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.
Real option theory suggests that values of growth options are
positively related to the volatility of firm value (or a firm’s cash flows).
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.
by real options theory, we document that this relationship is much stronger for R&D firms than for
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.
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.
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
See, e.g., Berk, Gren, & Naik (1999).
Brennan & Schwartz (1985) and McDonald & Siegel (1986).
See, for example, Grullon, Lyandres, & Zhdanov (2012).
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.
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.
KRAFT ET AL.