Loss Uncertainty, Gain Uncertainty, and Expected Stock Returns

We decompose the quadratic payoff on a stock into its loss and gain components and measure the premia associated with their fluctuations, called the loss and gain quadratic risk premium (QRP) respectively. The loss QRP interprets as the premium paid for downside risk hedging, while the gain QRP reads as the premium received for upside risk compensation. Long-short portfolio strategies based on the loss or gain QRP yield monthly risk-adjusted expected excess returns of up to 2.8%. This cross-sectional predictability survives a battery of robustness checks, and is reinforced among stocks experiencing limits to arbitrage, information asymmetry, and demand for lottery