Skewness, Basis Risk, and Optimal Futures Demand

Abstract

We propose a maximum-expected utility hedging model with futures where cash and futures returns follow a bivariate skew-normal distribution, such to consider the effect of skewness on the optimal futures demand. Relative to the benchmark of bivariate normality, skewness has a material impact when the agent is significantly risk averse. Pure hedging demand is either greater or smaller than minimum-variance demand, depending on the relative skewness of cash and futures positions. The difference between pure hedging and minimum-variance demand increases with basis risk, i.e. the imperfect correlation between cash and futures returns. When the agent is moderately but not infinitely risk averse, there is room for speculative positions, and the optimal futures demand is driven by both basis risk and the expected return on the futures market.