The Cross-Section of Volatility and Expected Returns

We examine how volatility risk, both at the aggregate market and individual stock level, is priced in the cross-section of expected stock returns. Stocks that have past high sensitivities to innovations in aggregate volatility have low average returns. We also find that stocks with past high idiosyncratic volatility have abysmally low returns, but this cannot be explained by exposure to aggregate volatility risk. The low returns earned by stocks with high exposure to systematic volatility risk and the low returns of stocks with high idiosyncratic volatility cannot be explained by the standard size, book-to-market, or momentum effects, and are not subsumed by liquidity or volume effects