Growth options and firm valuation

Publication Date01 March 2018
AuthorEduardo Schwartz,Holger Kraft,Farina Weiss
Date01 March 2018
DOIhttp://doi.org/10.1111/eufm.12141
DOI: 10.1111/eufm.12141
ORIGINAL ARTICLE
Growth options and firm valuation
Holger Kraft
1
|
Eduardo Schwartz
2
|
Farina Weiss
3
1
Goethe University, Faculty of Economics
and Business Administration, Frankfurt am
Main, Germany
Email: holgerkraft@finance.uni-frankfurt.de
2
UCLA Anderson School of Management,
Los Angeles
Email: eduardo.schwartz@anderson.uc la.educfc
3
Goethe University, Faculty of
Economics and Business Administration,
Frankfurt am Main, Germany
Email: weiss@safe.uni-frankfurt.de
Funding information
Holger Kraft gratefully acknowledges
financial support by Deutsche
Forschungsgemeinschaft (DFG) as well as
the Center of Excellence SAFE, funded by
the State of Hessen initiative for research
LOEWE. Farina Weiss gratefully
acknowledges financial support by the
Center of Excellence SAFE, funded by the
State of Hessen initiative for research
LOEWE.
Abstract
This paper studies the relationship between firm value
and a firms growth options. We find strong empirical
evidence that Tobins Q increases with firm-level
volatility. The significance mainly comes from R&D
firms, which have more growth options than non-R&D
firms. By decomposing firm-level volatility into its
systematic and unsystematic part, we document that only
idiosyncratic volatility has a significant effect on
valuation. Second, we analyze the relation of stock
returns to realized contemporaneous idiosyncratic vola-
tility and R&D expenses. Sorting on idiosyncratic
volatility yields a significant negative relationship
between portfolio alphas and contemporaneous idiosyn-
cratic volatility for non-R&D portfolios.
KEYWORDS
firm valuation, real options, volatility, R & D expenses, PCA
JEL CLASSIFICATION
G12
We thank participants of the 12th Colloquium on Financial Markets in Cologne, the Federal Reserve Bank of San Francisco
Seminar, the 20th Annual Meeting of the German Finance Association and the Arne Ryde Workshop in Financial
Economics in Lund for helpful comments and suggestions. We also thank Vikas Agarwal, Michael Brennan, Thomas
Dimpfl, Dieter Hess, and Paul Soederlind for valuable comments and discussions. Finally, we thank an anonymous referee
and John A. Doukas (the Editor) for their suggestions which we feel improved the quality of the paper. All remaining
errors are of course our own.
Eur Financ Manag. 2018;24:209238. wileyonlinelibrary.com/journal/eufm © 2017 John Wiley & Sons, Ltd.
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INTRODUCTION
The market value of a firm is the sum of the present value of the cash flows generated by the assets
in place and its growth options.
1
Real option theory suggests that values of growth options are
positively related to the volatility of firm value (or a firms cash flows).
2
Everything else equal,
we thus expect the market value of a firm to increase in volatility. Depending on whether a firm
belongs to a growing or mature industry, this dependence is more or less strong. For instance,
R&D as opposed to non-R&D firms are supposed to have more growth options and in turn should
be more affected by volatility. In this paper, we first study the relationship between firm value and
volatility and find empirical evidence that Tobins Q is positively related to a firmsstock
volatility that serves as a proxy for the volatility of the underlying growth options.
3
As suggested
by real options theory, we document that this relationship is much stronger for R&D firms than for
non-R&D firms.
Volatility however consists of a systematic and an unsystematic (idiosyncratic) part. By
definition, the systematic part should be priced and thus expected returns should be affected by
systematic volatility. In contrast standard capital-market theory suggests that idiosyncratic risk
has no effect on expected returns.
4
Therefore, the effects of these two volatility components on
firm value are different: although both components increase the value of growth options,
systematic volatility also increases discount rates that are used to discount future cash flows of a
firm. Hence, the effect of systematic volatility on firm value is ambiguous. We thus decompose
volatility into its systematic and unsystematic part. Our line of argument so far suggests that the
effect of unsystematic volatility should be stronger than the effect of systematic volatility.
Besides, the effect of unsystematic volatility should be the strongest for firms that have a lot of
growth options (e.g., R&D firms). Our empirical results support these predictions: whereas
Tobins Q is hardly affected by systematic volatility, there is a pronounced effect for unsystematic
volatility. In particular, the effect for R&D firm observations is significantly stronger than for
non-R&D firm observations.
Importantly, we also exte nd the existing literature by addressing concerns ab out missing factors
in the Fama-French model (see , for example, Chen & Petkova, 20 12). We perform a principal-
component analysis (PCA) on th e residuals of the Fama-Frenc h regressions that are used to
calculate the idiosyncrat ic volatillity. This allows us to tear out the systema tic part of these residuals
and to compute the trulyidios yncratic volatility which is the idiosyncratic volati lity after
subtracting the first two f actors of the PCA.
5
On average the first factor exp lains about 2% of the
remaining variation. Sinc e there is not much systemat ic variation left in the res iduals of the Fama-
French regressions, it turns out that our above described re sults stand even for this alt ernative
definition of idiosyncratic vol atility.
Finally, we analyze the relation of realized stock returns to realized contemporaneous idiosyncratic
volatility (ivol) and R&D expenses where we again split the whole sample into sub-samples of R&D
1
See, e.g., Berk, Gren, & Naik (1999).
2
Brennan & Schwartz (1985) and McDonald & Siegel (1986).
3
See, for example, Grullon, Lyandres, & Zhdanov (2012).
4
There are however models where unsystematic risk is priced. For instance, Merton (1987) sets up a model where investors
hold undiversified portfolios and thus demand a risk premium for unsystematic risk.
5
We thank an anonymous referee for this suggestion. This is similar to Herskovic, Kelly, Lustig, & Van Nieuwerburgh
(2016), but they perform a PCA on the excess returns, whereas we run it on the residuals of Fama-French regressions.
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