355

m (2001) 0.46095 0.55913 0.69872 0.74589 0.85758 0.92557

S (2001) - - 0.19165 0.42459 0.42230 0.46196

h (2001) - - 0.46687 0.59122 0.88095 0.92842

mon (2001) - - - - 0.21556 0.31994

m (Average) 0.57404 0.69519 0.82618 0.85354 0.93176 0.97316

S (Average) - - 0.33954 0.53883 0.49352 0.64193

h (Average) - - 0.59873 0.75275 0.91759 1.09696

mon (Average) - - - - 0.33784 0.40849

26

Table 2 Costs of Equity Capital for Property-Liability Insurers

YEAR Market

Value

Quartile

No. P&L

insurers

Cost of equity

estimated by

CAPM Model

Cost of equity

estimated by

FF3F Model

Cost of equity

estimated by

Momentum Model

1999 1(Small) 18 0.114108 0.178475 0.281790

2 18 0.099622 0.145112 0.239872

3 19 0.109323 0.182991 0.257896

4(Large) 19 0.122072 0.187191 0.199286

Total 74 0.111282 0.173442 0.244710

2000 1(Small) 19 0.107319 0.176141 0.298783

2 19 0.098818 0.158523 0.239936

3 19 0.108412 0.179412 0.250944

4(Large) 19 0.12021 0.174972 0.152325

Total 76 0.108689 0.172262 0.235497

2001 1(Small) 19 0.100445 0.160064 0.246353

2 19 0.088159 0.131602 0.179212

3 20 0.093929 0.154353 0.174536

4(Large) 20 0.09122 0.133717 0.186132

Total 78 0.093437 0.144934 0.196557

All Total 228 0.104577 0.163546 0.225588

Table 3 F-Test on Cost of Equity Capital for CAPM , FF3F and Momentum model

1999 2000 2001 Average

CAPM 0.111282 0.108689 0.093437 0.104577

FF3F 0.173442 0.172262 0.144934 0.163546

F-Test 33.78141***

98.09357***

10.16608**

29.65075***

1999 2000 2001 Average

FF3F 0.173442 0.172262 0.144934 0.163546

Momentum 0.244710 0.235497 0.196557 0.225588

F-Test 13.72607***

9.81529**

8.0046**

12.64174***

****** ,, are significant at the 1, 5 or 10 percent level, respectively.

27

Table 4 Cost of Equity Capital for Different Business Lines

Cost of equity

estimated by

CAPM Model

Cost of equity

estimated by

FF3F Model

Cost of equity

estimated by

Momentum Model

Cost of Equity Capital for Short-tail Line and Long-tail Line (Market Value Weight)

Short-tail Line 10.94470 18.47852 21.92094

Long-tail Line 12.13304 15.86151 17.76818

longshorttest CostCostF : 2.737830 1.54189 7.46783

**

Cost of Equity Capital for Personal Line and Commercial Line (Market Value Weight)

Personal Line 10.65128 13.78620 14.82267

Commercial Line 11.02611 17.44605 21.68727

commercialpersonaltest CostCostF : 0.36094 6.33700

** 16.95351

***

Cost of Equity Capital for Automobile, Workers’ compensation and other P&L

(Market Value Weight)

Automobile insurance 11.08254 11.92098 14.96861

Workers‘ compensation 9.84042 11.79052 15.49364

All other P&L lines of insurance 10.73661 18.53244 20.88048

ker: worautotest CostCostF 11.25529

*** 0.057894 1.12273

Allotherwortest CostCostF ker: 1.42898 52.41451

*** 6.19742

***

Allotherautotest CostCostF : 0.24772 29.52977

*** 9.29887

***