Capital Investment, Option Generation, and Stock

Returns1

Praveen Kumar

C.T. Bauer College of Business

University of Houston

Houston, TX 77204

pkumar@uh.edu

Dongmei Li

Rady School of Management

University of California, San Diego

La Jolla, CA 92093

dongmei@ucsd.edu

September 6, 2013

1We thank two anonymous referees for very helpful comments. We also give special thanks toJoao Gomes and thank Heitor Almeida, Jonathan Berk, Je¤rey Brown, Louis Chan, Jaewon Choi,Michael Cooper, Prachi Deuskar, Wayne Ferson, Slava Fos, Paolo Fulghieri, Andrew Grant, RichardGreen, Eric Ghysels, Dirk Hackbarth, David Hirshleifer, Gerard Hoberg, Elvis Jarnecic, Dirk Jen-ter, Charles Kahn, Nisan Langberg, Michael Lemmon, Neil Pearson, Graham Partington, GeorgePennacchi, Gordon Phillips, Josh Pollet, Je¤rey Ponti¤, Michael Roberts, Ken Singleton, LauraStarks, Sheridan Titman, Selale Tuzel, Neng Wang, Joakim Westerholm, Toni Whited, JianfengYu, Lu Zhang, Guofu Zhou, seminar participants at University of Illinois (Urbana-Champaign),the USC Conference on Financial Economics and Accounting, and University of Sydney for usefulcomments.

Abstract

Based on a real options model that distinguishes between purely option-exercising investment

and option-generating investment in innovative capacity (IC), we present new evidence on

the well-known capital investment anomalies. Theoretically, IC-related capital investment

may induce higher future investments, and have a positive e¤ect on future returns and

pro�tability if the systematic risk of the underlying assets and/or the exercise cost of the

new options are su¢ ciently high. We �nd robust supporting evidence for these predictions.

In particular, the negative relation between capital investment and future abnormal returns

does not hold in big R&D-intensive �rms. In contrast, this relation is signi�cantly positive for

these �rms (by the fourth/�fth year after the investment). The role of �rm size is consistent

with the view that larger �rms are �nancially able to undertake innovation projects that

generate riskier growth options.

Keywords : Capital investment, Option generation; Innovation capacity; Stock returns

JEL classi�cation codes: G34, G24, O31

The e¤ect of capital investment (and, more generally, asset growth) on future stock returns

has important implications for both asset pricing and corporate �nance. Recently, a number

of empirical studies highlight a signi�cantly negative relation between �rms�capital invest-

ment and subsequent abnormal stock returns � the so-called investment anomalies (e.g.,

Titman, Wei, and Xie (2004); Cooper, Gulen, and Schill (2008)).1 In particular, Titman et

al. (2004) document a negative relation between large increases in capital investment and

subsequent benchmark-adjusted returns, and Cooper et al. (2008) show that this relation

extends to asset growth, a gross measure of capital investment.

These investment anomalies have generated both behavioral and risk-based explanations.

For example, Titman et al. (2004) argue that investors underreact to empire building by

managers, while Cooper et al. (2008) suggest an initial overreaction to asset growth followed

by a correction. Meanwhile, a number of rational models in the literature predict a nega-

tive equilibrium relation between investment and future returns. In particular, real options

models predict a decline in systematic risk following the exercise of growth options.2 From

this perspective, the observed negative relation between investment and subsequent returns

is not an anomaly (see Cooper and Priestley (2011)).

These alternative interpretations have profoundly di¤erent implications: A systematic

misvaluation of capital investment by �nancial markets should have major implications for

corporate investment and �nancial policies, and would suggest formulation of trading strate-

gies to exploit this market ine¢ ciency.

In this paper, we present new evidence on these investment anomalies based on a real

options model that distinguishes between purely option-exercising versus option-generating

investment. Consistent with the model�s predictions, we document signi�cant cross-sectional

1Other related studies include Anderson and Garcia-Feijoo (2006), Lyandres, Livdan, and Zhang (2008),Xing (2008), Polk and Sapienza (2009), Li and Zhang (2010), Titman, Wei, and Xie (2011), Lam and Wei(2011), Lipson, Mortal, and Schill (2011), Stambaugh, Yu, and Yuan (2011), and Watanabe et al. (2012),among others.

2See, e.g., McDonald and Siegel (1986), Majd and Pindyck (1987), Berk, Green, and Naik (1999), Gomes,Kogan, and Zhang (2003), and Carlson, Fisher, and Giammarino (2006).

1

heterogeneity in the investment-return relation and in the e¤ects of investment on future

investment, pro�tability, and �rm risk. Speci�cally, the investment-return relation for big

R&D-intensive �rms is the opposite: investment predicts signi�cantly higher future returns.

Moreover, big R&D-intensive �rms that make substantial capital investment have higher

future investment, pro�tability, and systematic risk than the other �rms.

Intuitively, capital investment in traditional (or technologically mature) industries mainly

converts existing options to assets-in-place without generating new options. Therefore, the

�rm�s risk is reduced after the investment, and the usual negative investment-return relation

follows. In contrast, �rms in R&D-intensive industries can proactively generate new options

by, for example, investing in long-range research facilities and acquiring patents. This type

of capital investment builds or enhances innovative capacity (IC), the ability to generate

and commercialize future innovations, and hence can help generate future growth options

because innovations are often sources of new ideas and opportunities.3 Consequently, IC-

related capital investment (henceforth, IC investment) may raise, and not lower, �rm risk

and expected return if it facilitates the generation of risky growth options that �rms are

likely to exercise.

We show theoretically that IC investment can increase �rm risk and expected returns if

the systematic risk of newly generated options is greater than that of the initial assets-in-

place � either because of higher systematic risk of the underlying asset of the new option or

a su¢ ciently high exercising cost of the option. Larger R&D-intensive �rms are better po-

sitioned to internally �nance innovation projects with substantial development costs and/or

3See, e.g., Schumpeter (1942) and Maclaurin (1953). Although Furman, Porter, and Stern (2002) intro-duce the concept of IC, its importance in creating value from innovation is emphasized in the literature from avariety of perspectives. Lieberman and Montgomery (1987) show that �rst-movers of signi�cant innovationsexpropriate rents only if they maintain competitive advantage through IC and intangible knowledge-basedassets. Henderson and Cockburn (1996) highlight the importance of large research programs in realizingeconomies of scope and extracting rents from the internal and external knowledge spillovers. Adner (2012)suggests that value-creation from product innovations requires IC to provide ancillary innovations to increasemarket penetration and gain competitive advantage over potential imitators, such as the development of theiTunes platform by Apple to accompany the introduction of the iPod. Christensen (1997) argues that "dis-ruptive" innovations start on the periphery of industries, but are successively re�ned to displace technologyleaders.

2

higher (eventual) systematic risk and thereby avoid agency costs of external �nancing arising

from information asymmetry and moral hazard.4 Therefore, the model, in cross-sectional

terms, predicts that IC investment is more likely to increase �rm risk and expected returns

for these �rms. Furthermore, the model also implies higher future investment for these �rms

associated with exercising the newly created growth options. Combined with the decompo-

sition of the market-to-book equity ratio (MTB) (see Fama and French (2006)), our model

also implies that, controlling for MTB, bigger R&D-intensive �rms undertaking substantial

IC investment should have higher expected pro�tability compared with the other �rms since

IC investment can raise expected returns and future investment simultaneously if and only

if expected pro�tability is su¢ ciently high.

In addition, we deduce predictions from some of the approaches used in the literature

toward capital investment and stock returns. In particular, Cao, Simin, and Zhao (2008)

utilize the Galai and Masulis (1976) model to argue that managers of levered �rms have in-

centives to exercise those growth options that increase �rms�idiosyncratic volatility (IVOL),

based on the well-known risk shifting argument (Jensen and Meckling (1976)). If IC invest-

ment generates growth options and managers are disposed toward exercising options with

higher IVOL, then the risk shifting view implies an increase in �rms� IVOL following IC

investment. Whether this view can explain the investment-return dynamics depends on the

relation between IVOL and expected returns, which is still being debated in the literature.

Meanwhile, Titman et al. (2004) argue that investors�underreaction to managers�empire-

building predicts a negative investment-return relation, particularly for �rms with greater

investment discretion. Because this view (as well as the overreaction explanation mentioned

earlier) does not di¤erentiate between traditional and IC-related investment, it predicts a

negative relation of IC investment with subsequent returns, especially among �rms with

4See Hall (1992), Himmelberg and Petersen (1994), and Hall and Lerner (2010) for discussions on �nancialfrictions in R&D-intensive �rms. For more general models, see Greenwald, Stiglitz, and Weiss (1984) andMyers and Majluf (1984) for the hidden information problem and Jensen and Meckling (1976), Grossmanand Hart (1982), and Hart and Moore (1995) for the moral hazard problem.

3

greater investment discretion.

To test these various predictions, we identify �rms who more likely make IC investment

with R&D intensity, namely, the R&D-to-sales ratio, because R&D is the most widely used

proxy for innovative e¤orts (Rogers (1998)).5 We also use �rm- and industry-level proxies of

R&D intensity for robustness check. Moreover, rather than selecting a particular measure

of capital investment, we use asset growth and various measures of investment employed in

the recent literature.

Our empirical results provide strong support for the real options model. We �nd that for

big R&D-intensive �rms the investment-return relation is non-negative and is signi�cantly

positive in the fourth and �fth years after the investment event. These results are robust

to equal- and value-weighted portfolio analysis benchmarking with di¤erent factor models

(e.g., Fama and French (1992, 1993); Carhart (1997); Chen, Novy-Marx, and Zhang (2011)).

They are also con�rmed by the Fama-MacBeth (1973) cross-sectional regressions (and panel

regressions) that control for �rms�characteristics and other return predictors. Furthermore,

compared with the other �rms, big high R&D �rms with high capital investment have signi�-

cantly higher future investment and expected pro�tability.6 They also experience an increase

in systematic risk (market beta) subsequent to the investment on average. In contrast, for

low R&D �rms and small high R&D �rms, the investment-return relation is signi�cantly

negative. Moreover, they all experience a decrease in market beta after investment. We also

do not �nd signi�cantly higher post-investment IVOL for big high R&D �rms or a signi�cant

impact of investment discretion on the e¤ect of IC investment on subsequent returns.

Our study is unique in emphasizing the distinction between the IC-related capital in-

vestment that helps generate future growth options and the traditional capital investment

that purely exercises existing growth options. The analysis indicates that this distinction is

theoretically and empirically important in terms of the e¤ect of capital investment on sub-

5The R&D-to-assets ratio generates similar patterns.6From now on, we use �high R&D�and �R&D-intensive�interchangeably.

4

sequent stock returns, investment, pro�tability, and systematic risk; moreover, it potentially

helps di¤erentiate the alternative explanations of the investment anomalies.

We also contribute to the growing literature on the role of innovations in �nancial mar-

kets. While some studies relate technological innovations to aggregate stock market behavior

(Shiller (2000); Pastor and Veronesi (2009)), our analysis helps bridge the large literature

on the economics of innovation with the �nancial economics literature on the dynamics of

capital investment and stock returns.7 Understanding the interaction of innovation-driven

�rms with �nancial markets is important because growth opportunities generated by inno-

vations are central to the evolution of industries and economic growth (Schumpeter (1942)

and Romer (1990)). Our study highlights the rich dynamic patterns that exist for such �rms

in the data and generates an agenda for future research; for example, dynamic modeling and

empirical tests of the time-to-build aspects of IC and risks of growth options.

We organize the paper as follows. Section I develops testable predictions. Section II

describes the data and the empirical framework. Sections III and IV present the empirical

results, and Section V concludes.

I. Theoretical Predictions

In this section, we present a parsimonious real options model that focuses on the option

generating IC investment and develop implications of IC investment on expected returns,

future investment, expected pro�tability, and �rm risk. The model�s goal is to clarify the

core predictions, motivate the empirical tests, and help interpret their results. We also

develop testable implications from some of the alternative perspectives on these issues in the

literature.

A. IC Investment and Growth Option Generation7There is also a literature that �nds a positive relation of R&D expenditure and future stock returns (e.g.,

Chan, Lakonishok, and Sougiannis (2001) and Li (2011)). In contrast, our study analyzes the implicationsof option generation through IC-related capital investment on subsequent stock returns.

5

We extend real options models in the spirit of Berk, Green, and Naik (BGN) (1999) and

Carlson, Fisher, and Giammarino (CFG) (2004, 2006) to include the possibility of stochastic

growth option generation through IC investment by considering two types of �rms: those that

invest to purely exercise existing growth options (type-L �rms) and those that proactively

invest to develop their innovative capacity to generate innovations or new growth options

(type-H �rms). Type-L(H) �rms can be interpreted as low (high) R&D �rms discussed

earlier. Because the e¤ect of purely option-exercising investment on expected returns has

been theoretically modeled and empirically documented in the literature, we will restrict

attention to developing testable predictions with respect to IC investment by type-H �rms.

For simplicity, we assume �rms are all-equity �nanced.

A typical type-L �rm has an initial capital stock (K0L) that generates stochastic earnings

Y 0L;t = GL(K0L) exp(�t �

�2�2) at any period t, where GL(�) is a strictly increasing function,

and the earnings shock �t v i:i:d: N(�L; �2�):

8 To illustrate the purely option exercising

feature of traditional capital investment in the simplest manner, let the �rm have available

a manufacturing capacity expansion option whereby the capital stock can be increased to

K0L at a �xed investment XL: If the �rm exercises this option at s; then the earnings stream

following the investment becomes Y0L;s+� = GL(K

0L) exp(�s+� �

�2�2); � = 1; 2; ::.

Meanwhile, a typical type-H �rm may have initial (�old�) assets-in-place (AIP) that gen-

erate a stochastic earnings stream Y 0H;t = G0H(K

0H) exp(�t�

�2�2); where G0H(�) is a strictly in-

creasing function,K0H is the initial capital stock, and the earnings shock �t v i:i:d: N(�0H ; �2�):

However, the �rm can also make a one-time irreversible IC investment, XIC ; that allows it

to stochastically generate a technological innovation in the future, which the �rm has the

option to develop further with a �xed investment, XH :

To obtain analytical expressions for the comparative statics, we assume that, conditional

on arrival, the innovation has a positive NPV, but it becomes technologically obsolete (or the

8For notational ease, we take the unit production costs to be zero throughout; the comparative staticsare una¤ected by this assumption. We also assume that all model parameters are common knowledge andthat the �rms�investments are costlessly observable.

6

marketing opportunity is lost) if the �rm does not immediately exercise the option. In sum,

if a type-H �rm invests in IC at t; then conditional on the innovation arrival at t+s (s � 1),

the �rm will immediately develop the innovation with the investment XH , and generate

an additional (�new�) earnings stream Y nH;t+s+� = GnH(XH) exp("t+s+� � �2"2); � = 1; 2; ::.

Here, GnH(�) is an increasing function, and the earnings shock "t+s+� v i:i:d: N(�nH ; �2"): For

simplicity, we assume that "t+s+� is independent of �t+s+� .

The probability that the innovation will arrive in the next period, conditional on not

having arrived in the current period, is given by �(XIC ; �VH); where �VH is the �rm value at

the time of IC investment. Ceteris paribus, it is likely that � increases with IC investment

in a given period since IC facilitates innovation activities. Moreover, the literature argues

that innovation generation is positively related to �rms�intangible and tangible resources,

which typically increase with �rm value.9 Thus, we take �(XIC ; �VH) to be strictly increasing

in both arguments.10

B. Pricing Kernel, Systematic Risk, and Expected Returns

To examine the e¤ect of IC investment on a typical type-H �rm�s expected return, we

utilize an exogenous pricing kernel fmtg following mt+1 = mt exp(�r � �2�2� �t+1), where r

is the constant risk-free rate, and the shock �t v i:i:d: N(0; �2�). We denote the �systematic

risk�of the earnings streams for type-L �rms and for the initial and new businesses of type-

H �rms by positive parameters �L � Cov(�t; �t); �0H � Cov(�t; �t); and �

nH � Cov("t;

�t); respectively. We assume the systematic risk is positive to avoid dealing with extraneous

issues such as negative discount rates.

Note that in our model, the e¤ect of IC investment at t on subsequent expected returns

9Examples of intangible resources include a �rm�s �learning by doing�(Arrow (1962)), its managerial orentrepreneurial resources (Penrose (1959)), and its �knowledge capital�(Klette and Kortum (2004)). Exam-ples of tangible resources include the ability to internally �nance promising R&D directions expeditiously(Teece (1986), Katila and Shane (2005)).10These assumptions are consistent with the theoretical and empirical literature on innovations. For ex-

ample, Klette and Kortum (2004) assume that the �innovation production function� is increasing in R&Dinvestment and �rm size in terms of its knowledge capital. Huergo and Jaumendru (2004) �nd that, control-ling for �rm age, small �rm size (in terms of the number of workers) lowers the probability of innovation.We will return to the assumption of time-invariant � after reviewing the empirical results.

7

applies only up to the arrival (and exercise) of the growth option at t + s. We, therefore,

derive the �rm�s (ex-dividend) value and expected one-period gross return for the s periods

between IC investment and the arrival/exercise of the option. For expositional ease, we

undertake the derivations for periods t and t + 1, but given the stationarity assumptions

of our model, the analysis applies to all expected one-period returns up to the innovation

arrival and exercise.

Appendix A3 shows that, conditional on making IC investment, the value of a type-H

�rm (VH;t) can be expressed as the sum of the value of initial AIP (V AH;t) and the expected

value of the newly generated option (V GH;t), i.e., VH;t = VAH;t+�V

GH;t.

11 Appendix A3 also shows

that the type-H �rm�s expected one-period gross return at t (Et[Rt;t+1]) can be expressed

as a weighted average of the expected returns on the initial AIP (Et[RAt;t+1]) and the growth

option (Et[RGt;t+1]):

Et[Rt;t+1] =WAH;tEt[RAt;t+1] +WG

H;tEt[RGt;t+1]; (1)

where WAH;t �

V AH;tVH;t

and WGH;t �

�V GH;tVH;t

are the weights of AIP and the potential growth option

(GO) in the �rm value, respectively.

In addition, it follows from the de�nition of portfolio betas that a type-H �rm�s risk

(�FH;t) is a weighted average of the systematic risks of the AIP (�0H) and the GO (�

GH), i.e.,

�FH;t = WAH;t�

0H +W

GH;t�

GH , where �

GH is proportional to the systematic risk of the underlying

new business�earnings, �nH (see Appendix A6).

C. Comparative Statics and Predictions

C1. E¤ect of IC Investment on Expected Returns

As noted above, the existing real options literature generally focuses on the type-L �rms

and predicts a negative relation between the purely option-exercising investment and ex-

pected returns. However, for type-H �rms, IC investment can increase subsequent expected

returns if it creates new growth options with expected returns higher than that of the initial

11The derivation of the theoretical model, as well as the tables for robustness checks on the empiricalresults, are presented in an Appendix available at http://rady.ucsd.edu/faculty/directory/li/.

8

AIP, i.e., riskier options. To formalize this intuition, Appendix A4 shows that the e¤ect of

IC investment on subsequent expected returns is:

@Et[Rt;t+1]@XIC

=

V AH;tV

GH;t

V 2H;t

!�1(Et[RGt;t+1]� Et[RAt;t+1]); (2)

where �1 denotes @�@XIC

. Since �1 > 0, it is clear that@Et[Rt;t+1]@XIC

> 0 if Et[RGt;t+1] > Et[RAt;t+1].

It turns out that Et[RGt;t+1] increases with the risk of the underlying new business (�nH)

and the exercise cost (XH) (cf. Appendix A5). Thus, IC investment is likely to increase the

�rm�s expected returns if either �nH or XH is su¢ ciently high. More formally, Appendix A4

shows that:12

@Et[Rt;t+1]@XIC

=

V AH;tV 2H;t

!�1[V

n

H(1� exp(�0H � �nH)) +XH(exp(�0H)� 1)]: (3)

For �rms with non-zero initial AIP (i.e., V AH;t > 0), it is apparent from (3) that@Et[Rt;t+1]@XIC

>

0 if �nH � �0H , that is, the systematic risk of the underlying new business is at least as large

as that of the initial AIP. However, it is also clear that @Et[Rt;t+1]@XIC

> 0 even if �nH < �0H as

long as XH is su¢ ciently large (see Appendix A4).13

From an empirical perspective, we expect large type-H �rms to be more likely to under-

take ambitious innovation projects with high �nH and XH ; which they are better positioned

to �nance conditional on success. Many innovation projects require substantial investment

to develop, conditional on technical success.14 Furthermore, it is well known that �rms may

have to forego positive NPV projects because of the high cost of external �nancing caused

12Vn

H is the value of the underlying new business at the time of exercise.13Similarly, Appendix A6 shows that

@�FH;t@XIC

> 0 under the same conditions for @Et[Rt;t+1]@XIC

> 0:14For example, value-creation in the large pharmaceutical companies since the 1970s has emphasized

the �blockbuster�model that involves putting huge outlays in the development of a few drugs that have thepotential to generate tremendous global sales (Achilladelis (1999)). Similarly, both upstream and downstreamgrowth options in the oil and gas industry require immense amount of initial capital: for example, the deep-sea production platforms and the recent expansions in the re�ning sector each require multi-billion dollarup-front investment and the price tag of Exxon-Mobil�s Lique�ed Natural Gas (LNG) venture in Papua NewGuinea already exceeds $16 billion (Arbogast and Kumar (2013)).

9

by adverse selection and moral hazard problems. And these �nancial frictions appear to be

especially relevant for R&D-intensive �rms. Indeed, the ability to internally �nance risky

innovation projects is often argued to be a competitive advantage conferred by large �rm size

in the pharmaceutical and oil and gas industries (Cockburn and Henderson (2001), Arbogast

and Kumar (2013)). Therefore, the e¤ect of IC investment on subsequent expected returns

(cf. (3)) is more likely to be positive for larger �rms.15

C2. E¤ect of IC Investment on Future Investment and Pro�tability

Another implication of our model relates to future investment subsequent to IC invest-

ment. Since the option arrival probability increases in IC investment and �rm size, the

model implies that large type-H �rms with higher IC investment should have higher future

investment associated with exercising the newly generated growth options.16 The detailed

derivation is in Appendix A7.

Furthermore, one can derive additional predictions regarding expected pro�tability using

the decomposition of the market-to-book equity ratio (Mt

Bt) with clean surplus accounting

(see Fama and French (2006)):

Mt

Bt=

1X�=1

EthYt+�Bt� �Bt+�

Bt

iR�

; (4)

where �Bt+� is the change in book equity, and R is the expected gross return.17 Since IC

investment increases expected reinvestment of earnings, Eth�Bt+�Bt

i, it follows that, holding

Mt

Btconstant, expected return can rise if (and only if) expected pro�tability, Et

hYt+�Bt

i; is also

higher.

We can summarize these predictions in a base hypothesis:

Hypothesis 0: (i) The e¤ect of IC investment on subsequent expected return is more likely

15We also note that the IC e¤ect is zero for �rms with no initial AIP, which are typically small �rms.16In contrast, since type-L �rms simply exercise existing options, there should not be future investment

associated with option exercising (in our simple model).17We thank an anonymous referee for suggesting this approach.

10

to be positive if the �rm size is su¢ ciently large; (ii) Large �rms with higher IC investment

exhibit higher future investment; (iii) Large �rms with higher IC investment have higher

expected pro�tability controlling for the market-to-book equity ratio.

D. Predictions from Alternative Approaches

We can deduce additional predictions from some of the alternative approaches used in

the literature regarding capital investment and stock returns. As discussed in the introduc-

tion, the risk shifting view implies that managers of levered �rms, acting on behalf of equity

holders, have incentives to exercise those growth options that increase the �rm�s idiosyn-

cratic risk (IVOL), because the cost of higher IVOL is borne by debt holders, while equity

holders bene�t from higher equity value and lower market risk of equity. If IC investment

generates growth options and managers are disposed toward increasing a �rm�s IVOL, then

the prediction from the risk shifting perspective is:

Hypothesis A1: IC investment should lead to higher subsequent idiosyncratic volatility.

We note that the real options approach implicates changes in systematic risk (cf. Equa-

tion (3)), while the risk shifting perspective highlights the change in idiosyncratic risk follow-

ing IC investment. But whether the risk shifting approach can explain the investment-return

dynamics depends on the relation of IVOL to expected returns, an issue that is still being

debated in the literature.18

Finally, if investors underreact to �empire building�by managers (Titman et al. (2004)),

this argument should also apply to managers� incentives to undertake IC investment and

market reactions to such investment. Because Titman et al. (2004) argue that empire

building is facilitated by greater investment discretion proxied by low debt and high cash-

�ows, this behavioral approach suggests:

Hypothesis A2: The e¤ect of IC investment on subsequent expected return is more likely18While theoretical models (e.g., Merton (1987)) predict that IVOL is a priced risk factor under certain

conditions, there is no consensus in the empirical literature on the cross-sectional relation between IVOL andfuture stock returns. For example, while Ang et al. (2006) document a negative IVOL-return relation, Baliand Cakici (2008) �nd no robust relation between IVOL and returns, and Boehme et al. (2009) documenta positive IVOL-return relation for �rms satisfying the assumptions of Merton (1987).

11

to be negative among �rms with low debt and high cash-�ows, other things held �xed.

In sum, the real options, risk shifting, and behavioral approaches generate distinct pre-

dictions regarding the e¤ect of IC investment on subsequent expected return, investment,

expected pro�tability, and �rm risk. We now turn to the empirical tests of these hypotheses.

We �rst describe our data and empirical test design and then discuss the results.

II. Data and Empirical Test Design

A. Data and Identi�cation of IC Investment

Testing the hypotheses above requires distinguishing between IC investment that facili-

tates option generation and the traditional investment that purely exercises existing options.

Examples of IC investment include construction of long-range research facility, purchase of

R&D equipment/inventory with alternative future usage, and acquiring patents. These in-

vestments relate to innovation activities. However, instead of being reported separately or

included in R&D expenditures, they are included in capital expenditures and total assets

under current GAAP (generally accepted accounting principles). As we noted above, R&D

expenditures are the most widely used proxy for innovative e¤orts in the literature. Hence

we use R&D intensity and its various proxies in identifying �rms whose capital investment

is likely related to IC.

As noted in Section I, low R&D �rms correspond to the type-L �rms who invest mainly

to exercise existing growth options, while high R&D �rms correspond to the type-H �rms

who invest in IC to proactively create new innovations and generate new growth options.

We also note that high R&D �rms�capital investment includes both IC and non-IC related

investment. However, this noise biases the empirical analysis against �nding supporting

evidence for our model predictions since the literature documents a signi�cantly negative

investment-return relation.

As is well known, the accounting treatment of R&D spending has varied over time, which

necessitates careful sample selection to ensure consistency in interpreting the R&D expendi-

12

ture data. Prior to 1976, �rms had substantial discretion in determining what goes into R&D

and how they report it. The R&D reporting practice was standardized in 1975 (Financial

Accounting Standards Board Statement No. 2). Our sample, therefore, is from 1976 to 2011

and consists of �rms at the intersection of COMPUSTAT and CRSP (Center for Research

in Security Prices). We obtain accounting data from COMPUSTAT and stock returns data

from CRSP. All domestic common shares trading on NYSE, AMEX, and NASDAQ with ac-

counting and returns data available are included except �nancial �rms that have four-digit

standard industrial classi�cation (SIC) codes between 6000 and 6999 (�nance, insurance,

and real estate sectors). Moreover, following Fama and French (1993), we exclude closed-

end funds, trusts, American Depository Receipts, Real Estate Investment Trusts, units of

bene�cial interest, and �rms with negative book value of equity.19

Meanwhile, the conservative accounting convention of expensing almost all R&D spending

can lead to distortions when the accounting-based R&D spending measures are utilized (e.g.,

Franzen, Rodgers, and Simin (2007)). In particular, there may be heterogeneous exposure to

accounting-based distortions between �rms that report R&D expenditures and those that do

not. To mitigate these concerns, as a robustness check, we employ both �rm- and industry-

level proxies for R&D activities utilized in the literature (e.g., Cao et al. (2008)). Speci�cally,

for the �rm-level proxies we use market-to-book assets (MABA) and the reverse debt-to-

equity ratio (DTE), while at the industry-level we use technology-driven industries based on

the classi�cations in the literature (e.g., Chan et al. (2001)). To facilitate the comparison

with our base results, we also start the sample for the robustness check from 1976. However,

untabulated results show that starting the sample from 1968 for these R&D proxies generates

similar patterns.

For the investment measure, we focus on the asset growth (Cooper et al. (2008)) since

19To mitigate back�lling bias, we require �rms to be listed on Compustat for at least two years. Finally,following Fama and French (2006), we also exclude �rms with total assets below $25 million to reduce thein�uence of very small �rms. However, including these very small �rms generates similar results (untabu-lated).

13

it is a gross measure of investment. However, Appendix B shows that our results are robust

to the other measures utilized by the recent literature (e.g., the investment-to-capital ratio

in Polk and Sapienza (2009); the growth in capital expenditure in Xing (2008), and the

investment-to-assets ratio in Lyandres, Livdan, and Zhang (2008)).

To further address the potential e¤ect of conservative accounting of R&D spending on

the investment measure, we also construct the asset growth measure based on adjusted total

assets. Following Franzen et al. (2007), we compute adjusted total assets in year t as (total

assetst + R&Dt + 0.8*R&Dt�1 + 0.6*R&Dt�1 + 0.4*R&Dt�3 + 0.2*R&Dt�4). The results

are similar as shown in Appendix B.

B. Empirical Test Design

The investment anomalies in the literature are established by cross-sectional tests through

portfolio sorts and Fama and MacBeth (FM) cross-sectional regressions. To facilitate com-

parison with the literature, we test those predictions developed in Section I with similar

approaches. Since Hypothesis 0 emphasizes the role of both the type of the investment and

the �rm size, we use independent (triple) sorts on R&D intensity, �rm size, and asset growth

(AG) to test the predictions on post-investment expected returns, investments, pro�tability,

and risk. In addition, we examine the e¤ect of IC investment on subsequent returns through

the FM regressions. As a robustness check, we also utilize panel regressions with standard

errors clustered at the �rm- and year-levels (see Appendix B) and �nd similar results.

For portfolio sorts, at the end of June of each year t from 1977 to 2011, we sort �rms

independently into two R&D portfolios and ten investment portfolios based on R&D-to-sales

(RDS) and AG in �scal year ending in calendar year t� 1; respectively.20 We also sort �rms

independently into Small and Big groups based on the NYSE median size breakpoint at the

end of June of year t. We then form a high-minus-low (10 � 1) investment hedge portfolio20Based on the accounting standardization for R&D expenditures, it is reasonable to assume that �rms

with missing R&D expenditure data in our sample period are those that have zero R&D. Speci�cally, toform the two RDS groups, we assign �rms with missing RDS to the low RDS group and the rest to the highRDS group. Assigning �rms with zero RDS to the low RDS group or forming three instead of two RDSgroups generates similar results.

14

within each RDS-size group. We report the average monthly returns and abnormal returns

(relative to di¤erent factor models) for these portfolios over each of the non-overlapping �ve

years after the portfolio formation. In particular, following the literature (e.g., Cooper et

al. (2008)), Year 1 is from July of year t to June of year t + 1, Year 2 is from July of year

t+ 1 to June of year t+ 2, and so on. To test the other predictions from Section I, we also

calculate, for each high AG portfolio, the average investment, pro�tability, market beta, and

idiosyncratic volatility for the �ve post-sorting years.

To examine the e¤ect of IC investment on subsequent returns while controlling for MTB,

we conduct FM cross-sectional regressions of individual stocks�monthly returns in each of

the �ve post-sorting years on a set of independent variables that includes MTB. Moreover,

we use FM regressions to test the prediction of behavioral models (cf. Hypothesis A2 in

Section I), using �rms�debt-to-cash �ows ratio to measure investment discretion. The (unt-

abluated) results from using the debt-to-assets ratio and the cash �ow-to-assets ratio as

separate measures of investment discretion are similar.

Although the return computation does not involve overlapping periods, as a robustness

check, we adjust the standard errors for autocorrelation and heteroscedasticity for both

the portfolio analysis and the FM regressions following the literature (e.g., Hansen (1982),

Rossi, Simin, and Smith (2013)). The results are similar (see Appendix B). We note that

the computation of monthly returns over di¤erent (sequential) years is consistent with the

comparative statics of Section I, which are expressed in terms of expected one-period return

(cf. Equation (3)). In addition, we focus on abnormal returns in the portfolio analysis to

facilitate the comparison with the investment anomalies literature. Furthermore, Da, Guo,

and Jagannathan (2012) and Grullon, Lyandres, Zhdanov (2012) suggest that an asset pricing

model is likely to generate abnormal returns if it does not take into account real options.

C. Summary Statistics

We report in Table 1 the time-series average of the cross-sectional mean characteristics

of the portfolios formed from independent triple sorts on RDS, size, and AG. For each

15

portfolio, we report the average AG, market capitalization (size), book-to-market equity

(BTM), market-to-book assets (MABA), and the debt-to-equity ratio (DTE). All variables

are de�ned in the table notes. These characteristics are measured at the end of year t � 1

except size (in millions), which is measured at the end of June of year t. Although we do

not report the level of RDS, by construction, low RDS �rms have missing RDS, while high

RDS �rms are R&D active.

The AG spread (the di¤erence between the average AG in the highest and lowest AG

portfolios) is similar across the low and high RDS groups controlling for size, although it

is slightly larger for smaller �rms in both R&D groups. This evidence suggests that the

heterogeneity in the investment-return relation (reported later) is not driven by di¤erences

in the investment spread. Big high R&D �rms are signi�cantly larger than the other �rms

with a combined market capitalization over 64% of the whole sample. These �rms also have

the lowest BTM controlling for AG. In addition, there is a negative relation between BTM

and AG in each of the four RDS-size groups.

The �rm-level R&D proxies are highly correlated with RDS. Table 1 shows that high

RDS �rms have higher MABA and lower leverage (DTE) than low RDS �rms controlling for

size and AG. Furthermore, big high RDS �rms have the highest MABA and lowest leverage

controlling for AG. In fact, untabulated results show that the Spearman rank correlation

between RDS and MABA (DTE) is 0.37 (�0.44).

III. Empirical Results

A. Post-sorting Stock Returns

A.1 Sort on Capital Investment

To benchmark our sample with the literature, we �rst con�rm the investment anomalies.

Table 2 reports the average monthly returns and abnormal returns (alphas) relative to the

Carhart (1997) four-factor model for the investment portfolios and the high-minus-low in-

16

vestment portfolio in each of the �ve non-overlapping post-sorting years.21 The investment

portfolios are formed in the same way as discussed in Section II.

We �nd a signi�cantly negative relation between AG and equal-weighted (EW) returns

and alphas. In fact, this relation is signi�cantly negative for at least �ve years after the

event. However, the relation between AG and value-weighted (VW) returns and alphas is

much weaker. For VW returns, the relation is signi�cantly negative in Year 1 but with

a much smaller magnitude (less than half) compared with EW returns. For VW alphas,

there is no signi�cantly negative relation even in Year 1. In fact, the relation is positive and

marginally signi�cant in Year 5, in which the VW Carhart alpha of the hedge portfolio is

0:41% (t = 1:73) per month.

These results indicate that the investment-return dynamics in our overall sample are

consistent with the literature: there is a signi�cantly negative impact of AG on subsequent

EW portfolio returns and alphas, but this relation is considerably weaker for VW portfolios.

Furthermore, Table 2 highlights a signi�cantly positive e¤ect of capital investment on VW

alphas �ve years after the AG event, which has not been emphasized (to our knowledge) in

the literature.

We next test the theoretical predictions regarding the e¤ect of IC investment on subse-

quent returns using R&D intensity to identify �rms that are likely to make IC investment.

A.2 Triple Sorts on R&D, Size, and Capital Investment

The real options model in Section I predicts that the e¤ect of IC investment on subsequent

expected returns is more likely to be positive for larger �rms (cf. Hypothesis 0 (i)), while

the behavioral approach predicts a negative IC investment-return relation (cf. Hypothesis

A2). Therefore, based on the real options model, we expect a positive AG e¤ect among

big high R&D �rms, but a negative AG e¤ect among the others. However, based on the

behavioral explanations, we expect a negative AG e¤ect regardless R&D or size. As our

21We obtain Carhart�s (1997) four factors returns and the one-month Treasury bill rate from KennethFrench�s website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.

17

�rst test of these distinct predictions, we present the results from independent triple sorts

on R&D intensity, �rm size, and asset growth as described in Section II.

Table 3 indicates that the AG e¤ect for big high R&D �rms is signi�cantly di¤erent

from that of the other groups of �rms. For these �rms, Panel A shows that the VW AG

e¤ect is insigni�cant in the �rst three years, but is signi�cantly positive in Years 4 and 5.

These e¤ects are also economically signi�cant with the VW hedge portfolio earning abnormal

returns (relative to the Carhart factor model) of 0:58% and 0:70% per month in Years 4 and

5, respectively. In contrast, the AG e¤ect is signi�cantly negative for low R&D �rms (both

small and big) and small high R&D �rms in Year 1. Panel B shows similar patterns for EW

portfolios. In particular, the monthly EW Carhart alpha of the hedge portfolio formed in

big high R&D �rms is 0:54% in Year 4.

The negative AG e¤ect for low R&D �rms is consistent with the view that purely option-

exercising investment reduces expected returns as discussed in the existing real options lit-

erature. The negative AG e¤ect in small high R&D �rms and the positive AG e¤ect in

big high R&D �rms con�rm the importance of size in IC investment e¤ect as discussed in

Section I. As mentioned earlier, we �nd similar results for the other investment measures in

Appendix B.

Overall, the portfolio analysis provides new evidence on the investment anomalies, which

is consistent with the real options model that distinguishes between the option-generating

investment and the purely option-exercising investment. We further examine the e¤ect of

IC investment by big high R&D �rms in the FM regressions below.

A.3 Fama-MacBeth Regressions

Table 4 reports the time-series average slopes and intercepts and their time-series t-

statistics (in parentheses) from the following monthly FM regressions of individual stocks�

returns in each of the �ve non-overlapping post-sorting years (Year 1 to Year 5) on a set of

18

independent variables:

Rt+i;t+i+1 = a+ b1 � AG+ b2 � AG �HRDS_Big + b3 �HRDS_Big + b4 � ln(Size) +

b5 � ln(BTM) + b6 �Momentum+ "i; (5)

where Rt+i;t+i+1 (i = 0; 1; : : : ; 4) is the monthly returns from July of year t + i to June of

year t+ i+ 1, AG is the asset growth in year t� 1, HRDS_Big is a dummy variable that

equals 1 for �rms with high RDS and market capitalization above the NYSE median size

breakpoints based on RDS in year t� 1 and size at the end of June of year t, ln(Size) is the

natural log of market capitalization measured at the end of June of year t+ i, ln(BTM) is

the natural log of the book-to-market equity ratio in year t�1, andMomentum is measured

by the cumulative returns over the prior 11 months with a one-month gap. All independent

variables (except the dummy variable) are winsorized at the top and bottom 1% to mitigate

the in�uence of outliers.

We test Hypothesis 0 (i) by examining the slopes of AG and the interaction term, AG �

HRDS_Big. b1 represents the AG e¤ect for the other �rms, i.e., low R&D �rms and small

high R&D �rms. b2 is the di¤erence in the AG e¤ect between big high RDS �rms and the

others. Therefore, the model predicts that (b1 + b2) is positive, although we expect this

quantity to be positive in the fourth or �fth year from the portfolio analysis.

Similar to the portfolio analysis, we �nd that the AG e¤ect for the other �rms (b1) is

signi�cantly negative in each of the �ve post-sorting years. However, this negative e¤ect

is moderated for big high R&D �rms as b2 is positive in each of the �ve years. Moreover,

the gross AG e¤ect for big high R&D �rms, (b1 + b2), is positive in Years 4 and 5 and is

statistically signi�cant (as shown in untabulated results). In sum, the theoretical prediction

is supported in the fourth and �fth years after the AG event. In addition, Table 4 con�rms

the well-known size, BTM, and momentum e¤ects on cross-sectional stock returns.

Overall, these analyses show that the e¤ect of IC investment on subsequent returns is

19

positive if the �rm is su¢ ciently large. Clearly, for big high R&D �rms, capital investment

does not negatively impact subsequent returns. Thus, these results support a primary pre-

diction of a real options model of capital investment that can stochastically generate new

growth options.

However, the results for big high R&D �rms in Tables 3 and 4 do di¤er from the real

options model in one aspect: the signi�cantly positive e¤ect of AG on subsequent returns

occurs only in the fourth and/or the �fth years. That is, the data indicate a time-variation

in the investment-return relation: the AG e¤ect on subsequent returns appears to increase

with time, at least in the �ve years after the AG event, as opposed to the time-invariance (up

to the arrival/exercise of the newly created growth option) from our theoretical framework.

The time-invariance of expected one-period return in our model stems from the simple

assumption of a time-invariant positive probability of innovation arrival from the time of IC

investment. This assumption is consistent with the theoretical literature on innovation that

typically models innovation arrival as outcomes of a Poisson process (e.g., Dasgupta and

Stiglitz (1980), Klette and Kortum (2004)).22

In practice, however, it takes time to build IC and innovation generation programs to full

productivity. Speci�cally, even if IC investment at t were perfectly observable, it would not

necessarily imply that IC functioning has reached full productivity at t; typically, further

investment may be needed to complete the setting up of innovative capacity. In other words,

there will be a positive innovation arrival probability only after the R&D programs or IC

become fully functional. The importance of time-to-build in explaining the data is well

known (Kydland and Prescott (1982) and onwards), and a straightforward extension of our

model to allow the option arrival probability to be 0 until IC is fully functional may be more

22Suppose that innovation arrival follows a Poisson process with parameter �. If the innovation has notarrived till period t + � , then the probability that the innovation will arrive in the next period (i.e., in theinterval length normalized to 1) is � � 1 � exp(��). In particular, if � is a strictly increasing function of(XIC ; �VH), then �(XIC ; �VH) is a time-invariant function that is strictly increasing in its arguments. And,as we mentioned in Section I, the positive relation of � to IC investment and �rm size is consistent with thetheoretical innovation literature.

20

consistent with the empirical results of our study.23

B. Post-sorting Investment, Pro�tability, and Risk

We now test the theoretical predictions regarding future investment and pro�tability (see

Hypothesis 0 (ii) and (iii)) through portfolio analysis. We also test the implication of our

model on systematic risk as well as Hypothesis A1 on idiosyncratic risk. We form portfolios

based on independent triple sorts on RDS, size, and AG as in Table 3. Since the investment-

return relation is mainly driven by the high AG portfolios (see Table 3), we focus on these

�rms in the comparison across di¤erent R&D and size groups. We present the results in

Table 5, where �LSH�(�LBH�) denotes the high AG portfolio in the low R&D and small (big)

size group, and �HSH�(�HBH�) denotes the high AG portfolio in the high R&D and small

(big) size group.

B.1 Post-sorting Investment

The model predicts that �rms that invest in IC (high R&D �rms) should exhibit high

future investment associated with exercising newly generated growth options. On the other

hand, if low R&D �rms generally invests to purely exercise existing options, we expect rela-

tively low future investment for these �rms. Furthermore, since the probability of generating

new options increases with �rm size, the model predicts that HBH �rms exhibit higher future

investment compared with the other groups of �rms.

We measure future investment by the sum of R&D expenditure and capital investment

(labeled by "total investment") since R&D includes both research and development costs.

To facilitate comparison across the groups, we scale total investment in each of the �ve

post-sorting years by total assets (TIA) or by net PPE (TIK) in year t� 1.24

23For example, following Kydland and Prescott (1982), suppose that setting up IC requires passing throughJ stages and that on average n < J stages are completed during one year. For simplicity, let the innovationprobability be zero before the completion of the J stages (although this assumption can be easily relaxed).Then, conditional on XIC ; �t+� (XIC ; �VH) = 0 if � < [J=n], but �t+� (XIC ; �VH) = 1 � exp(��(XIC ; �VH))if � � [J=n] (where [x] denotes the smallest inetger greater than or equal to x and � is described in theprevious footnote).24Scaling total investment by lagged assets or lagged net PPE follows the de�nitions of the investment-

to-assets ratio (IA) (Lyandres et al. (2008)) and the investment-to-capital ratio (IK) (Polk and Sapienza(2009)).

21

Consistent with the predictions, Panel A1 of Table 5 shows that on average high R&D

�rms have higher TIA than low R&D �rms in each of the �ve years. Furthermore, HBH �rms

exhibit the highest TIA in each of these �ve years. The t-test indicates that the di¤erence in

average TIA between the HBH �rms and the LSH �rms is signi�cant at the 1% level. The

pattern for TIK is similar as shown in Panel A2.

B.2 Post-sorting Pro�tability

The model also predicts that the HBH portfolio should have higher expected pro�tability

compared with the other groups. Our method for estimating expected pro�tability follows

Fama and French (2006) and is based on adjusted net income to mitigate the potential

distortion in net income due to the conservative accounting of R&D expenses. Following

Franzen et al. (2007), we compute adjusted net income in year t as (Net Incomet + R&Dt

�0.2*(R&Dt�1 + R&Dt�2 + R&Dt�3 + R&Dt�4 + R&Dt�5)). Pro�tability in each of the

�ve post-sorting years is the adjusted net income scaled by book equity in year t:

Consistent with the theoretical prediction, Panel B shows that on average the HBH

portfolio has the highest expected pro�tability among the four portfolios in each of the

�ve post-sorting years. And the t-tests indicate that the di¤erence in the average expected

pro�tability between the HBH portfolio and the LSH portfolio is signi�cant at the 1% level.

The pattern for realized pro�tability is similar in untabulated results.

B.3 Change in Systematic Risk and Idiosyncratic Risk

Our model illustrates that creating new growth options with higher systematic risk can

lead to an increase in �rm risk and a positive investment-return relation. On the other

hand, generating options with lower systematic risk or purely exercising existing options can

lead to a decrease in �rm risk and a negative investment-return relation. Therefore, the

model implies an increase in systematic risk after the AG event for the HBH portfolio, but

a decrease in systematic risk for the others.

To test this implication, we report (in Panel C of Table 5) the market beta in the AG

event year and the beta averaged over the �ve post-sorting years for the high AG portfolios

22

across the R&D-size groups. The results con�rm the model�s implication. In particular, we

�nd that the average post-sorting beta is higher than the beta in the AG event year for

the HBH portfolio. But the pattern is the opposite for the other �rms.25 Furthermore, the

t-tests indicate that the HBH portfolio has signi�cantly higher beta than the LSH portfolio

both in and after the AG event year. Reporting the average post-sorting betas helps reduce

the estimation errors. However, in untabulated results, we �nd that the pattern is the same

for market beta in each of the �ve post-sorting years.

As noted in Section I (see Hypothesis A1), the risk shifting approach implies that if capital

investment of high R&D �rms can create new growth options and managers are disposed

toward exercising those options with higher IVOL, these �rms�IVOL should increase. In

Panel C of Table 5, we report the IVOL in the AG event year and the IVOL averaged over

the �ve post-sorting years for the high AG portfolios across the R&D-size groups. (The

computation of IVOL follows the literature and is detailed in the table description.) The

results show that on average IVOL is reduced after the AG event for all the four portfolios.

C. Test of the �Empire-Building�Hypothesis

As noted in Section I, behavioral approaches explain the negative investment-return

relation through distorted market reactions (under- or over-reactions) to capital investment

and do not distinguish option-generating IC investment from the purely option-exercising

investment. In particular, the �empire-building�argument of Titman et al. (2004) suggests

that the e¤ect of IC investment on subsequent return is negative, especially for �rms with

greater investment discretion (low debt and high cash-�ows) (see Hypothesis A2). To test

25The results for small high R&D �rms are consistent with these �rms undertaking growth option gen-eration projects with lower systematic risk possibly due to the di¢ culty in externally �nancing projectswith high systematic risk (see Section I). But smaller �rms tend to have lower rates of survival (e.g., Evans(1987)) and if the failure rate is positively related to the systematic risk of new projects, then the averagepost-sorting systematic risk reported here could be biased downwards. However, we note that our sampleincludes only public �rms; hence, the small high R&D �rms in our sample are larger on average than newentrants or �start ups� (see, e.g., Pagano, Panetta, and Zingales (1998), Aslan and Kumar (2011)). Inaddition, untabulated results show that most of the small high R&D �rms in our sample have positive cash�ow on average, and the cash �ow-to-lagged assets ratio of such �rms in the highest AG decile is 5%.

23

this prediction, we modify the FM regressions used in Table 4 (cf. Equation (5)) as:

Rt+i;t+i+1 = a+ b1 � AG+ b2 � AG �HRDS_LDCF + b3 �HRDS_LDCF +

b4 � ln(Size) + b5 � ln(BTM) + b6 �Momentum+ "i; (6)

where HRDS_LDCF is a dummy variable that equals 1 for �rms with high RDS and

debt-to-cash �ow below the sample median. The �empire-building� argument predicts a

signi�cantly negative coe¢ cient b2. However, Table 6 shows that b2 is positive and insigni�-

cant in each of the �ve post-sorting years. The results for the other investment measures are

similar as shown in Appendix B. In addition, in untabulated results, we �nd that measuring

investment discretion with the debt-to-assets ratio or the cash �ow-to-assets ratio separately

generates similar patterns.

IV. Robustness Checks

Since about half of Compustat �rms have missing R&D expenditures, this may limit

the power of our tests above. In addition, most R&D costs are fully expensed under the

conservative accounting. There may be heterogeneous exposure to this practice between �rms

that report R&D expenditures and those that do not (e.g., Franzen et al. (2007)). To address

these concerns, we conduct robustness checks using �rm- and industry-level proxies for R&D

intensity following the literature. Speci�cally, for the �rm-level proxies we use market-to-

book assets (MABA) and the reverse debt-to-equity ratio (DTE), while at the industry-level

we use technology-driven industries based on the classi�cations in the literature (e.g., Chan

et al. (2001), Grullon et al. (2012)).

For tests with the �rm-level proxies, we report the results for MABA in the paper and

similar results for the reverse DTE in Appendix B. Table 7 presents the portfolio analysis

analogous to that undertaken in Table 3, except that we use high (low) MABA to identify

�rms with IC (non-IC) related investment. The results are similar to those in Table 3. In

24

particular, we �nd a signi�cantly positive relation between AG and the abnormal returns

for big high MABA �rms in Year 4 or 5. For example, the VW Carhart alpha of the hedge

investment portfolio formed in these �rms is 0:75% per month (t = 2:19): In contrast, the

relation is signi�cantly negative in Year 1 or 3 for the other �rms. In Table 8, we con�rm

this pattern through the FM regressions similar to the set-up in Table 4.

For tests with the industry-level proxies, we show the FM regressions results in Table 9.

We �nd that the AG e¤ect on future returns for big �rms operating in technology-driven

industries is positive by Year 5, consistent with the results from using �rm-level proxies. We

also use adjusted asset growth to address the potential distortion in the investment measure

due to the conservative accounting of R&D, and again �nd similar results (see Appendix B).

Overall, the robustness checks reinforce the view that for large type-H �rms IC invest-

ment has a signi�cantly positive e¤ect on future returns and that the investment anomalies

are consistent with a real options model that distinguishes between the option-generating

investment and the purely option-exercising investment.

V. Summary and Conclusions

A large number of studies document a signi�cantly negative e¤ect of capital investment

on subsequent abnormal stock returns. This investment-return relation appears consistent

with both behavioral explanations through �nancial markets� under- or over-reaction to

investment and equilibrium real options models in which �rms undertake investment to

convert available risky growth options to assets-in-place of lower systematic risk. However,

in many innovation-driven industries, �rms proactively use capital investment to generate

future growth options; for example, by investing in long-range research facilities and acquiring

patents to build long-run innovative capacity (IC). Yet, the implication of such IC-related

capital investment on subsequent returns, investments, expected pro�tability, and systematic

risk has not been explored in the literature. We examine these issues both theoretically and

empirically.

25

Constructing a rational real options model that focuses on the e¤ect of option-generating

IC investment on equilibrium returns, we �nd theoretically that IC investment can have a

positive e¤ect on subsequent returns if it creates new growth options riskier than the initial

assets-in-place � either because of higher systematic risk of the underlying asset of the new

option or a su¢ ciently high exercising cost of the option. Consistent with this prediction, we

�nd that the cross-sectional relation of asset growth and various measures of capital invest-

ment to subsequent abnormal returns is signi�cantly positive for large �rms that have high

R&D intensity or operate in technology-driven industries. In contrast, low R&D �rms or

small high R&D �rms show a negative relation. The role of �rm size supports the view that

it is �nancially more feasible for bigger �rms to undertake innovation projects that generate

riskier growth options. Furthermore, consistent with the model�s other predictions, we �nd

that bigger high R&D �rms have signi�cantly higher future investment, expected pro�tabil-

ity, and average systematic risk than the other �rms following the investment event. However,

we do not �nd a signi�cant e¤ect of IC investment on subsequent idiosyncratic volatility or

evidence that �empire building�impacts the relation of IC investment to subsequent returns.

Apart from providing new evidence on the investment anomalies that is consistent with

a rational explanation, our analysis also has implications for the large theoretical literature

that examines innovations at the �rm level. For tractability, the literature typically models

innovation arrival as a Poisson process, which implies a stationary or time-invariant inno-

vation probability per unit of time. However, our empirical results indicate that �nancial

markets price the signi�cant probability of innovation arrival and/or development some peri-

ods after IC investment. These results are consistent with the view that building innovative

capacity and creating new growth options requires �time to build�(Kydland and Prescott

(1982)). Careful dynamic modeling of the relation of option-generating capital investment

to the arrival and exercise of growth options and empirical tests of the implications of such

models for the evolution of returns, investments, and �rm risks is an important area for

future research.

26

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33

 

Table 1. Summary statistics

At the end of June of each year t from 1977 to 2011, we sort firms independently into two R&D portfolios (low and high) based on R&D expenditure scaled by sales (RDS) in fiscal year ending in calendar year t – 1, two size portfolios (small and big) based on NYSE median size breakpoints at the end of June of year t, and ten investment portfolios based on asset growth (AG) in fiscal year ending in calendar year t – 1. For each portfolio, we report the time-series mean of cross-sectional average characteristics measured in the fiscal year ending in calendar year t – 1 except Size (market equity in millions) measured at the end of June in year t. BTM denotes book-to-market equity. Following Cao, Simin, and Zhao (2008), we compute market-to-book assets (MABA) as (Total Assets – Total Common Equity + Price × Common Shares Outstanding)/Total Assets, and debt-to-equity ratio (DTE) as (Debt in Current Liabilities + Total Long-Term Debt + Preferred Stock)/(Common Shares Outstanding × Price). Financial firms and firms with assets below $25 million are excluded.

RDS Rank Size Rank AG Rank AG Size BTM MABA DTE

Low Small 1 (Low) -0.20 137 1.62 1.18 2.35

5 0.07 224 1.10 1.25 0.90

10 (High) 1.62 227 0.75 1.77 1.12

Big 1 (Low) -0.19 3807 0.87 1.48 0.97

5 0.07 5113 0.80 1.52 0.75

10 (High) 1.14 3907 0.55 2.20 0.65

High Small 1 (Low) -0.20 132 1.18 1.43 0.97

5 0.07 222 1.00 1.42 0.57

10 (High) 1.42 237 0.58 2.36 0.48

Big 1 (Low) -0.19 4816 0.72 1.76 0.54

5 0.07 8799 0.60 1.77 0.40

10 (High) 1.20 6348 0.37 3.53 0.30

34

 

Table 2. Returns and alphas of investment portfolios

At the end of June of each year t, we sort firms into investment deciles based on asset growth (AG) in fiscal year ending in calendar year t – 1 and form a high-minus-low (10-1) asset growth portfolio. We then compute monthly equal-weighted (EW) and value-weighted (VW) portfolios returns for the next 60 months. The table reports the average portfolio returns and intercepts (alphas in percentage) from regressions of time series portfolio excess returns in each of the five non-overlapping post-sorting years on the Carhart (1997) four factors returns. Year 1 is from July of year t to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t + 5. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. The heteroscedasticity-robust t-statistics are reported in parentheses. Financial firms and firms with assets below $25 million are excluded. The sample period for stock returns is from July of 1977 to December 2011.

Panel A. Monthly Returns

Year 1(Low) 5 10(High) 10-1 1(Low) 5 10(High) 10-1

1 1.74 1.38 0.61 -1.13 1.21 1.07 0.71 -0.50

(4.79) (5.54) (1.66) (-6.95) (4.25) (4.90) (2.17) (-2.60)

2 1.54 1.38 0.87 -0.68 1.16 1.06 0.93 -0.23

(4.33) (5.46) (2.32) (-4.65) (4.02) (4.77) (2.77) (-1.14)

3 1.57 1.33 1.19 -0.38 1.19 0.88 1.10 -0.09

(4.60) (5.28) (3.26) (-3.33) (4.35) (4.04) (3.43) (-0.48)

4 1.42 1.43 1.18 -0.24 0.82 1.02 1.00 0.18

(4.39) (5.52) (3.29) (-2.07) (2.90) (4.59) (2.88) (0.91)

5 1.46 1.35 1.14 -0.33 1.00 0.98 1.17 0.18

(4.35) (5.15) (3.20) (-2.63) (3.37) (4.27) (3.65) (0.82)

Panel B. Monthly Carhart Alphas

Year 1(Low) 5 10(High) 10-1 1(Low) 5 10(High) 10-1

1 0.55 0.27 -0.35 -0.90 -0.01 0.05 -0.26 -0.25

(3.42) (3.90) (-2.74) (-6.15) (-0.06) (0.68) (-2.37) (-1.38)

2 0.41 0.31 -0.10 -0.51 -0.06 0.11 -0.02 0.04

(2.67) (4.09) (-0.67) (-3.37) (-0.46) (1.33) (-0.15) (0.21)

3 0.51 0.29 0.18 -0.34 0.12 -0.06 0.12 0.00

(3.61) (3.78) (1.19) (-2.80) (0.96) (-0.74) (0.97) (-0.01)

4 0.40 0.42 0.17 -0.23 -0.14 0.16 0.12 0.26

(2.78) (4.66) (1.33) (-1.98) (-0.93) (1.69) (0.92) (1.42)

5 0.47 0.34 0.24 -0.23 -0.06 0.02 0.35 0.41

(3.06) (3.92) (2.06) (-1.69) (-0.35) (0.20) (2.51) (1.73)

AG Deciles (EW) AG Deciles (VW)

AG Deciles (EW) AG Deciles (VW)

35

 

Table 3. Alphas of investment portfolios formed in R&D-size groups

At the end of June of each year t from 1977 to 2011, we sort firms independently into two R&D portfolios based on R&D expenditure scaled by sales (RDS) in fiscal year ending in calendar year t – 1 and ten investment portfolios based on asset growth in fiscal year ending in calendar year t – 1. We also sort firms independently into small and big groups based on NYSE median size breakpoint at the end of June of year t. We form a high-minus-low (10-1) investment portfolio within each RDS-size group. We then compute monthly equal-weighted (EW) and value-weighted (VW) portfolio returns for the next 60 months for these portfolios. The table reports the intercepts (alphas) in percentage from regressions of the time series of monthly portfolio returns in excess of one month Treasury bill rate on the Carhart (1997) four factors returns in each of the five non-overlapping post-sorting years. Year 1 is from July of year t to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t + 5. The heteroscedasticity-robust t-statistics are reported in parentheses. The sample period for stock returns is from July 1977 to December 2011. Financial firms and firms with assets below $25 million are excluded.

Size  Year  1 10  10-1 1 10 10-1 1 10 10-1 1 10 10-1

Small  1  -0.15 -0.71 -0.56  0.03 -0.38 -0.41 0.36 -0.39 -0.75 0.73  -0.31 -1.04

(-1.07) (-4.96)  (-3.16)  (0.20) (-3.07) (-2.25) (2.01) (-1.97) (-3.93) (3.57)  (-1.62) (-5.75)

2  -0.52 -0.58 -0.06  0.13 0.06 -0.07 0.17 -0.39 -0.56 0.66  0.08 -0.58

(-3.02) (-3.41)  (-0.29)  (0.86) (0.35) (-0.33) (0.93) (-1.95) (-3.14) (3.37)  (0.49) (-3.17)

3  -0.10 -0.21 -0.12  0.09 0.00 -0.09 0.40 -0.08 -0.49 0.58  0.36 -0.23

(-0.57) (-1.22)  (-0.53)  (0.54) (-0.02) (-0.40) (2.32) (-0.41) (-2.31) (3.09)  (1.87) (-1.47)

4  -0.01 -0.19 -0.18  0.00 -0.15 -0.16 0.34 0.12 -0.22 0.59  0.21 -0.37

(-0.07) (-1.02)  (-0.73)  (0.02) (-0.76) (-0.64) (1.83) (0.71) (-1.19) (3.55)  (1.25) (-2.34)

5  -0.18 -0.29 -0.11  0.15 -0.13 -0.29 0.29 0.02 -0.27 0.68  0.31 -0.38

(-0.89) (-1.34)  (-0.44)  (0.64) (-0.65) (-1.03) (1.49) (0.11) (-1.21) (3.62)  (1.99) (-2.03)

Big  1  0.12  -0.44 -0.56  -0.01 0.01 0.02 0.14 -0.35 -0.49 0.05  0.00 -0.06

(0.62) (-2.54)  (-2.36)  (-0.04) (0.05) (0.06) (0.81) (-2.27) (-2.33) (0.28)  (-0.02) (-0.25)

2  -0.28 -0.20 0.07  0.03 0.30 0.28 -0.22 -0.14 0.08  0.12  0.30 0.18

(-1.34) (-1.00)  (0.26) (0.14) (1.46) (1.01) (-1.12) (-0.83) (0.35) (0.61)  (1.37) (0.69)

3  0.37  -0.32 -0.70  0.16 0.39 0.23 0.47 -0.07 -0.55 0.34  0.54 0.20

(1.63) (-1.69)  (-2.59)  (0.90) (2.05) (0.91) (2.35) (-0.43) (-2.44) (1.72)  (2.62) (0.78)

4  0.02  -0.25 -0.27  -0.09 0.49 0.58 -0.07 -0.17 -0.10 0.09  0.63 0.54

(0.09) (-1.19)  (-0.97)  (-0.44) (2.73) (2.13) (-0.37) (-0.84) (-0.37) (0.45)  (3.27) (2.44)

5  -0.07 -0.15 -0.07  0.01 0.70 0.70 -0.07 -0.03 0.04  0.25  0.70 0.45

(-0.32) (-0.80)  (-0.27)  (0.03) (3.41) (2.07) (-0.30) (-0.16) (0.14) (0.92)  (3.54) (1.27)

AG Deciles AG Deciles

Panel A. Value-weighted Carhart alphas Panel B. Equal-weighted Carhart alphas

AG Deciles AG Deciles

High RDS Low RDS High RDSLow RDS 

36

 

   Table 4. Fama-MacBeth regressions of stock returns on investment—interaction with R&D and size

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in each of the five non-overlapping post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t + 5. Investment is measured by asset growth (AG) in the fiscal year ending in calendar year t – 1. Ln(Size) is the natural logarithm of market equity at the beginning of each period. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Momentum is the cumulative return over the prior 11 months with a one-month gap. HRDS_Big is a dummy variable that equals 1 if a firm’s R&D expenditure scaled by sales in year t – 1 is nonmissing and its market capitalization is above the NYSE median size breakpoint. All independent variables (except dummies) are winsorized at the top and bottom 1%.

Year AG AG*HRDS_Big HRDS_Big ln(Size) ln(BTM) Momentum Intercept

1 -0.71 0.53 0.18 -0.11 0.16 0.55 1.83

(-7.40) (3.48) (2.10) (-2.23) (2.10) (2.50) (4.31)

2 -0.38 0.22 0.32 -0.16 0.06 0.49 1.99

(-4.48) (1.46) (3.52) (-3.00) (0.75) (2.17) (4.61)

3 -0.20 0.21 0.33 -0.17 -0.01 0.45 2.00

(-2.18) (1.28) (3.32) (-3.21) (-0.13) (2.02) (4.75)

4 -0.16 0.32 0.32 -0.18 -0.02 0.29 2.05

(-1.72) (1.92) (3.26) (-3.43) (-0.33) (1.26) (4.89)

5 -0.30 0.65 0.28 -0.16 -0.02 0.26 1.97

(-2.94) (3.41) (2.75) (-3.18) (-0.30) (1.09) (4.68)

37

 

Table 5. Future investment, profit, and risk of the investment portfolios formed in R&D-size groups

At the end of June of each year t from 1977 to 2011, we sort firms independently into two R&D portfolios, ten investment portfolios, and two size portfolios based on R&D expenditure scaled by sales (RDS) and asset growth in fiscal year ending in calendar year t – 1, and NYSE median size breakpoint at the end of June of year t, respectively. LSH (LBH) refers to the portfolio of firms with low RDS, small (big) size, and highest asset growth. HSH (HBH) refers to the portfolio of firms with high RDS, small (big) size, and highest asset growth. The table reports these portfolios’ average investment, profitability, beta, and idiosyncratic volatility (IVOL) in Panels A, B, and C, respectively, over the five non-overlapping post-sorting years. Year i refers to year t + i (i = 1, 2, 3, 4, 5). Total investment is the sum of capital expenditure and R&D expenditure. We scale total investment in year i by total assets or net PPE in year t – 1. Expected profitability is estimated as in Fama and French (2006). Profitability in year i is defined as adjusted net income before extraordinary items in year t + i scaled by book equity in year t. Following Franzen, Rodgers, and Simin (2007), we compute adjusted net income in year t as (Net Incomet + R&Dt

– 0.2*(R&Dt – 1 + R&Dt – 2 + R&Dt – 3 + R&Dt – 4 + R&Dt – 5)). To compute firms’ market beta, we first estimate monthly market beta by regressing stock returns over the prior 60 months (with a minimum of 12 months) on market returns (CRSP value-weighted index). We then compute the average monthly beta in the same year. Lag(Beta) is the portfolio average beta in year t – 1. Avg(Beta) is beta averaged over the five post-sorting years. IVOL is computed as the standard deviation of the residuals from regressing daily stock returns over the past year (with a minimum of 31 trading days) on the Fama-French three factors returns. The t-statistics in parentheses are from t-tests of the equality of mean investment, profitability, beta, and IVOL across the HBH and LSH portfolios. Financial firms and firms with assets below $25 million are excluded. All measures are winsorized at the top and bottom 1% level.

Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5

LSH 0.16 0.18 0.21 0.24 0.28 0.94 0.98 1.03 1.20 1.34

LBH 0.16 0.18 0.20 0.23 0.24 0.67 0.76 0.82 0.98 1.04

HSH 0.19 0.22 0.24 0.28 0.32 2.77 2.76 2.89 3.32 3.63

HBH 0.25 0.29 0.33 0.38 0.43 2.45 2.81 3.13 3.60 3.99

t (HBH-LSH) (11.83) (10.86) (9.73) (8.32) (7.62) (12.31) (12.94) (12.88) (11.63) (11.12)

Year 1 Year 2 Year 3 Year 4 Year 5 Lag(Beta) Avg(Beta) Lag(IVOL) Avg(IVOL)

LSH 0.06 0.08 0.10 0.12 0.13 1.24 1.22 3.44% 3.31%

LBH 0.12 0.13 0.14 0.16 0.17 1.24 1.19 2.39% 2.32%

HSH 0.06 0.08 0.10 0.11 0.15 1.61 1.57 3.78% 3.54%

HBH 0.13 0.15 0.16 0.17 0.20 1.57 1.67 2.91% 2.78%

t (HBH-LSH) (18.52) (19.77) (19.21) (16.30) (17.96) (11.65) (15.93) (-10.41) (-11.44)

A1. Total investment/Assets A2. Total investment/Net PPE

Panel B. Expected profitabilityRDS/Size/AG

Rank

Panel A. Future investment

RDS/Size/AG Rank

Panel C. Beta and IVOL

38

 

Table 6. Fama-MacBeth regressions of stock returns on investment—interaction with R&D and investment discretion

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in each of the five non-overlapping post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t + 5. Investment is measured by asset growth (AG) in the fiscal year ending in calendar year t – 1. Ln(Size) is the natural logarithm of market equity at the beginning of each period. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Momentum is the cumulative return over the prior 11 months with a one-month gap. HRDS_LDCF is a dummy variable that equals 1 if a firm’s R&D expenditure scaled by sales in year t – 1 is nonmissing and its debt-to-cash flow ratio (investment discretion) is below the sample median. The debt-to-cash flow ratio is the ratio of long-term debt to cash flows computed as operating income before depreciation minus interest expense, income taxes, and dividends. All independent variables (except dummies) are winsorized at the top and bottom 1%.

Year AG AG*HRDS_LDCF HRDS_LDCF ln(Size) ln(BTM) Momentum Intercept

1 -0.75 0.18 0.26 -0.10 0.19 0.56 1.69

(-7.23) (1.22) (4.07) (-2.04) (2.44) (2.53) (4.10)

2 -0.41 0.08 0.22 -0.13 0.08 0.47 1.84

(-4.62) (0.62) (3.73) (-2.68) (1.04) (2.09) (4.40)

3 -0.27 0.21 0.20 -0.14 0.01 0.44 1.85

(-2.70) (1.48) (3.34) (-2.94) (0.12) (1.96) (4.56)

4 -0.19 0.07 0.21 -0.15 -0.01 0.29 1.88

(-1.92) (0.51) (3.36) (-3.07) (-0.13) (1.25) (4.64)

5 -0.26 0.00 0.20 -0.13 -0.01 0.26 1.80

(-2.35) (0.01) (3.03) (-2.84) (-0.19) (1.06) (4.45)

39

 

Table 7. Robustness check—alphas of investment portfolios formed in firm-level R&D proxy and size groups At the end of June of each year t from 1977 to 2011, we sort firms independently into two portfolios based on R&D proxy in fiscal year ending in calendar year t – 1 and ten investment portfolios based on asset growth in fiscal year ending in calendar year t – 1. We also sort firms independently into small and big groups based on NYSE median size breakpoint at the end of June of year t. We proxy R&D by the market-to-book assets (MABA) ratio defined in Table 1. We form a high-minus-low (10-1) investment portfolio within each MABA-size group. We then compute monthly equal-weighted (EW) and value-weighted (VW) portfolio returns for the next 60 months for these portfolios. The table reports the intercepts (alphas) in percentage from regressions of the time series of portfolio returns in excess of one month Treasury bill rate on the Carhart (1997) four factors returns in each of the five non-overlapping post-sorting years. The heteroscedasticity-robust t-statistics are reported in parentheses. The sample period for stock returns is from July 1977 to December 2011. Financial firms and firms with assets below $25 million are excluded.

Size Year  1  10  10-1  1 10 10-1 1 10 10-1  1  10 10-1

Small 1  0.13 -0.26 -0.40 -0.25 -0.61 -0.36 0.70 -0.17 -0.87  0.30  -0.37 -0.67

(1.02)  (-1.61)  (-1.98)  (-1.68) (-5.58) (-2.02) (3.82) (-0.92) (-4.52)  (1.49)  (-1.82) (-3.70)2  -0.26 -0.33 -0.07 0.08 -0.23 -0.31 0.50 -0.08 -0.58  0.39  -0.13 -0.52

(-1.88)  (-1.95)  (-0.35)  (0.44) (-1.59) (-1.57) (2.77) (-0.42) (-3.32)  (1.85)  (-0.74) (-2.70)3  -0.12 -0.32 -0.20 0.09 -0.03 -0.12 0.50 0.00 -0.50  0.51  0.26 -0.26

(-0.77)  (-1.57)  (-0.89)  (0.48) (-0.19) (-0.54) (2.99) (0.02) (-2.67)  (2.40)  (1.39) (-1.48)4  0.00 -0.37 -0.37 0.06 -0.15 -0.22 0.48 0.15 -0.33  0.43  0.18 -0.25

(-0.03)  (-1.92)  (-1.72)  (0.28) (-0.95) (-0.83) (2.99) (0.79) (-1.84)  (2.11)  (1.25) (-1.33)5  -0.06 -0.20 -0.13 0.17 -0.28 -0.45 0.50 0.31 -0.19  0.63  0.15 -0.48

(-0.39)  (-0.93)  (-0.57)  (0.59) (-1.53) (-1.33) (2.96) (1.42) (-0.89)  (3.05)  (1.04) (-2.30)Big 1  0.00 -0.23 -0.23 0.07 -0.08 -0.16 0.20 -0.30 -0.50  0.10  -0.09 -0.18

(-0.01)  (-1.08)  (-0.84)  (0.34) (-0.61) (-0.59) (1.01) (-1.45) (-1.90)  (0.50)  (-0.60) (-0.80)2  -0.07 -0.13 -0.06 -0.01 0.17 0.18 -0.07 -0.05 0.02  0.12  0.21 0.09

(-0.38)  (-0.54)  (-0.19)  (-0.05) (1.08) (0.67) (-0.31) (-0.20) (0.07) (0.64)  (1.18) (0.39)3  0.20 -0.59 -0.79 0.16 0.36 0.19 0.53 -0.23 -0.76  0.34  0.40 0.06

(0.93)  (-2.25)  (-2.43)  (0.83) (2.30) (0.76) (2.19) (-0.93) (-2.38)  (1.87)  (2.10) (0.24)4  -0.07 -0.25 -0.19 -0.04 0.25 0.30 0.18 -0.26 -0.44  -0.01  0.48 0.49

(-0.28)  (-0.73)  (-0.50)  (-0.20) (1.51) (1.07) (0.80) (-0.95) (-1.50)  (-0.04) (2.68) (2.07)

5  0.01 -0.70 -0.71 -0.10 0.65 0.75 0.04 -0.44 -0.48  0.09  0.61 0.52(0.06)  (-2.32)  (-2.07)  (-0.38) (3.64) (2.19) (0.14) (-1.48) (-1.37)  (0.38)  (3.96) (1.78)

Panel A. Value-weighted Carhart alphas Panel B. Equal-weighted Carhart alphas

Low MABA  High MABA Low MABA High MABAAG Deciles  AG Deciles AG Deciles AG Deciles

40

 

Table 8. Robustness check—Fama-MacBeth regressions of stock returns on investment, firm-level R&D proxy, and other variables

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in each of the five non-overlapping post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t + 5. Investment is measured by asset growth (AG) in the fiscal year ending in calendar year t – 1. HMABA_Big is a dummy variable that equals 1 if a firm’s market-to-book assets ratio (MABA) in year t – 1 is above median and its market capitalization is above the NYSE median size breakpoint. We compute market-to-book assets as (Total Assets – Total Common Equity + Price × Common Shares Outstanding)/Total Assets. Ln(Size) is the natural logarithm of market equity at the beginning of each period. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Momentum is the cumulative return over the prior 11 months with a one-month gap. All independent variables (except dummies) are winsorized at the top and bottom 1%.

Year AG AG*HMABA_Big HMABA_Big ln(Size) ln(BTM) Momentum Intercept

1 -0.70 0.37 0.17 -0.11 0.18 0.56 1.83

(-7.37) (2.69) (1.85) (-2.30) (2.22) (2.51) (4.46)

2 -0.37 0.13 0.31 -0.16 0.08 0.49 2.00

(-4.36) (0.94) (3.13) (-3.11) (1.02) (2.17) (4.81)

3 -0.21 0.20 0.24 -0.16 0.01 0.45 1.98

(-2.26) (1.35) (2.36) (-3.17) (0.12) (2.00) (4.87)

4 -0.15 0.20 0.24 -0.17 0.00 0.29 2.02

(-1.62) (1.23) (2.46) (-3.42) (-0.03) (1.25) (5.02)

5 -0.30 0.49 0.21 -0.16 0.00 0.27 1.95

(-3.06) (2.94) (2.14) (-3.16) (-0.01) (1.10) (4.81)

41

 

Table 9. Robustness check—Fama-MacBeth regressions of stock returns on investment, industry-level R&D proxy, and other variables

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in each of the five non-overlapping post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t + 5. Investment is measured by asset growth (AG) in the fiscal year ending in calendar year t – 1. Tech_Big is a dummy variable that equals 1 for firms with market capitalization above the NYSE median size breakpoint and operating in Fama and French (1997) industries 27 (precious metals), 28 (mining), 30 (oil and natural gas) based on four-digit SIC code, and in the following industries based on three- or two-digit SIC code: computer programming, software, and services (SIC 737), drugs and pharmaceuticals (SIC 283), computers and office equipment (SIC 357), measuring instruments (SIC 38), electrical equipment excluding computers (SIC 36), communications (SIC 48), and transportation equipment (SIC 37). Ln(Size) is the natural logarithm of market equity at the beginning of each period. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Momentum is the cumulative return over the prior 11 months with a one-month gap. All independent variables (except the dummies) are winsorized at the top and bottom 1%.

Year AG AG*Tech_Big Tech_Big ln(Size) ln(BTM) Momentum Intercept

1 -0.69 0.35 0.10 -0.10 0.16 0.55 1.79

(-7.38) (1.97) (0.70) (-2.06) (2.07) (2.50) (4.21)

2 -0.38 0.33 0.30 -0.14 0.05 0.48 1.94

(-4.63) (1.92) (2.38) (-2.77) (0.68) (2.12) (4.51)

3 -0.20 0.24 0.28 -0.15 -0.02 0.44 1.94

(-2.26) (1.19) (2.30) (-2.97) (-0.22) (1.97) (4.64)

4 -0.15 0.07 0.27 -0.16 -0.04 0.29 1.97

(-1.64) (0.38) (2.19) (-3.14) (-0.50) (1.25) (4.74)

5 -0.30 0.61 0.18 -0.14 -0.04 0.26 1.89

(-3.03) (2.94) (1.64) (-2.86) (-0.55) (1.07) (4.52)