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...

The paper shows that lottery-like stocks are hedges against unexpected increases in market volatility. The loading on the aggregate volatility risk factor explains low returns to stocks with high maximum returns in the past (Bali, Cakici, and Whitelaw, 2011) and high expected skewness (Boyer,...