Does idiosyncratic volatility proxy for risk exposure?

We decompose aggregate market variance into an average correlation component and an average variance component. Only the latter commands a negative price of risk in the cross section of portfolios sorted by idiosyncratic volatility. Portfolios with high (low) idiosyncratic volatility relative to the Fama-French (1993) model have positive (negative) exposures to innovations in average stock variance and therefore lower (higher) expected returns. These two findings explain the idiosyncratic volatility puzzle of Ang et al. (2006, 2009). The factor related to innovations in average variance also reduces the pricing errors of book-to-market and momentum portfolios relative to the Fama-French (1993) model