Growth to Value: Option Exercise and the Cross-Section of Equity Returns

Abstract

We put forward an equilibrium model that links the cross-sectional variation in expected equity returns to firms' life cycle dynamics. The model features two sources of risks: short and long-run fluctuations in aggregate consumption, as in Bansal and Yaron (2004). Growth assets in the model are options on assets in place (i.e., value assets). The cost of option exercise, endogenously determined in equilibrium, is highly sensitive to long-run consumption risks. This provides a hedge against risks in assets in place, making growth options less risky and generating the value premium. The model is also able to endogenize the size premium: small firms in the model are highly exposed to low-frequency consumption risks as they are more likely to fail in bad times; hence, in equilibrium, small firms carry a high risk premium. In the model, the null hypothesis of the conditional CAPM/CCAPM fails: the value and size effects persist even after controlling for market risk or exposure to contemporaneous consumption innovations. We calibrate the model and show that it is able to account for the observed patterns in mean returns on book-to-market and size sorted portfolios, as well as the failure of the CAPM/CCAPM in the data.

Keywords: Value Premium, Cross Section, Long-Run Risk, Real Options

JEL Classification: G12