The Relation between Idiosyncratic Volatility and Returns: A Growth Option Model with Stochastic Volatility and Jumps

Abstract

We develop a zero beta industry model of growth options to explain the conflicting empirical findings on the relation between stock returns and idiosyncratic return volatility at the firm level. By allowing for the volatility of the underlying idiosyncratic choice variables to exhibit independent switches between a high and low volatility regime, we show that the options’ constant expected returns are composed of (i) a state dependent drift term that relates positively with the volatility regime, and (ii) a state dependent sporadic jump term that relates inversely with the volatility regime, even though the sources of uncertainty are not priced. Our model is able to jointly explain why stock returns and idiosyncratic volatility are contemporaneously positively correlated in the cross section of stocks (Duffee (1995), and why high idiosyncratic volatility stock portfolios significantly under perform their low volatility counterparts (Ang, Hodrick, Xing, and Zhang (2006) and Ang, Hodrick, Xing, and Zhang (2009), among other regularities. At a more general level, we propose a new perspective for understanding the puzzling view that idiosyncratic volatility may seem to be priced in the cross section of stocks.