Optimal hedging with higher moments

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 decisions. We examine the entire hyperbolic absolute risk aversion (HARA) family of utilities which include quadratic, logarithmic, power and exponential utility functions. We provide an illustration of our methodology using an example of a passenger airline hedging its fuel exposure.

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 is, however, 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 a 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.