Is Idiosyncratic Volatility Risk Priced? Evidence from the Physical and Risk-Neutral Distributions

Abstract

We use simultaneous data from equity, index and option markets in order to estimate a single-factor market model in which idiosyncratic volatility is allowed to be priced. We model the index dynamics' physical distribution as a mean-reverting stochastic volatility process as in Heston (1993), and the equity returns as single-factor models with stochastic idiosyncratic volatility terms. We derive theoretically the underlying assets' risk-neutral distributions, and we estimate the parameters of both P and Q distributions using a joint likelihood function. We document the existence of a common factor structure in option implied idiosyncratic variances. We show that the average idiosyncratic variance, which proxies for the common factor, is priced in the cross section of equity returns, and that it reduces the pricing error when added to the Fama-French model. We find that the idiosyncratic volatilities differ under the P and Q measures, and we estimate the price of this idiosyncratic volatility risk, which turns out to be significantly different from zero for all the stocks in our sample. We construct portfolios that only load on the idiosyncratic variance, and we propose a measure of idiosyncratic variance risk premium. Further, we show that these premiums are not explained by the usual equity risk factors. Finally, we explore the implications of our results for the estimation of the conditional equity betas.