Optimal Hedging with Higher Moments

Abstract

This study proposes a utility-based framework for the determination of optimal hedge ratios that can allow for the impact of higher moments on hedging decision. We examine the entire hyperbolic absolute risk aversion (HARA) family of utilities which include quadratic, logarithmic, power and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for non-zero higher moments is better than the performance of the simpler OLS hedge ratio. The picture however is not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by theoretical analysis of optimal hedging decisions and we uncover a novel link between optimal hedge ratios and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position.

Keywords: utility-based hedging, OLS, non-normality risk, commodity futures, skewness, kurtosis

JEL Classification: G13, C53