Optimal hedging in a futures market with background noise and basis risk

Abstract

This paper examines hedging behavior in an incomplete market in which there exists an unhedgeable and uninsurable independent background risk. In the case of a basis risk that satisfies the regressibility property, the background risk might be partly endogenous. Background risk generally has an ambiguous effect on the optimal hedge ratio. However, if preferences exhibit standard risk aversion and the background risk is fully exogenous, the qualitative effect of the added background risk is determinate and depends on the direction of any bias in the futures market. In all cases, the speculative component of the hedge ratio is reduced in the presence of background risk. When the background risk is a basis risk and futures prices exhibit normal backwardation, this qualitative effect need not hold and it depends in part on the direction of regressability for spot and futures prices.