Two high Sharpes, 2.5 versus 1.5: is the gap real?

Question

Strategy A has an annualized Sharpe of 2.5 over 6 years; Strategy B has an annualized Sharpe of 1.5 over 6 years. They are independent, roughly normal.

Is the difference in Sharpe ratios statistically significant at the 5% level?

Accepted Answer

Each Sharpe's error bar. With \operatorname{SE}(SR) \approx \sqrt{(1 + 	frac{1}{2}SR^2)/T} and T = 6: \operatorname{SE}A = \sqrt{\frac{1 + 3.125}{6}} = \sqrt{0.6875} \approx 0.83,\qquad \operatorname{SE}B = \sqrt{\frac{1 + 1.125}{6}} = \sqrt{0.354} \approx 0.60. Standard error of the difference. \operatorname{SE}{	ext{diff}} = \sqrt{0.6875 + 0.354} = \sqrt{1.0415} \approx 1.02. Test the gap. z = \frac{2.5 - 1.5}{1.02} \approx 0.98. Verdict. A z of 0.98 is well below 2, so the gap is not significant. This drives home a subtle point: high Sharpes carry large error bars (the standard error gro…

Two high Sharpes, 2.5 versus 1.5: is the gap real?

Your answer

More Statistics questions