We develop a novel methodology to measure the risk premiumof higher-order cumulants (closely related to the moments of a distribution) based on leveraged ETFs. We show that the risk premiumon these ETFs reflects the difference between physical and risk-neutral cumulants, which we call the cumulant risk premium (CRP). We show that the CRP is different from zero across asset classes (equities, bonds, commodities, currencies, and volatility) and is large in times of stress. We illustrate that highly leveraged strategies are extremely exposed to higher-order cumulants. Our results have implications for hedge funds, factor models, momentum strategies, and options.