A Sharpe of 2.0 from just 3 years: how wide is the error bar?

Question

A young fund reports an annualized Sharpe ratio of 2.0 estimated from just 3 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 say whether the Sharpe is reliably above 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 = 2.0 and T = 3: \operatorname{SE} \approx \sqrt{\frac{1 + 	frac{1}{2}(2.0)^2}{3}} = \sqrt{\frac{1 + 2}{3}} = \sqrt{1} = 1.0. Confidence interval. Roughly two standard errors on each side: 2.0 \pm 1.96 	imes 1.0 \approx (0.04,\ 3.96). The interval just barely clears zero, so the Sharpe is (marginally) significant, but the error bar is enormous, a full 1.0. A h…

A Sharpe of 2.0 from just 3 years: how wide is the error bar?

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