The Cumulant Risk Premium

Abstract

We develop a novel methodology to measure the risk premium of higher-order cumulants (closely
related to the moments of a distribution) based on leveraged ETFs. We show that the risk premium on 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.

Keywords: Cumulants, leverage, ETF, CAPM, factor models, VIX

JEL Classification: G1, G12, G13, G23