Capital Investment, Option Generation, and Stock
Returns1
Praveen Kumar
Dongmei Li
C.T. Bauer College of Business
Rady School of Management
University of Houston
University of California, San Diego
Houston, TX 77204
La Jolla, CA 92093
[email protected]
[email protected]
September 6, 2013
1 We
thank two anonymous referees for very helpful comments. We also give special thanks to
Joao 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, Richard
Green, Eric Ghysels, Dirk Hackbarth, David Hirshleifer, Gerard Hoberg, Elvis Jarnecic, Dirk Jenter, Charles Kahn, Nisan Langberg, Michael Lemmon, Neil Pearson, Graham Partington, George
Pennacchi, Gordon Phillips, Josh Pollet, Je¤rey Ponti¤, Michael Roberts, Ken Singleton, Laura
Starks, Sheridan Titman, Selale Tuzel, Neng Wang, Joakim Westerholm, Toni Whited, Jianfeng
Yu, 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 useful
comments.
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 investment 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 negative 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 strategies 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
1
Other 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.
2
See, 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, ICrelated 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-inplace — 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 positioned to internally …nance innovation projects with substantial development costs and/or
3
See, e.g., Schumpeter (1942) and Maclaurin (1953). Although Furman, Porter, and Stern (2002) introduce the concept of IC, its importance in creating value from innovation is emphasized in the literature from a
variety of perspectives. Lieberman and Montgomery (1987) show that …rst-movers of signi…cant innovations
expropriate rents only if they maintain competitive advantage through IC and intangible knowledge-based
assets. Henderson and Cockburn (1996) highlight the importance of large research programs in realizing
economies 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 increase
market penetration and gain competitive advantage over potential imitators, such as the development of the
iTunes platform by Apple to accompany the introduction of the iPod. Christensen (1997) argues that "disruptive" innovations start on the periphery of industries, but are successively re…ned to displace technology
leaders.
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 decomposition 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 incentives 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 investment 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’empirebuilding 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
4
See Hall (1992), Himmelberg and Petersen (1994), and Hall and Lerner (2010) for discussions on …nancial
frictions in R&D-intensive …rms. For more general models, see Greenwald, Stiglitz, and Weiss (1984) and
Myers and Majluf (1984) for the hidden information problem and Jensen and Meckling (1976), Grossman
and 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 investment 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 sub5
6
The R&D-to-assets ratio generates similar patterns.
From 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 markets. 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 innovations 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 Generation
7
There 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 implications
of 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 (KL0 ) that generates stochastic earnings
0
= GL (KL0 ) exp(
YL;t
2
t
and the earnings shock
2
t
) at any period t, where GL ( ) is a strictly increasing function,
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
0
KL at a …xed investment XL : If the …rm exercises this option at s; then the earnings stream
0
2
0
following the investment becomes YL;s+ = GL (KL ) exp(
s+
2
);
= 1; 2; ::.
Meanwhile, a typical type-H …rm may have initial (“old”) assets-in-place (AIP) that gen0
0
) exp(
erate a stochastic earnings stream YH;t
= G0H (KH
2
t
2
); where G0H ( ) is a strictly in-
0
creasing function, KH
is the initial capital stock, and the earnings shock
t
v i:i:d: N (
0
H;
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
8
For notational ease, we take the unit production costs to be zero throughout; the comparative statics
are una¤ected by this assumption. We also assume that all model parameters are common knowledge and
that 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
2
"
n
an additional (“new”) earnings stream YH;t+s+
= GnH (XH ) exp("t+s+
2
);
Here, GnH ( ) is an increasing function, and the earnings shock "t+s+ v i:i:d: N (
simplicity, we assume that "t+s+ is independent of
t+s+
= 1; 2; ::.
n
H;
2
" ):
For
.
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
2
utilize an exogenous pricing kernel fmt g following mt+1 = mt exp( r
is the constant risk-free rate, and the shock
t
v i:i:d: N (0;
2
2
t+1 ),
where r
). We denote the “systematic
risk”of the earnings streams for type-L …rms and for the initial and new businesses of typeH …rms by positive parameters
t );
L
Cov( t ;
t );
0
H
Cov( t ;
t );
and
n
H
Cov("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
9
Examples of intangible resources include a …rm’s “learning by doing” (Arrow (1962)), its managerial or
entrepreneurial resources (Penrose (1959)), and its “knowledge capital”(Klette and Kortum (2004)). Examples of tangible resources include the ability to internally …nance promising R&D directions expeditiously
(Teece (1986), Katila and Shane (2005)).
10
These assumptions are consistent with the theoretical and empirical literature on innovations. For example, Klette and Kortum (2004) assume that the ‘innovation production function’ is increasing in R&D
investment and …rm size in terms of its knowledge capital. Huergo and Jaumendru (2004) …nd that, controlling 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
A
…rm (VH;t ) can be expressed as the sum of the value of initial AIP (VH;t
) and the expected
G
A
G 11
value of the newly generated option (VH;t
), i.e., VH;t = VH;t
+ VH;t
. Appendix A3 also shows
that the type-H …rm’s expected one-period gross return at t (Et [Rt;t+1 ]) can be expressed
A
as a weighted average of the expected returns on the initial AIP (Et [Rt;t+1
]) and the growth
G
]):
option (Et [Rt;t+1
A
A
G
G
Et [Rt;t+1 ] = WH;t
Et [Rt;t+1
] + WH;t
Et [Rt;t+1
];
A
VH;t
VH;t
A
where WH;t
G
and WH;t
G
VH;t
VH;t
(1)
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
(
F
H;t )
F
H;t
is a weighted average of the systematic risks of the AIP (
A
= WH;t
0
H
G
+ WH;t
new business’earnings,
G
H,
where
n
H
G
H
0
H)
and the GO (
G
H ),
i.e.,
is proportional to the systematic risk of the underlying
(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 expected 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
11
The derivation of the theoretical model, as well as the tables for robustness checks on the empirical
results, 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:
A
G
VH;t
VH;t
2
VH;t
@Et [Rt;t+1 ]
=
@XIC
where
1
denotes
@
.
@XIC
Since
1
!
G
1 (Et [Rt;t+1 ]
> 0, it is clear that
A
Et [Rt;t+1
]);
@Et [Rt;t+1 ]
@XIC
(2)
A
G
].
] > Et [Rt;t+1
> 0 if Et [Rt;t+1
n
H)
G
] increases with the risk of the underlying new business (
It turns out that Et [Rt;t+1
and the exercise cost (XH ) (cf. Appendix A5). Thus, IC investment is likely to increase the
…rm’s expected returns if either
n
H
or XH is su¢ ciently high. More formally, Appendix A4
shows that:12
@Et [Rt;t+1 ]
=
@XIC
A
VH;t
2
VH;t
!
n
1 [VH (1
exp(
0
H
n
H ))
+ XH (exp(
0
H)
A
For …rms with non-zero initial AIP (i.e., VH;t
> 0), it is apparent from (3) that
0 if
n
H
0
H,
(3)
1)]:
@Et [Rt;t+1 ]
@XIC
>
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
n
H
<
0
H
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 undern
H
take ambitious innovation projects with high
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
12
13
n
VH is the value of the underlying new business at the time of exercise.
@
F
@E [R
]
> 0 under the same conditions for t@Xt;t+1
> 0:
Similarly, Appendix A6 shows that @XH;t
IC
IC
14
For 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 the
potential to generate tremendous global sales (Achilladelis (1999)). Similarly, both upstream and downstream
growth options in the oil and gas industry require immense amount of initial capital: for example, the deepsea production platforms and the recent expansions in the re…ning sector each require multi-billion dollar
up-front investment and the price tag of Exxon-Mobil’s Lique…ed Natural Gas (LNG) venture in Papua New
Guinea 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 investment. 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
t
) with clean surplus accounting
the decomposition of the market-to-book equity ratio ( M
Bt
(see Fama and French (2006)):
Mt
=
Bt
1
X
=1
Et
h
Yt+
Bt
Bt+
Bt
R
i
;
(4)
Bt+ is the change in book equity, and R is the expected gross return.17 Since IC
h
i
investment increases expected reinvestment of earnings, Et BBt+
, it follows that, holding
t
i
h
Yt+
Mt
constant,
expected
return
can
rise
if
(and
only
if)
expected
pro…tability,
E
; is also
t
Bt
Bt
where
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
15
We also note that the IC e¤ect is zero for …rms with no initial AIP, which are typically small …rms.
In contrast, since type-L …rms simply exercise existing options, there should not be future investment
associated with option exercising (in our simple model).
17
We thank an anonymous referee for suggesting this approach.
16
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 introduction, 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 idiosyncratic 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. Equation (3)), while the risk shifting perspective highlights the change in idiosyncratic risk following 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 likely
18
While 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 and
future stock returns. For example, while Ang et al. (2006) document a negative IVOL-return relation, Bali
and Cakici (2008) …nd no robust relation between IVOL and returns, and Boehme et al. (2009) document
a 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 predictions 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 facilitates 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 investments 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 expendi12
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 accounting 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 closedend 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 industrylevel 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-toequity 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
19
To 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 the
in‡uence of very small …rms. However, including these very small …rms generates similar results (untabulated).
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 comparison 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
20
1) investment hedge portfolio
Based 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, to
form the two RDS groups, we assign …rms with missing RDS to the low RDS group and the rest to the high
RDS group. Assigning …rms with zero RDS to the low RDS group or forming three instead of two RDS
groups 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 (untabluated) 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 in16
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 subsequent 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
21
We obtain Carhart’s (1997) four factors returns and the one-month Treasury bill rate from Kenneth
French’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 optionexercising investment reduces expected returns as discussed in the existing real options literature. 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 tstatistics (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) +
(5)
b5 ln(BT M ) + b6 M omentum + "i ;
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(BT M ) is
the natural log of the book-to-market equity ratio in year t
1, and M omentum 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 prediction 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
22
Suppose that innovation arrival follows a Poisson process with parameter . If the innovation has not
arrived till period t + , then the probability that the innovation will arrive in the next period (i.e., in the
interval 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 the
theoretical 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 investmentreturn 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 relatively 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
23
1.24
For example, following Kydland and Prescott (1982), suppose that setting up IC requires passing through
J stages and that on average n < J stages are completed during one year. For simplicity, let the innovation
probability 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 the
previous footnote).
24
Scaling total investment by lagged assets or lagged net PPE follows the de…nitions of the investmentto-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
25
The results for small high R&D …rms are consistent with these …rms undertaking growth option generation projects with lower systematic risk possibly due to the di¢ culty in externally …nancing projects
with 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 average
post-sorting systematic risk reported here could be biased downwards. However, we note that our sample
includes only public …rms; hence, the small high R&D …rms in our sample are larger on average than new
entrants or “start ups” (see, e.g., Pagano, Panetta, and Zingales (1998), Aslan and Kumar (2011)). In
addition, 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(BT M ) + b6 M omentum + "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-tobook 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 investment 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 investment 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…tability, 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 innovation 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 periods 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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32
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
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
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
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
Big
High
Small
Big
33
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
AG Deciles (EW)
Year
1
2
3
4
5
1(Low)
1.74
(4.79)
1.54
(4.33)
1.57
(4.60)
1.42
(4.39)
1.46
(4.35)
5
1.38
(5.54)
1.38
(5.46)
1.33
(5.28)
1.43
(5.52)
1.35
(5.15)
10(High)
0.61
(1.66)
0.87
(2.32)
1.19
(3.26)
1.18
(3.29)
1.14
(3.20)
AG Deciles (VW)
10-1
-1.13
(-6.95)
-0.68
(-4.65)
-0.38
(-3.33)
-0.24
(-2.07)
-0.33
(-2.63)
1(Low)
1.21
(4.25)
1.16
(4.02)
1.19
(4.35)
0.82
(2.90)
1.00
(3.37)
5
1.07
(4.90)
1.06
(4.77)
0.88
(4.04)
1.02
(4.59)
0.98
(4.27)
10(High) 10-1
0.71
-0.50
(2.17)
(-2.60)
0.93
-0.23
(2.77)
(-1.14)
1.10
-0.09
(3.43)
(-0.48)
1.00
0.18
(2.88)
(0.91)
1.17
0.18
(3.65)
(0.82)
Panel B. Monthly Carhart Alphas
AG Deciles (EW)
Year
1
2
3
4
5
1(Low)
0.55
(3.42)
0.41
(2.67)
0.51
(3.61)
0.40
(2.78)
0.47
(3.06)
5
0.27
(3.90)
0.31
(4.09)
0.29
(3.78)
0.42
(4.66)
0.34
(3.92)
10(High)
-0.35
(-2.74)
-0.10
(-0.67)
0.18
(1.19)
0.17
(1.33)
0.24
(2.06)
AG Deciles (VW)
10-1
-0.90
(-6.15)
-0.51
(-3.37)
-0.34
(-2.80)
-0.23
(-1.98)
-0.23
(-1.69)
34
1(Low)
-0.01
(-0.06)
-0.06
(-0.46)
0.12
(0.96)
-0.14
(-0.93)
-0.06
(-0.35)
5
10(High) 10-1
0.05
-0.26
-0.25
(0.68)
(-2.37) (-1.38)
0.11
-0.02
0.04
(1.33)
(-0.15)
(0.21)
-0.06
0.12
0.00
(-0.74)
(0.97)
(-0.01)
0.16
0.12
0.26
(1.69)
(0.92)
(1.42)
0.02
0.35
0.41
(0.20)
(2.51)
(1.73)
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 valueweighted (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.
Panel A. Value-weighted Carhart alphas
Panel B. Equal-weighted Carhart alphas
Low RDS Low RDS
High RDS
AG Deciles
Size Year Small 1 1
-0.15
(-1.07)
2 -0.52
(-3.02)
3 -0.10
(-0.57)
4 -0.01
(-0.07)
5 -0.18
(-0.89)
Big 1 0.12 (0.62)
2 -0.28
(-1.34)
3 0.37 (1.63)
4 0.02 (0.09)
5 -0.07
(-0.32)
10-1
-0.71
-0.56 (-4.96) (-3.16) -0.58
-0.06 (-3.41) (-0.29) -0.21
-0.12 (-1.22) (-0.53) -0.19
-0.18 (-1.02) (-0.73) -0.29
-0.11 (-1.34) (-0.44) -0.44
AG Deciles
AG Deciles
10 -0.56 (-2.54) (-2.36) 1
10
10-1
0.03
-0.38
-0.41
0.36
(-3.07)
(-2.25)
(2.01)
-0.07
0.17
(-0.33)
(0.93)
0.09
0.00
-0.09
0.40
(0.54)
(-0.02)
(-0.40)
(2.32)
0.00
-0.15
-0.16
0.34
0.12
-0.22
(0.02)
(-0.76)
(-0.64)
(1.83)
(0.71)
(-1.19)
0.15
-0.13
-0.29
0.29
0.02
-0.27
(0.64)
(-0.65)
(-1.03)
(1.49)
(0.11)
(-1.21)
-0.01
0.01
0.02
0.14
-0.35
-0.49
(-0.04)
(0.05)
(0.06)
(0.81)
0.30
0.28
(1.01)
-0.27 (-1.19) (-0.97) -0.15
-0.07 (-0.80) (-0.27) -0.39
-0.56
(-1.95) (-3.14)
-0.08
-0.49
(-0.41) (-2.31)
(-2.27) (-2.33)
-0.14
0.08 (-1.12) (-0.83)
(0.35)
-0.22
0.16
0.39
0.23
0.47
(0.90)
(2.05)
(0.91)
(2.35)
-0.09
0.49
0.58
-0.07
(-0.44)
(2.73)
(2.13)
0.01
0.70
0.70
(0.03)
(3.41)
(2.07)
35
-0.75
0.06
(1.46)
-0.25
-0.39
(-1.97) (-3.93)
(0.35)
0.03
-0.70 10-1
0.13
(0.14)
-0.32
AG Deciles
10
(0.86)
0.07 (-1.69) (-2.59) 1
(0.20)
(-1.00) (0.26)
-0.20
High RDS
-0.07
-0.55
(-0.43) (-2.44)
-0.17
-0.10
(-0.37) (-0.84) (-0.37)
-0.03
0.04 (-0.30) (-0.16)
(0.14)
-0.07
1
10
10-1
0.73 -0.31
-1.04
(3.57) (-1.62) (-5.75)
0.66 0.08
-0.58
(3.37) (0.49) (-3.17)
0.58 0.36
-0.23
(3.09) (1.87) (-1.47)
0.59 0.21
-0.37
(3.55) (1.25) (-2.34)
0.68 0.31
-0.38
(3.62) (1.99) (-2.03)
0.05 0.00
-0.06
(0.28) (-0.02) (-0.25)
0.12 0.30
0.18
(0.61) (1.37)
(0.69)
0.34 0.54
0.20
(1.72) (2.62)
(0.78)
0.09 0.63
0.54
(0.45) (3.27)
(2.44)
0.25 0.70
0.45
(0.92) (3.54)
(1.27)
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
1
2
3
4
5
AG
AG*HRDS_Big
HRDS_Big
ln(Size)
-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)
-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)
-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)
-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)
-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)
36
ln(BTM) Momentum Intercept
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.
Panel A. Future investment
A1. Total investment/Assets
RDS/Size/AG
Rank
Year 1
A2. Total investment/Net PPE
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
(9.73)
(8.32)
(7.62)
(12.31)
(12.94)
(12.88)
(11.63)
(11.12)
t (HBH-LSH) (11.83) (10.86)
Panel C. Beta and IVOL
Panel B. Expected profitability
RDS/Size/AG
Rank
Year 1
Year 2
Year 3
Year 4
Year 5
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%
(11.65)
(15.93)
(-10.41)
(-11.44)
t (HBH-LSH) (18.52) (19.77) (19.21)
(16.30) (17.96)
37
Lag(Beta) Avg(Beta) Lag(IVOL) Avg(IVOL)
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-tocash 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
1
2
3
4
5
AG
AG*HRDS_LDCF HRDS_LDCF
ln(BTM) Momentum Intercept
-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)
-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)
-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)
-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)
-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)
38
ln(Size)
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 nonoverlapping 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.
Panel A. Value-weighted Carhart alphas
Low MABA High MABA
AG Deciles AG Deciles
10-1
Size Year 1 10-1 10 1
10
Small 1 0.13 -0.26 -0.40
-0.25 -0.61 -0.36
(1.02) (-1.61) (-1.98) (-1.68) (-5.58) (-2.02)
2 -0.26 -0.33 -0.07
0.08 -0.23 -0.31
(-1.88) (-1.95) (-0.35) (0.44) (-1.59) (-1.57)
3 -0.12 -0.32 -0.20
0.09 -0.03 -0.12
(-0.77) (-1.57) (-0.89) (0.48) (-0.19) (-0.54)
4 0.00 -0.37 -0.37
0.06 -0.15 -0.22
(-0.03) (-1.92) (-1.72) (0.28) (-0.95) (-0.83)
5 -0.06 -0.20 -0.13
0.17 -0.28 -0.45
(-0.39) (-0.93) (-0.57) (0.59) (-1.53) (-1.33)
Big 1 0.00 -0.23 -0.23
0.07 -0.08 -0.16
(-0.01) (-1.08) (-0.84) (0.34) (-0.61) (-0.59)
2 -0.07 -0.13 -0.06
-0.01 0.17
0.18
(-0.38) (-0.54) (-0.19) (-0.05) (1.08) (0.67)
3 0.20 -0.59 -0.79
0.16
0.36
0.19
(0.93) (-2.25) (-2.43) (0.83) (2.30) (0.76)
4 -0.07 -0.25 -0.19
-0.04 0.25
0.30
(-0.28) (-0.73) (-0.50) (-0.20) (1.51) (1.07)
5 0.01 -0.70 -0.71
-0.10 0.65
0.75
(0.06) (-2.32) (-2.07) (-0.38) (3.64) (2.19)
39
Panel B. Equal-weighted Carhart alphas
Low MABA
High MABA
AG Deciles
AG Deciles
10-1 10-1
1
10
1 10
0.70 -0.17 -0.87 0.30 -0.37 -0.67
(3.82) (-0.92) (-4.52) (1.49) (-1.82) (-3.70)
0.50 -0.08 -0.58 0.39 -0.13 -0.52
(2.77) (-0.42) (-3.32) (1.85) (-0.74) (-2.70)
0.50
0.00 -0.50 0.51 0.26 -0.26
(2.99) (0.02) (-2.67) (2.40) (1.39) (-1.48)
0.48
0.15 -0.33 0.43 0.18 -0.25
(2.99) (0.79) (-1.84) (2.11) (1.25) (-1.33)
0.50
0.31 -0.19 0.63 0.15 -0.48
(2.96) (1.42) (-0.89) (3.05) (1.04) (-2.30)
0.20 -0.30 -0.50 0.10 -0.09 -0.18
(1.01) (-1.45) (-1.90) (0.50) (-0.60) (-0.80)
-0.07 -0.05 0.02 0.12 0.21 0.09
(-0.31) (-0.20) (0.07) (0.64) (1.18) (0.39)
0.53 -0.23 -0.76 0.34 0.40 0.06
(2.19) (-0.93) (-2.38) (1.87) (2.10) (0.24)
0.18 -0.26 -0.44 -0.01 0.48 0.49
(0.80) (-0.95) (-1.50) (-0.04) (2.68) (2.07)
0.04 -0.44 -0.48 0.09 0.61 0.52
(0.14) (-1.48) (-1.37) (0.38) (3.96) (1.78)
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 onemonth gap. All independent variables (except dummies) are winsorized at the top and bottom 1%.
Year
1
2
3
4
5
AG
AG*HMABA_Big HMABA_Big ln(Size)
-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)
-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)
-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)
-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)
-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)
40
ln(BTM) Momentum Intercept
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
1
2
3
4
5
AG
-0.69
(-7.38)
-0.38
(-4.63)
-0.20
(-2.26)
-0.15
(-1.64)
-0.30
(-3.03)
AG*Tech_Big
0.35
(1.97)
0.33
(1.92)
0.24
(1.19)
0.07
(0.38)
0.61
(2.94)
Tech_Big
0.10
(0.70)
0.30
(2.38)
0.28
(2.30)
0.27
(2.19)
0.18
(1.64)
41
ln(Size)
-0.10
(-2.06)
-0.14
(-2.77)
-0.15
(-2.97)
-0.16
(-3.14)
-0.14
(-2.86)
ln(BTM) Momentum Intercept
0.16
0.55
1.79
(2.07)
(2.50)
(4.21)
0.05
0.48
1.94
(0.68)
(2.12)
(4.51)
-0.02
0.44
1.94
(-0.22)
(1.97)
(4.64)
-0.04
0.29
1.97
(-0.50)
(1.25)
(4.74)
-0.04
0.26
1.89
(-0.55)
(1.07)
(4.52)