Over the period 1927:Q1 to 2005:Q4, the average CAPM-based idiosyncratic variance (IV) and stock market variance jointly forecast stock market returns. This result holds up quite well in a number of robustness checks, and we show that the predictive power of the average IV might come from its close relation with systematic risk omitted from CAPM. First, high lagged returns on high IV stocks predict low future returns on the market as a whole. Second, returns on a hedging portfolio that is long in stocks with low IV and short in stocks with high IV perform as well as the value premium in explaining the cross-section of stock returns. Third, realized variance of the hedging portfolio or of the value premium is closely correlated with the average IV, and these variables have similar predictive power for stock returns.