Profitability anomaly and aggregate volatility risk

Firms with lower profitability have lower expected returns because such firms perform better than expected when market volatility increases. The better-than-expected performance arises because unprofitable firms are distressed and volatile, their equity resembles a call option on the assets, and call options value increases with volatility, all else fixed. Consistent with this hypothesis, the profitability anomaly and its exposure to aggregate volatility risk are stronger for distressed and volatile firms; for such firms, aggregate volatility risk explains roughly half of the profitability anomaly, while in single sorts on profitability about 70% of the anomaly is explained.