Small firms usually have high idiosyncratic volatility. The size effect says they should earn high returns. The idiosyncratic volatility says just the opposite. This is why the size effect seems weak. When I sort stocks on residual size, orthogonalized to idiosyncratic volatility, I find the size effect alive and well in all periods. Sorting on residual size also eliminates the small growth anomaly and the negative size effect for growth firms. Residual size sorts produce a better pricing factor I call RSMB. RSMB is less correlated with HML and BVIX. Replacing SMB with RSMB makes the HML betas of new issues large and negative instead of zero.

I hypothesize that high volatility losers are low-risk firms, because the option-like nature of leverage makes volatile losers a good hedge against aggregate volatility risk. I find that the relation between momentum and idiosyncratic volatility is indeed strong for highly levered firms and absent for low leverage firms. This result is primarily driven by the low returns earned by high volatility losers. I also find that business-cycle related variables are able to predict most of the momentum differential between high and low volatility portfolios.

I predict that the hedging ability of high volatility and growth firms against adverse aggregate volatility shocks is greater when idiosyncratic volatility is high. Idiosyncratic volatility is high at earnings announcements. I argue that the well-known underperformance of growth stocks around earnings announcements can be explained by the risk shift. I find a similar pattern for the idiosyncratic volatility discount, especially if it is measured for growth stocks. The underperformance of growth and high volatility firms around earnings announcements can be traced back to the decrease in their HML and BVIX betas.

One of the attributes of high-quality accounting is conservatism. In the light of the recent evidence that low idiosyncratic risk firms earn high future returns, I hypothesize that conservative accounting firms also earn high future returns. I estimate the conservatism premium to be around 15 bp per month. The conservatism premium appears unrelated to the size effect, the accrual anomaly, and even the idiosyncratic volatility discount. I find that the conservatism premium is higher for growth stocks and can be partly explained by the exposure to aggregate volatility risk. I also find that the conservatism premium is higher for highly levered firms.