Futures Hedges under Basis Heteroscedasticity

Abstract

Minimum variance and mean-variance optimizing hedges are developed when basis risk exhibits heteroscedasticity; that is, the variance of the difference between spot and futures prices is not constant but rises with the level of spot prices. Two different hedging objectives are modeled and optimized. The resulting optimality conditions are then interpreted both analytically and intuitively. Simulations are run to determine whether the model proposed here is superior to the traditional model in terms of minimizing the hedger’s terminal wealth. The resulting hedge ratios are shown to differ from those that are obtained for the traditional homoscedastic basis case, but consistent with the extant theoretical paradigm, the demand for futures contacts is dichotomized into pure hedging and pure speculative components. The simulations demonstrate that, under the statistical assumptions invoked, the proposed model implies uniformly less hedging and a lower variance of terminal wealth compared with the traditional model.