Growth options and firm valuation

• Published date: 01 March 2018
• Author: Eduardo Schwartz,Holger Kraft,Farina Weiss
• Date: 01 March 2018
• DOI: http://doi.org/10.1111/eufm.12141

DOI: 10.1111/eufm.12141

ORIGINAL ARTICLE

Growth options and firm valuation

Holger Kraft

1

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Eduardo Schwartz

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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 firm’s growth options. We find strong empirical

evidence that Tobin’s 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;24:209–238. 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 firm’s 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 Tobin’s Q is positively related to a firm’sstock

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

Tobin’s 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 ‘truly’idios 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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