Is a Sharpe of 0.5 over 2 years distinguishable from zero?

Question

A strategy reports an annualized Sharpe ratio of 0.5 estimated from 2 years of returns. Treat the returns as roughly independent and normal.

Estimate the standard error of the Sharpe ratio, build an approximate 95% confidence interval, and decide whether it is distinguishable from zero.

Accepted Answer

The formula. For roughly independent, normal returns, the standard error of an annualized Sharpe over T years is approximately \operatorname{SE}(\widehat{SR}) \approx \sqrt{\frac{1 + 	frac{1}{2}SR^2}{T}}. Plug in the numbers. With SR = 0.5 and T = 2: \operatorname{SE} \approx \sqrt{\frac{1 + 	frac{1}{2}(0.5)^2}{2}} = \sqrt{\frac{1 + 0.125}{2}} = \sqrt{0.5625} = 0.75. Confidence interval. Roughly two standard errors on each side: 0.5 \pm 1.96 	imes 0.75 \approx 0.5 \pm 1.47 = (-0.97,\ 1.97). The interval is enormous and straddles zero, so a Sharpe of 0.5 over two years is completely indisti…

Is a Sharpe of 0.5 over 2 years distinguishable from zero?

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