A wide Sharpe-difference interval that includes zero

Question

Comparing two strategies, the 95% confidence interval for the difference in their Sharpe ratios (strategy A minus strategy B) is $[-0.1,\ 0.9]$ .

Decide whether A's Sharpe is significantly higher than B's at the 5% level, and say whether the interval supports "the two are equal."

Accepted Answer

Apply the duality rule. The difference is significant at 5% if and only if the 95% interval excludes the null value of 0 (no difference). The interval [-0.1,\ 0.9] contains 0, so the difference is not significant at the 5% level. You cannot claim A beats B. Does it support "they are equal"? No. The interval reaches all the way up to 0.9, which would be a large Sharpe advantage for A, while only dipping slightly below 0. So the data are quite consistent with A being meaningfully better; they just cannot rule out no difference. A non-significant result here means "we cannot tell," not "they are…

A wide Sharpe-difference interval that includes zero

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