Optimal hedging via large deviation

•Futures hedges that minimize underperformance probabilities are proposed.•The statistical theory of large deviations is tailor-made for this purpose.•Optimal hedge ratios are estimated, both parametrically and nonparametrically.

The criterion of minimizing the cumulative hedged returns’ probability of underperforming a benchmark provides a framework for evaluating short-term hedges that are rolled over to produce longer-term hedges. Large deviations theory can be used to either parametrically or nonparametrically estimate underperformance probabilities for cumulative hedged returns produced by roll-overs, providing a straightforward way to find optimal hedge ratios. Optimal hedges using soybean futures are constructed to illustrate the procedures, and their relationship to the popular hedging criteria that are motivated by normality.