How noisy is an estimated Sharpe ratio?
Asked at DE Shaw
You estimate a strategy's Sharpe ratio from i.i.d. (roughly normal) return observations. The point estimate looks good, but you need to know how much of it is luck.
State the standard error of an estimated Sharpe ratio, and evaluate it for a per-period Sharpe of measured over months.
Show a hint
The Sharpe estimator is a ratio of a noisy mean to a noisy standard deviation. Both the numerator's and denominator's fluctuations feed the error bar, and the denominator's part ties back to the variance of the sample variance.