Tail risk premium in the crude oil market

Although tail events are infrequent, their potential impacts on financial risk management are significant. This paper examines the differentiation between the tail risk premium (TRP) and the variance risk premium (VRP) in the crude oil market, exploring their respective predictive power for crude oil futures returns at different horizons. Empirical results reveal that, while TRP's magnitude is considerably smaller than VRP's, its predictive power is more significant and informative. Specifically, short-maturity (long-maturity) TRP negatively (positively) predicts one-month-ahead futures returns, even after incorporating well-known predictors in the commodity market, such as the basis and momentum. The negative predictability of short- maturity TRP reverses to positive when we extend the forecast horizon to two months ahead. Using various trading strategies, we confirm that models incorporating TRP outperform those without it, yielding higher account balances, Sharpe ratios, and Omega ratios.