Never a Dull Moment: Entropy Risk in Commodity Markets

We develop a new approach to determine investors' risk compensations for all distributional moments of a security. Using the concept of entropy, a summary of all moments of a risky security, we derive the relationship between expected returns and their compensation for entropy risk. Entropy risk premium (ERP), the difference of entropy under the physical and risk-neutral measures, indicates the cost to financially hedge against changes in risks associated with the entire return distribution. We find that ERP carries significant predictive power for the cross-section of commodity returns even after removing its variance, skewness and kurtosis risk components.