Risk premia: asymmetric tail risks and excess returns

We present extensive evidence that “risk premium” is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit a linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry, Short Vol, Bonds, Credit) and their negative skewness. We find a clear exception to this rule: trend following (and perhaps the FamaFrench “High minus Low”), that has positive skewness and positive excess returns, suggesting that some strategies are not risk premia but genuine market anomalies. Based on our results, we propose an objective criterion to assess the quality of a risk-premium portfolio.