The Jobson-Korkie-Memmel Sharpe Test

Comparing two strategies by which has the higher Sharpe ratio is easy, but a naive comparison ignores sampling error: with only a few years of data, one strategy could look better than another purely by luck. The Jobson-Korkie test (with Memmel's later correction to the variance formula) provides a proper hypothesis test for whether an observed gap between two Sharpe ratios, $\widehat{SR}_1 - \widehat{SR}_2$, is statistically distinguishable from zero. Its key feature is that it correctly accounts for the correlation between the two strategies' returns — two strategies traded over the same historical period and same market conditions are rarely independent, and ignoring that correlation would understate how much of the Sharpe gap could arise from shared noise rather than genuine skill difference.

The test produces a $z$-statistic whose sign and magnitude indicate which strategy has the higher risk-adjusted return and how confident that ranking is; a $z$-statistic below about 2 in absolute value generally means the observed Sharpe difference could plausibly be noise, and a longer track record or higher-frequency data is needed before declaring one strategy definitively better.

This test is a standard step before retiring an old strategy in favor of a new one, or before allocating more capital to whichever of two live strategies currently shows the higher Sharpe ratio: without it, a manager risks switching capital based on a gap that a slightly different sample period would have shown running the other way.