Put an error bar on a Sharpe of 1.5 over 5 years

Question

A fund reports an annualized Sharpe ratio of 1.5 estimated from 5 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

Why the Sharpe has an error bar. A Sharpe ratio is estimated from a finite sample, so it is a noisy number, not a fact. For roughly independent, normal returns, a standard approximation (Lo, 2002) for the standard error of an annualized Sharpe measured over T years is \operatorname{SE}(\widehat{SR}) \approx \sqrt{\frac{1 + 	frac{1}{2}SR^2}{T}}. In words: the uncertainty shrinks with the square root of the number of years, and it grows a little as the Sharpe itself gets larger (a bigger Sharpe has a bit more estimation noise). Plug in the numbers. With SR = 1.5 and T = 5: \operatorname{SE} \a…

Put an error bar on a Sharpe of 1.5 over 5 years

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