This paper analyzes the single period portfolio selection problem on the location-scale return family. The skew normal distribution, after recentering and reparameterization, is shown to be in this family. The recentered and reparameterized distribution, called factor-recentered skew normal, can...

We find that firms’ left-tail risk is a strong positive predictor of future bear spread returns, suggesting that the options market underreacts to firms’ left-tail risk and the downside protection provided by bear spreads is not adequately priced. The underreaction to firms' left-tail risk...