A post hoc test on the Sharpe ratio

TL;DR

This paper introduces a post hoc statistical test for the Sharpe ratio, allowing for pairwise comparisons after initial hypothesis rejection, applicable under simple correlation structures among asset returns.

Contribution

It presents a novel post hoc testing method for the Sharpe ratio, analogous to Tukey's test, with demonstrated control of type I error and moderate power.

Findings

Test maintains nominal type I rate across various conditions

Moderately powerful under reasonable alternatives

Applicable under simple correlation structures among assets

Abstract

We describe a post hoc test for the Sharpe ratio, analogous to Tukey's test for pairwise equality of means. The test can be applied after rejection of the hypothesis that all population Signal-Noise ratios are equal. The test is applicable under a simple correlation structure among asset returns. Simulations indicate the test maintains nominal type I rate under a wide range of conditions and is moderately powerful under reasonable alternatives.