Real Options, Volatility, and Stock Returns GUSTAVO GRULLON, EVGENY LYANDRES, and ALEXEI ZHDANOV * ABSTRACT We provide evidence that the positive relation between firm-level stock returns and firm-level return volatility is due to firms’ real options. Consistent with real option theory, we find that the positive volatility- return relation is much stronger for firms with more real options and that the sensitivity of firm value to changes in volatility declines signifi- cantly after firms exercise their real options. We reconcile the evidence at the aggregate and firm levels by showing that the negative relation at the aggregate level may be due to aggregate market conditions that simultaneously affect both market returns and return volatility. * Gustavo Grullon is with the Jesse H. Jones Graduate School of Business, Rice Univeristy. Evgeny Lyandres is with the School of Management, Boston University. Alexei Zhdanov is with the University of Lausanne and Swiss Finance Institute. The authors thank Rui Abuquerque, Yakov Amihud, Doron Avramov, Clifford Ball, Alexander Barinov, Jonathan Berk, Gennaro Bernile, Nicolas Bollen, Jacob Boudoukh, Tim Burch, Murray Carlson, Lauren Cohen, Fran¸ cois Degeorge, Darrell Duffie, Rafi Eldor, Wayne Ferson, Amit Goyal, Dirk Hackbarth, Campbell Harvey (the Ed- itor), Ohad Kadan, Markku Kaustia, Matti Keloharju, Timo Korkeamaki, Moshe Levy, Lubomir Litov, Hong Liu, Roni Michaely, Barb Ostdiek, Dino Palazzo, Brad Paye, Neil Pearson, Gordon Phillips, Lukasz Pomorski, Amir Rubin, Jacob Sagi, Dan Segal, Anjan Thakor, Yuri Tserlukevich, Masahiro Watanabe, James Weston, Zvi Wiener, Yuhang Xing, Guofu Zhou, an associate editor, an anonymous referee, and seminar participants at Aalto School of Economics, Hebrew Univer- sity, Interdisciplinary Center Herzliya, Louisiana State University, Rice University, Texas A&M International University, Vanderbilt University, Washington University at Saint Louis, University of Illinois at Urbana-Champaign, University of Miami, University of Texas at San Antonio, 2008 University of British Columbia Winter Finance Conference, 2008 Rotschild Caesarea Center Con- ference, 2008 European Finance Association Meetings, 2011 Finance Down Under Conference, and 2011 Napa Valley Conference for helpful comments and suggestions. The authors also thank Her- nan Ortiz-Molina for help with using union membership data and Sarah Diez for valuable research assistance.
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Real Options, Volatility, and Stock Returns
GUSTAVO GRULLON, EVGENY LYANDRES, and ALEXEI ZHDANOV∗
ABSTRACT
We provide evidence that the positive relation between firm-level
stock returns and firm-level return volatility is due to firms’ real options.
Consistent with real option theory, we find that the positive volatility-
return relation is much stronger for firms with more real options and
that the sensitivity of firm value to changes in volatility declines signifi-
cantly after firms exercise their real options. We reconcile the evidence
at the aggregate and firm levels by showing that the negative relation
at the aggregate level may be due to aggregate market conditions that
simultaneously affect both market returns and return volatility.
∗Gustavo Grullon is with the Jesse H. Jones Graduate School of Business, Rice Univeristy.Evgeny Lyandres is with the School of Management, Boston University. Alexei Zhdanov is with theUniversity of Lausanne and Swiss Finance Institute. The authors thank Rui Abuquerque, YakovAmihud, Doron Avramov, Clifford Ball, Alexander Barinov, Jonathan Berk, Gennaro Bernile,Nicolas Bollen, Jacob Boudoukh, Tim Burch, Murray Carlson, Lauren Cohen, Francois Degeorge,Darrell Duffie, Rafi Eldor, Wayne Ferson, Amit Goyal, Dirk Hackbarth, Campbell Harvey (the Ed-itor), Ohad Kadan, Markku Kaustia, Matti Keloharju, Timo Korkeamaki, Moshe Levy, LubomirLitov, Hong Liu, Roni Michaely, Barb Ostdiek, Dino Palazzo, Brad Paye, Neil Pearson, GordonPhillips, Lukasz Pomorski, Amir Rubin, Jacob Sagi, Dan Segal, Anjan Thakor, Yuri Tserlukevich,Masahiro Watanabe, James Weston, Zvi Wiener, Yuhang Xing, Guofu Zhou, an associate editor,an anonymous referee, and seminar participants at Aalto School of Economics, Hebrew Univer-sity, Interdisciplinary Center Herzliya, Louisiana State University, Rice University, Texas A&MInternational University, Vanderbilt University, Washington University at Saint Louis, Universityof Illinois at Urbana-Champaign, University of Miami, University of Texas at San Antonio, 2008University of British Columbia Winter Finance Conference, 2008 Rotschild Caesarea Center Con-ference, 2008 European Finance Association Meetings, 2011 Finance Down Under Conference, and2011 Napa Valley Conference for helpful comments and suggestions. The authors also thank Her-nan Ortiz-Molina for help with using union membership data and Sarah Diez for valuable researchassistance.
It is well established in the asset pricing literature that aggregate market returns are
negatively correlated with aggregate market volatility (e.g., French, Schwert, and
Stambaugh (1987), Campbell and Hentschel (1992), and Duffee (1995)). One pos-
sible explanation for this negative relation is the “leverage effect” hypothesis (e.g.,
Black (1976) and Christie (1982)), which states that when stock prices fall, firms
become more levered, raising the volatility of stock returns. Another explanation,
due to French, Schwert, and Stambaugh (1987), holds that because an increase in
systematic volatility raises risk premia and expected future stock returns, an unex-
pected change in (systematic) volatility is likely to reduce firm values, leading to a
negative association between volatility and contemporaneous returns.
Contrary to the evidence at the aggregate level, however, Duffee (1995) finds
that stock returns and volatility are positively correlated at the firm level. This
empirical finding has important theoretical implications because it is inconsistent
with the leverage and risk premia hypotheses, and it challenges the conventional
wisdom on the relation between volatility and asset prices.
The main contribution of our paper is twofold. First, we provide a rational
explanation for the positive contemporaneous relation between firm-level returns and
firm-level volatility documented in Duffee (1995). Second, we provide an explanation
for the difference between the aggregate volatility-return relation and the firm-level
volatility-return relation. Surprisingly, despite the importance of these issues to our
understanding of the role of volatility in asset pricing, research on these topics has
been very limited (e.g., Albuquerque (2012) and Duffee (2002)).
We hypothesize that the positive relation between firm-level returns and firm-
level volatility may be due to real options that firms possess. One of the main
implications of real options theory is that a real option’s value is increasing in the
1
volatility of an underlying process (i.e., demand volatility, cost volatility, or overall
volatility of profits). The main rationale for this relation is that since firms can
change their operating and investment decisions to mitigate the effects of bad news
(e.g., reduce production, shut down operations, defer investments) and amplify the
effects of good news (e.g., expand production, restart operations, expedite invest-
ments), an increase in the volatility of an underlying process can have a positive
effect on firm value. That is, since operating and investment flexibility increases the
convexity of firm value with respect to the value of its underlying assets, firm value
is an increasing function of volatility, due to Jensen’s inequality. Therefore, if real
options constitute a substantial component of firm value, then it is possible that
the positive return-volatility relation documented in Duffee (1995) is driven by the
presence of these options. We test this hypothesis empirically and find numerous
pieces of supportive evidence.
First, we examine whether the value of firms with abundant investment op-
portunities is more sensitive to changes in underlying volatility than the value of
assets-in-place-based firms. The more investment opportunities a firm has, the more
discretion it has with respect to the timing of its investments and hence the larger
the value of its real options. Thus, if the positive relation between returns and
changes in volatility is due to the presence of real options, whose values are increas-
ing in volatility, then the sensitivity of firm value to volatility should be stronger
among firms with more investment opportunities. Using a battery of proxies for in-
vestment opportunities, we find that the positive contemporaneous relation between
returns and changes in volatility is very strong among firms that are likely to have
abundant investment opportunities, while it is substantially weaker among assets in
place-based firms. Specifically, we find that the volatility-return relation is stronger
2
among young firms, small firms, high R&D firms, and high growth firms.
Second, since the value of real options comes from the ability of firm managers to
change their decisions as new information arrives, we also investigate whether proxies
for operating flexibility can explain cross-sectional differences in the volatility-return
relation. Consistent with the prediction that volatility creates value when managers
have flexibility to alter their investment and operating decisions, we find that the
relation between volatility and stock returns is stronger among firms with fewer op-
erational constraints (e.g., firms in non-unionized industries) and firms that appear
to be able to respond better to resolutions of uncertainty (e.g., firms with higher
convexity of value with respect to earnings and sales).
Third, we investigate how the sensitivity of firm values to changes in volatility
evolves as a firm’s mix of growth options and assets in place changes over time. On
the one hand, a firm develops and accumulates real options. On the other hand, it
exercises these options by investing when the value of the benefits from investing
is high enough to offset the value of the option to wait. Thus, the sensitivity of
firm value to changes in volatility is expected to be increasing as the firm builds
up its real options, and it is expected to decline when the firm exercises (part of)
them. To test this prediction, we use spikes in firms’ investment levels, issues of
seasoned equity, and spikes in external financing in general to proxy for instances
of real option exercises. Consistent with the theory, we find that the sensitivity of
firm value to changes in underlying volatility increases prior to real option exercises,
drops sharply following exercises of real options, and then starts rising again as firms
start to build up new real options. This evidence strongly suggests that part of the
positive relation between returns and volatility is driven by the effect of volatility
on the value of real options.
3
Fourth, we demonstrate that the volatility-return relation is much stronger in
industries that have been shown to have plenty of growth and strategic options (high-
tech, pharmaceutical, and biotechnology industries) and high levels of operating
flexibility (natural resources industry). Furthermore, we perform a within-industry
analysis using a sample of oil and gas firms to investigate more deeply the effect
of volatility on stock returns. We focus on oil and gas firms because they provide
a unique setting for testing the predictions of the real options theory. Since these
firms have valuable timing options on developing their undeveloped proven reserves,
one could use their undeveloped and developed reserve estimates as proxies for their
mix of real options and assets in place. Using hand-collected data on oil and gas
firms’ reserves, we find that, consistent with the theory, the return-volatility relation
is stronger among firms with a higher proportion of undeveloped reserves.
In addition, we examine the effect of the return-volatility relation on the per-
formance of asset pricing models. Based on the insights of McDonald and Siegel
(1985) and Berk, Green, and Naik (1999), Da, Guo, and Jagannathan (2012) argue
that in the presence of real options, the CAPM may explain the expected returns
on a firm’s underlying assets but not necessarily the expected returns on its equity.
This is because when firms possess real options, equity risk becomes a nonlinear
function of the risk of the underlying assets. Consistent with this argument, Da,
Guo, and Jagannathan (2012) show that the presence of real options seems to ex-
plain the poor performance of the CAPM. We exploit this result to test our main
hypothesis. If real options are an important determinant of the positive relation
between volatility and stock returns, then the CAPM, or any asset pricing model
that does not account for real options, should perform better for firms with a weak
return-volatility relation (firms with relatively few real options) than for firms with
4
a strong return-volatility relation (firms with abundant real options). Our empir-
ical results are consistent with the real options theory. Using Gibbons, Ross, and
Shanken’s (1989) test, we find that the CAPM, as well as Fama and French (1993)
three-factor model, cannot be rejected within a subsample of firms with a relatively
weak return-volatility relation, but the models are comfortably rejected within a
subsample of firms with a relatively strong return-volatility relation.
In general, we believe that our paper provides an explanation for the positive
contemporaneous relation between firm-level returns and firm-level volatility docu-
mented in Duffee (1995). The sensitivity of the value of real options to underlying
volatility seems to be an important reason for the cross-sectional variation in the
relation between returns and contemporaneous changes in volatility and for the
evolution of this relation around investment and financing spikes. These findings
complement the existing literature examining the effects of real options on asset
prices (e.g., Berk, Green, and Naik (1999) and Carlson, Fisher, and Giammarino
(2004)).
While the real options hypothesis is consistent with the positive relation be-
tween volatility and stock returns at the firm level, it cannot explain the negative
correlation between these variables at the aggregate level. We argue that the nega-
tive relation between aggregate stock returns and aggregate return volatility could
be driven by an omitted variable problem. Because investors tend to be more un-
certain about future real output growth during economic downturns (e.g., Veronesi
(1999)), periods of high stock return volatility could coincide with periods of low
stock returns even if the direct effect of volatility on firm value is positive. That
is, volatility may increase when stock prices decline not because the fundamental
relation between these variables is negative, but because both variables are affected
5
by the same underlying macroeconomic factors. Thus, regressing aggregate stock
returns on aggregate market volatility could lead to inferences that are very dif-
ferent from those obtained in a setting in which aggregate (market) conditions are
controlled for.
We address this issue by focusing on firm-level stock returns rather than on
aggregate returns. Using individual stock returns instead of aggregate returns allows
us to control simultaneously for aggregate factors (proxies for market conditions)
and aggregate volatility. Consistent with the aggregate evidence, regressions of firm-
level returns on aggregate volatility alone reveal a strong negative return-volatility
relation. However, once we control for aggregate market factors (aggregate market
returns, HML, and SMB), aggregate volatility becomes unrelated to stock returns.
More interestingly, we find that aggregate volatility has a positive effect on the
value of real options-based firms and a negative effect on the value of assets in
place-based firms after controlling for market conditions. These results seem to
reconcile the aggregate-level negative relation between volatility and returns with
the positive relation at the firm level.
The remainder of the paper is organized as follows. In Section I we discuss and
motivate our measure of volatility, summarize the data, and present selected sum-
mary statistics. In Section II we estimate the relation between returns and changes
in volatility for subsets of firms characterized by different mixes of real options and
assets in place. Section III investigates the effect of operating flexibility on the
volatility-return relation. Section IV examines the evolution of the relation between
returns and changes in volatility around times of significant changes in firms’ mix of
real options and assets in place. In Section V we perform an industry-level analysis
of the relation between returns and contemporaneous changes in volatility. In Sec-
6
tion VI we examine the effect of the volatility-return relation on the performance
of asset pricing models. Section VII provides evidence that aggregate volatility is
unrelated to stock returns after controlling for underlying market conditions and
examines the relation between returns and aggregate volatility for subsamples of
real options-based and assets in place-based firms. In Section VIII we discuss the
results of robustness checks. Section IX summarizes and concludes.
I. Measure of Volatility, Data Sources, and Summary
Statistics
A. Measure of Volatility
Theoretically, the value of a firm’s real options is increasing in the volatility of
an underlying process (e.g., McDonald and Siegel (1986)). However, many aspects
of uncertainty regarding potential projects, which include but are not limited to
demand shocks (changes in consumer tastes), supply shocks (changes in production
technologies), and institutional changes, are unobservable. Moreover, even if the
realizations of these shocks were observable ex-post, their expectations, which affect
the value of real options, would not be known. If stock prices incorporate the value
of real options, then the volatility of stock prices is expected to be related to the
volatility of the underlying valuation processes. This justifies the use of measures
stock return volatility as proxies for underlying volatility, as in Leahy and Whited
(1996) and Bulan (2005).
We follow Ang et al. (2006, 2009) and Duffee (1995), among others, and estimate
firm i’s volatility during month t as the standard deviation of the firm’s daily returns
7
during month t,
V OLi,t =
√√√√∑τ∈t
(ri,τ − ri,t)2
nt − 1, (1)
where ri,τ is the natural logarithm of day τ ∈ t gross excess return on firm i’s
stock, ri,t is the mean of the logarithms of gross daily returns on firm i’s stock
during month t, and nt is the number of nonmissing return observations during
month t. We use logarithmic returns to mitigate the potential mechanical effect of
return skewness (see Duffee (1995) and Kapadia (2007)) on the relation between
returns and contemporaneous return volatilities. The change in volatility in month
t, ∆V OLi,t, is computed as the difference between the estimated volatility in month
t and the estimated volatility in month t− 1:
∆V OLi,t = V OLi,t − V OLi,t−1. (2)
B. Main Data Sources and Summary Statistics
We obtain daily stock returns, used in estimating volatilities and factor load-
ings, and monthly returns, used as the dependent variable in our regressions, from
CRSP daily and monthly return files, respectively. Daily and monthly factor returns
and risk-free rates are from Ken French’ website (http:// mba.tuck.dartmouth.edu/
pages/faculty/ken.french/data library.html). The time frame of our analysis is from
January 1964 to December 2008. Following Ang et al. (2006), among others, we
eliminate utilities (SIC codes between 4900 and 4999) and financials (SIC codes be-
tween 6000 and 6999) from the sample. Our sample contains over 3 million monthly
observations with nonmissing returns and volatility estimates.
Accounting variables used to compute firm characteristics, measures of invest-
ment opportunities (firm size, R&D expenditures, and sales growth), measures of op-
erating flexibility (sensitivity of firm value to profits and sales), as well as measures of
8
investment and financing spikes, are from COMPUSTAT. We obtain firms’ founding
and incorporation years, used to compute firm age, from Boyan Jovanovic’s website
(www.nyu.edu/econ/user/jovanovi). Dates of firms’ earnings announcements used
to estimate some of the measures of operating flexibility are from I/B/E/S. Data on
membership in labor unions are obtained from the Union Membership and Cover-
age database (www.unionstats.com), described by Hirsch and Macpherson (2003).1
We obtain data on seasoned equity offerings (SEOs), used in our event-time tests,
from Thomson Financial’s Securities Data Company. Finally, for our analysis of the
effects of real options on the return-volatility relation in the oil and gas industry,
we hand-collect data on developed and total proven oil and gas reserves for 72 oil
firms between 1995 and 2009 from firms’ annual reports.
We present summary statistics for returns, return volatilities, and changes in
return volatility in Table I, which also includes summary statistics for measures of
investment opportunities and managerial flexibility, which we discuss below. The Insert Ta-
ble I heremean excess return in our sample is 0.6% per month or about 7.2% per year. The
mean (median) daily firm-level stock return standard deviation is 3.17% (2.45%).
Our firm-level volatility estimates using daily data are similar to those reported
in Ang et al. (2006). The small positive mean change in volatility (0.007%) is
consistent with the positive time trend in volatility (e.g., Campbell et al. (2001)
and Cao, Simin, and Zhao (2008)). The standard deviation of the month-to-month
change in return volatility is 1.83%.
II. Return-Volatility Relation and Investment
Opportunities
We begin by verifying that the positive relation between firm-level volatility and
9
firm-level returns documented in Duffee (1995, 2002) and Albuquerque (2012) holds
in our sample. In particular, we estimate monthly cross-sectional Fama-MacBeth
(1973) regressions of individual firm returns, ri,t, net of the risk-free rate, rf,t, on
contemporaneous changes in firm-level volatility, ∆V OLi,t, and a vector of firm
characteristics, xi,t, most of which are known at the beginning of month t:
Using individual stock returns instead of aggregate market returns as the dependent
variable allows us to simultaneously control for market factors as well as aggregate
volatility. We use a panel data approach to estimate the parameters of (18) and,
following Petersen (2009), cluster standard errors by month.
As evident from the first column in Panel B, in which aggregate factor returns are
excluded from (18), the coefficient on the change in aggregate volatility is negative
and highly significant, similar to the aggregate evidence in Panel A. Augmenting the
regressions by the contemporaneous return on the market portfolio, in the second
column, reduces the magnitude of the coefficient on the change in market volatility
by about two-thirds, but it remains negative and significant. Further augmenting
the regressions by returns on the SMB and HML factor mimicking portfolios, in
the third column, results in zero relation between returns and changes in aggregate
33
volatility.
Finally, in Panel C we investigate the relation between firm-level returns and
aggregate volatility changes by examining the coefficient on the change on aggre-
gate volatility across different portfolios based on proxies for growth options and
proxies for operating flexibility. To conserve space we only report the coefficients on
∆V OLm,t. Consistent with the theory, we find that aggregate volatility has a posi-
tive effect on the value of real options-based firms and a negative effect on the value
of assets in place-based firms. Specifically, we find that small firms, young firms,
high R&D firms, high growth firms, and more flexible firms have a strong positive
aggregate volatility-return relation while large firms, old firms, low R&D firms, low
growth firms, and less flexible firms tend to have a much weaker and sometimes
negative relation between returns and changes in aggregate volatility. This result
is important, as it demonstrates that the negative relation between aggregate mar-
ket returns and contemporaneous volatility is not necessarily inconsistent with the
positive relation at the firm level. Further, it shows that real options are important
even at the aggregate level.
VIII. Robustness Checks
In this section we examine the robustness of our results. First, we examine
whether month-to-month changes in daily return volatilities are driven by transitory
jumps in stock prices as opposed to permanent changes in the diffusion component
of stock price evolution. We then proceed to examine possible nonlinearities in the
relation between firm value and changes in volatility and the potential joint effects
of shocks to volatility and shocks to liquidity on returns. Next, we examine whether
the “leverage hypothesis” or the “resale option hypothesis” can potentially explain
34
some of the results. Finally, we examine the robustness of our results involving oil
and gas firms to controlling for expected changes in oil return volatility. In this
section, to save space, we do not tabulate the results but instead discuss the main
findings. The results that we discuss below are available in the Internet Appendix.9
A. Are Changes in Return Volatility Driven by Jumps in Daily Stock Prices?
Throughout the paper we use the volatility of daily stock returns as a proxy
for the volatility of the process underlying firm value. However, an alternative
interpretation of month-to-month changes in daily stock return volatility is that
they mainly reflect transitory jumps in daily stock prices. If high return volatility in
a given month is driven by large daily returns that occurred during that month, then
we could observe a positive relation between monthly returns and return volatility.
In this subsection we discuss a battery of tests designed to distinguish between
the two interpretations discussed above. We begin by computing the correlations
among return volatility, V OLi,t, month-to-month change in volatility, ∆V OLi,t,
maximum daily return within a month, MAXi,t, and minimum daily return within
the month, MINi,t. If the positive return-volatility relation is driven by positive
daily price jumps, we should expect to find a higher (absolute) correlation between
∆V OLi,t and MAXi,t than between ∆V OLi,t and MINi,t. However, the former
correlation is 0.338, while the latter one is -0.354, inconsistent with the hypothesis
that the positive return-∆V OL relation is driven primarily by positive daily price
jumps.
Second, if changes in return volatility are driven entirely by transitory price
jumps, we would expect changes in volatility to reverse completely. To examine
whether this is the case, we analyze the evolution of volatility before and after large
volatility shocks. Specifically, we track volatility for 12 months before and after firm-
35
months in which the change in volatility is in the top or bottom 10% of the sample.
Close to half of positive and negative changes in volatility seem to be permanent,
in the sense that they are not reversed within 12 months.
Third, to ensure that our results are not driven by positive price jumps, we
estimate the return-∆V OL relation while omitting potential jumps from the sample.
Specifically, we replicate the cross-sectional tests in Tables III and IV while excluding
the top 5% and bottom 5% of daily returns, and obtain results similar to those in
the body of the paper. The Internet Appendix reports the results obtained using
the middle 90% of return observations.
Fourth, Frazzini and Lamont (2007) show that returns around earnings an-
nouncements are typically positive, and trading volume around earnings announce-
ments is abnormally high. If abnormal volume is associated with abnormal return
volatility, then the positive return-∆V OL relation may be driven by the effect of
earnings announcements. To ensure that this is not the case, we repeat the cross-
sectional tests while excluding earnings announcement firm-months and obtain re-
sults consistent with those in Tables III and IV.
Fifth, we remove the potential mechanical relation between returns and return
volatility by computing them on different days. Specifically, we compute monthly
returns while using returns on even days, and compute return volatility using returns
on odd days. If the return-∆V OL relation is driven by jumps in daily stock prices,
we should not see any relation between returns and return volatility when they
are computed on different days. However, the cross-sectional results stay intact,
suggesting that they are not driven by daily stock price jumps.
Finally, we repeat the tests while extracting the diffusion component of stock
return volatility. In particular, we follow the methodology proposed by Barndorff-
36
Nielsen and Shephard (2004, 2006) and Andersen, Bollerslev, and Diebold (2007)
to separate the continuous sample path variation from the discontinuous jump part
of the variation using the realized bipower variation measure. We then repeat the
cross-sectional tests while using the estimates of the diffusion component of the price
process instead of raw price changes and obtain results similar to those reported in
the body of the paper.
Overall, the tests discussed in this subsection suggest that the relation between
proxies for the mix of real options and assets in place and the sensitivity of returns
to changes in volatility are not driven by positive daily price jumps.
B. Nonlinearities in the Return-∆V OL Relation
To verify that potential nonlinearities in the return-∆V OL relation do not drive
our results, we estimate regressions in which instead of interacting ∆V OL with
measures of real options directly, we use a four-by-one vector of interaction variables,
defined as the product of the contemporaneous change in return volatility and a
dummy variable equal to one if the firm belongs to the second (third, fourth, fifth)
real options quintile, and equal to zero otherwise. The results indicate that in the
majority of specifications the return-∆V OL relation is monotonically increasing as
we move from the lowest real options quintile to the highest real options quintile.
C. The Joint Effects of Volatility and Liquidity
Bandi, Moise, and Russell (2008) show that shocks to market liquidity and
shocks to market volatility jointly affect market returns. To investigate the joint
effects of changes in firm-level volatility and firm-level liquidity on returns, we aug-
ment the regressions in (5) by including month-to-month changes in Amihud’s (2002)
illiquidity measure. Including this measure in the set of explanatory variables does
37
not change the coefficients on the change in volatility substantially. The coeffi-
cients on illiquidity innovation are negative in all specifications, consistent with
increases (decreases) in illiquidity leading to contemporaneous drops (increases) in
stock prices.
D. Leverage Hypothesis
A potential concern is that there could be sizeable differences in asset volatility
across the various subsamples in split-sample tests. We address this concern as
follows. We first split the sample each month into deciles of leverage. We then
split each of the 10 subsamples into quintiles of volatility levels. Comparing the
return-volatility relation across leverage subsamples while controlling for volatility
reveals that generally there is no particular pattern in the relation between leverage
and the sensitivity of returns to volatility.
E. Resale Option Hypothesis
Scheinkman and Xiong (2003) develop a theoretical model in which overconfi-
dence generates divergence of opinion among investors about the true value of an
asset. They show that, in the presence of short-selling constraints, these hetero-
geneous beliefs create a situation in which a buyer of an asset receives an implicit
option to resell the asset at a higher price to a more overconfident investor. Be-
cause the value of this resale option is increasing in the volatility of the fundamental
process, the price bubble generated by the resale option is positively correlated
with volatility. Therefore, the resale option hypothesis provides an alternative ex-
planation for the positive relation between changes in volatility and stock returns
documented by Duffee (1995).
Although Battalio and Schultz (2006), Schultz (2008), and Griffin et al. (2011)
38
do not find evidence supporting some of the main predictions of the resale option
hypothesis, in this subsection we examine whether this hypothesis can explain the
positive volatility-return relation at the firm level. As demonstrated by Scheinkman
and Xiong (2003), the sensitivity of the price bubble to changes in the volatility
of the underlying asset increases as the level of overconfidence increases. Thus, if
the resale option hypothesis is partially responsible for our results, then the posi-
tive relation between changes in volatility and stock returns should be stronger in
times when investors’ confidence is relatively high. To test this prediction, we use
Baker and Wurgler’s (2006) measure of investor sentiment to proxy for the level of
overconfidence in the market. This proxy seems to be a natural measure to test the
resale option hypothesis because it tends to be high during episodes that have been
classified as “irrational bubbles” and it has been shown to capture overvaluation in
the cross-section of stock returns (see Baker and Wurgler (2006)).
To examine the effect of overconfidence on the volatility-return relation, we aug-
ment the regression in (5) by including an additional term in which we interact
the measure of investor sentiment with the change in volatility. Contrary to the
predictions of the resale option hypothesis, we do not find any evidence that the
sensitivity of stock prices to changes in volatility increases during periods of high
investor sentiment. This evidence points out to an alternative interpretation of the
investor sentiment measure – it could be that investors are optimistic and enthu-
siastic in those years, not because of any irrational exuberance, but because the
economy is doing well. Therefore, because firms are more likely to exercise their
real options during good economic times, the sensitivity of stock prices to changes
in volatility declines during those periods. Overall, our results do not support the
idea that the resale option drives the observed positive correlation between stock
39
returns and changes in volatility.
F. Controlling for Expected Changes in Volatility of Oil Returns
Carlson, Khokher, and Titman (2007) show theoretically and empirically that
future volatility of oil returns is higher when the forward curve is steeply upward
sloping (in contango) or downward sloping (backwardated). Thus, it could be argued
that changes in oil return volatility used in the tests in Section V.B may be partially
predictable. To address this concern, we follow Carlson, Khokher, and Titman
(2007) and estimate the unexpected component of changes in oil return volatility.
Specifically, we first de-seasonalize oil return volatility by regressing it on 12 monthly
dummy variables. We then regress de-seasonalized oil return volatility on the de-
seasonalized slope of the term structure of oil futures, obtained from Tick data, and
its square.10 We next compute month-to-month unexpected changes in oil return
volatility as the month-to-month differences in the residuals of this regression. Using
the unexpected component of the change in oil return volatility instead of the raw
change in oil return volatility does not affect the qualitative results.
IX. Conclusions
In this paper we provide evidence suggesting that an important reason for the
positive contemporaneous relation between firm-level returns and firm-level volatil-
ity, first documented by Duffee (1995), is the presence of real options. Consistent
with the theoretical argument that the value of a real option is increasing in the
volatility of the underlying process, we find that firms with more real options exhibit
a stronger sensitivity of firm value to underlying volatility.
Using various proxies for the proportion of firm value represented by investment
40
opportunities, we show that the value of firms with abundant investment oppor-
tunities is highly sensitive to changes in volatility, while firms that derive most of
their values from existing assets exhibit substantially lower sensitivities of values to
volatility. In addition, we find that the cross-sectional relation between volatility and
returns is stronger for firms that have more operating flexibility and more convex
value functions. We also find that firms with plenty of growth and strategic options
(high-tech firms, pharmaceuticals, and biotechnological firms) and with high levels
of operating flexibility (natural resources firms) tend to exhibit a stronger volatility-
return relation. In addition, we focus on the oil and gas industry, for which we are
able to construct industry-specific measures of the mix of real options and assets
in place and of the volatility of the underlying process (oil price). We find results
consistent with the large-sample evidence.
Time-series results further reinforce the real options hypothesis. Using peri-
ods of abnormally high investment activity and abnormally high financing activity,
and in particular SEOs, as proxies for real option exercise times, we find a highly
economically and statistically significant decline in the sensitivity of firm values to
volatility around times of real option exercises, consistent with the hypothesis that
a reduction in the amount of remaining real options reduces the sensitivity of firm
value to underlying volatility.
We also build on recent findings on the effects of real options on the perfor-
mance of asset pricing models. Da, Guo, and Jagannathan (2012) show that in
the presence of real options, the CAPM cannot explain equity returns because eq-
uity expected returns become nonlinear functions of the expected returns of the
underlying projects. Thus, if the positive correlation between volatility and returns
is mainly driven by real option effects, then one would expect the performance of
41
the CAPM (or any other asset pricing model) to be stronger within subsamples of
firms with a relatively weak return-volatility relation (i.e., firms with relatively few
real options). Consistent with this logic, we find that the CAPM and Fama and
French (1993) three-factor model perform better within subsamples of firms with a
relatively weak relation between returns and changes in volatility than within sub-
samples of firms with a relatively strong return-volatility relation. This provides
another piece of evidence linking the positive return-volatility relation at the firm
level to real options.
Finally, our paper suggests a rational explanation for the discrepancy between
the negative volatility-return relation at the aggregate level and the positive relation
at the firm level. We argue that the negative relation between aggregate returns and
aggregate volatility could be driven by common underlying economic factors affect-
ing both variables. Consistent with this argument, we show that after controlling
for aggregate market conditions, aggregate volatility has no relation with individ-
ual stock returns. Moreover, the relation between firm-level returns and aggregate
volatility tends to be significantly positive for real options-based firms, while it is
much weaker and sometimes negative for assets in place-based firms.
In general, our findings support the real options-based explanation for the pos-
itive relation between volatility and returns. This result sheds light on the funda-
mental issue of how volatility affects asset prices.
42
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Notes
1These data use the Census Industry Classification (CIC) to classify industries,
which we map into Standard Industry Classification (SIC) codes and North Ameri-
can Industry Classification System (NAICS) in order to match them with Compustat
and CRSP.
2Here and below, the standard errors of the Fama-MacBeth (1973) estimates are
computed using Newey-West (1987) heteroskedasticity and autocorrelation consis-
tent variance-covariance matrices.
3The presence of leverage can also generate convexity in the value function (e.g.,
Galai and Masulis (1976)). However, we show below that our results are not driven
by the leverage effect.
4We exclude firm-years for which we cannot unambiguously assign the timing
relative to a spike. This occurs for firm-years with fewer than three years since the
last spike and fewer than three years until the next spike.
5We match firms based on their size and book-to-market ratio following Barber
and Lyon (1997) and Lyon, Barber, and Tsai (1999).
6Similar to investment spikes, when examining the return-∆V OL relation around
SEOs, we exclude firm-months within two years of at least two SEO events.
7This classification is broadly consistent with the definition used in Chemmanur,
He, and Nandy (2010), who define high-tech industries based on three-digit SIC
codes.
8We convert cubic feet of natural gas to barrels of oil equivalent by multiplying
51
the former by 0.0001767.
9The Internet Appendix is available on the Journal of Finance website at http://www.afajof.org/Supplements.asp
10As in Carlson, Khokher, and Titman (2007), the slope of the term structure of
oil futures is computed using the nearest and third-nearest contracts.
52
Table ISummary Statistics
This table presents summary statistics for returns, measures of volatility and changes in these measures, as wellas for measures of investment opportunities and operating flexibility used in cross-sectional tests. Returns dataare from CRSP. Accounting data are from COMPUSTAT. The sample period is 7/1963-12/2008. A stock’s excessreturn is the difference between its monthly return and monthly risk-free return. Volatility and its change refersto monthly volatility of logarithmic daily returns. Book assets are in millions of dollars. Age is the differencebetween the current year and the founding year, incorporation year, or the first year that the firm’s stock appears inmonthly CRSP files, in that order of availability. R&D / assets, is the ratio of R&D expenditures and lagged bookassets. Future sales growth is defined as the difference between sales four years after the year of the observationover sales in the year following the year of the observation divided by sales in the year following the year of theobservation. Earnings convexity is the estimated coefficient on the squared earnings surprise in the firm-leveltime-series regression of returns on earnings announcement days. Sales convexity is the estimated coefficienton the squared sales surprise in the firm-level time-series regression of returns on earnings announcement days.Union membership is at the industry level and is obtained from the Union Membership and Coverage database.
Union membership 0.106 0.117 0.009 0.060 0.364 1,315,294
53
Table IIReturns and Contemporaneous Changes in Volatility
This table presents regressions of firm-level excess returns on the estimated loading on the market factor,beginning-of-year log book-to-market ratio, log market equity, six-month lagged return for months -7 to -2 rel-ative to the observation month, monthly trading volume normalized by the number of shares outstanding, andmonth-to-month change in firm-level volatility, ∆V OLi,t. The sample period is 7/1963 to 12/2008. We estimatethe regressions monthly and report time-series means of coefficient estimates along with t-statistics obtained usingNewey-West autocorrelation and heteroskedasticity consistent standard errors of monthly coefficient estimates inparentheses. R2 refers to the average monthly R2.
Table IIIReturns, Contemporaneous Changes in Volatility, and Investment Opportunities
This table presents regressions of firm-level excess returns on the estimated loading on the market factor,beginning-of-year log book-to-market ratio, log market equity, six-month lagged return for months -7 to -2 relativeto the observation month, monthly trading volume normalized by the number of shares outstanding, month-to-month change in firm-level volatility, ∆V OLi,t, and an interaction variable equal to the product of ∆V OLi,t
and one of the four investment opportunity measures: log(book assets), log(age), log(R&D to assets), and futuresales growth. See Section III for definitions of the investment opportunities measures. We normalize each ofthe investment opportunity measures by subtracting its in-sample mean and dividing the difference by in-samplestandard deviation. The sample period is 7/1963 to 12/2008. We estimate the regressions monthly and reporttime-series means of coefficient estimates along with t-statistics obtained using Newey-West autocorrelation andheteroskedasticity consistent standard errors of monthly coefficient estimates in parentheses. R2 refers to theaverage monthly R2. We also present a summary of the economic effects of investment opportunity measures onthe ∆V OLi,t-return relation. Low (high) investment opportunities means that the effect of ∆V OLi,t on returnsis calculated using the value of the proxy for investment opportunities at two standard deviations below (above)the mean. Large ∆V OLi,t refers to ∆V OLi,t that is two standard deviations above the mean; such change equals3.66%.
Table IVReturns, Contemporaneous Changes in Volatility, and Measures of Flexibility
This table presents regressions of firm-level excess returns on the estimated loading on the market factor,beginning-of-year log book-to-market ratio, log market equity, six-month lagged return for months -7 to -2 relativeto the observation month, monthly trading volume normalized by the number of shares outstanding, month-to-month change in firm-level volatility, ∆V OLi,t, and an interaction variable equal to the product of ∆V OLi,t andone of the three flexibility measures: earnings convexity, sales convexity, and union membership. See Section IVfor details on estimation of the flexibility measures. We normalize each of the flexibility measures by subtractingits in-sample mean and dividing the difference by the in-sample standard deviation. The sample period is 7/1985to 12/2008. We estimate the regressions monthly and report time-series means of coefficient estimates alongwith t-statistics obtained using Newey-West autocorrelation and heteroskedasticity consistent standard errors ofmonthly coefficient estimates in parentheses. R2 refers to the average monthly R2. We also present a summaryof the economic effects of the flexibility measures on the ∆V OLi,t-return relation. Low (high) flexibility meansthat the effect of ∆V OLi,t on returns is calculated using the value of the proxy for flexibility at two standarddeviations below (above) the mean. Large ∆V OLi,t refers to ∆V OLi,t that is two standard deviations above themean; such change equals 3.66%.
57
Proxy for flexibility
Earnings convexity Sales convexity Union membership
Table VThe Relation between Returns and Changes in Volatility around Investment Spikes
This table presents regressions of firm-level excess returns on the market factor, beginning-of-year log book-to-market ratio, log market equity, six-month lagged return for months -7 to -2 relative to the observation month,monthly trading volume normalized by the number of shares outstanding, and month-to-month change in firm-level volatility, ∆V OLi,t, estimated separately for subsamples of firms-months belonging to years [-2, 2] relativeto an investment-spike year, SEO, or a financing spike year. Specifically, for each firm-month we compute therelative timing of the previous spike (SEO) and the next spike (SEO) and form five subsamples (four subsamplesfor SEO firms), consisting of firms with two years to the next spike, one year to the next spike, the spike year,one year after the spike, and two years after the spike (two years before the SEO and two years after). Panel Apresents results for investment spike firms. An investment spike is a firm-year in which a firm’s investment rateis at least three times higher than its time-series median. Panel B presents results for SEO firms. The date ofan SEO is its filing date, or issue date if filing date is unavailable. Panel C presents results for financing spikefirms. Financing spikes are firm-years in which the combination of net new issues of equity and debt exceed 10%of beginning-of-year book assets. The sample period is 1/1970 to 12/2008. We estimate the regressions monthlyand report time-series means of the coefficient on the change in volatility estimates along with their t-statisticsobtained using standard errors of monthly coefficient estimates in parentheses. The numbers in brackets are thet-statistics for the differences between the estimated coefficient on the change in volatility in year 1 and that inyear -1 relative to the investment spike, SEO, or financing spike. We report similar results for matched firms,defined in Section V. The difference row refers to the mean change in the coefficient on change in volatility betweenyear -1 and year 1 for sample firms minus that for matched firms, with t-statistics in parentheses.
Table VIReturns, Contemporaneous Changes in Volatility, and Industry-Wide Real Option
Indicators
This table presents cross-sectional regressions of excess returns on the market factor, beginning-of-year log book-to-market ratio, log market equity, six-month lagged return for months -7 to -2 relative to the observation month,monthly trading volume normalized by the number of shares outstanding, month-to-month change in firm-levelvolatility, ∆V OLi,t, and three interaction variables, defined as the product of ∆V OLi,t and an indicator vari-able equal to one if a firms belongs to a high-tech industry, natural resources industry, and pharmaceutical orbiotechnology industry respectively. The sample period is 7/1963 to 12/2008. We define high-tech industries asFama-French (1997) industries 22 (electrical equipment), 32 (telecommunications), 35 (computers), 36 (computersoftware), 37 (electronic equipment), and 38 (measuring and control equipment). We define natural resourcesindustries as Fama-French industries 27 (precious metals), 28 (mining), and 30 (oil and natural gas). We definepharmaceutical and biotechnology industries as Fama-French industries 12 (medical equipment) and 13 (phar-maceutical products). We estimate the regressions monthly and report time-series means of coefficient estimatesalong with t-statistics obtained using Newey-West autocorrelation and heteroskedasticity consistent standard er-rors of monthly coefficient estimates in parentheses. R2 refers to the average monthly R2. We also present theimpact of large ∆V OLi,t on returns for various industry groups. Large ∆V OLi,t refers to ∆V OLi,t that is twostandard deviations above the mean; such change equals 3.66%.
61
Market 0.108(3.09)
Log(B/M) 0.715(8.89)
Log(Equity value) -0.131(-2.81)
Lag(6-month return) -0.001(-0.58)
Volume 2.751(11.26)
∆ Volatility 0.826(7.08)
∆ Volatility * High tech 0.383(4.25)
∆ Volatility * Natural resources 0.400(4.01)
∆ Volatility * Pharmaceuticals 0.242(2.35)
R2 0.110
# Months 539
Impact of large ∆V OLi,t on return
High tech 4.43%
Natural resources 4.49%
High tech 3.91%
High tech 3.02%
62
Table VIIReturns of Oil and Gas Firms and Contemporaneous Changes in Volatility of Oil
Returns
This table presents panel regressions of oil and gas firms’ excess returns on the market factor, beginning-of-yearlog book-to-market ratio, log market equity, six-month lagged return for months -7 to -2 relative to the observationmonth, monthly trading volume normalized by the number of shares outstanding, monthly relative change in oilprice (monthly oil return), month-to-month change in oil price volatility, and interaction variables equal to theproduct of the proportion of undeveloped oil/gas/total reserves and month-to-month change in oil price volatility.The sample period is 1/1995 to 12/2009. Oil and gas firms are those belonging to Fama-French (1997) industry30. Relative oil price changes and their volatilities are computed using Brent Crude oil daily prices. See SectionVI for a discussion of developed and undeveloped reserves. Standard errors are clustered by month. We alsopresent a summary of the economic effects of the proportion of undeveloped reserves on the ∆OILV OLi,t-returnrelation. No (high) undeveloped reserves means that the effect of ∆OILV OLi,t on returns is calculated using thevalue of the proxy for the proportion of undeveloped reserves at zero (two standard deviations above the mean).Large ∆OILV OLi,t refers to ∆OILV OLi,t that is two standard deviations above the mean; such change equals1.95%.
Panel A presents regressions of aggregate (value-weighted) monthly excess return on aggregate volatility andmonth-to-month change in aggregate volatility. Aggregate volatility and change in it refers to the volatility of thevalue-weighted monthly return on all listed stocks. Panel B presents regressions of firm-level excess returns onchanges in aggregate volatility and the Fama and French (1993) three factor returns (MKTRF, HML, and SMB).Panel C presents regressions of firm-level excess returns on changes in aggregate volatility and the Fama andFrench (1993) three factor returns for subsamples of firms grouped by measures of investment opportunities andby measures of flexibility. Only the coefficients on the change in volatility are reported. The last column reportsthe difference between the estimated coefficients on the change in aggregate volatility between the extreme realoptions groups. The sample period is 7/1963 to 12/2008. t-statistics are reported in parentheses. In Panel A,t-statistics are obtained using Newey-West autocorrelation and heteroskedasticity-consistent standard errors. Weestimate panel regressions in Panels B and C and cluster standard errors by month.
Panel A. Dependent variable - aggregate excess return
Aggregate volatility -3.06(-8.57)
∆ Aggregate volatility -3.88(-8.65)
R2 0.118 0.122
# Observations 540 539
Panel B. Dependent variable - firm-level excess return