Basic bootstrap interval for a Sharpe ratio

Question

Your estimated Sharpe ratio on the original sample is $\hat{\theta} = 1.20$ . Bootstrapping gives a 2.5th percentile of $0.90$ and a 97.5th percentile of $1.60$ for the resampled Sharpe values.

Construct the 95% basic (reverse-percentile) bootstrap confidence interval.

Accepted Answer

The basic interval reflects the bootstrap quantiles through twice the estimate, swapping the tails: \left[\, 2\hat{	heta} - q{0.975}, \;\; 2\hat{	heta} - q{0.025} \,ight]. Plug in \hat{	heta} = 1.20, q{0.025} = 0.90, q{0.975} = 1.60. 	ext{lower} = 2(1.20) - 1.60 = 2.40 - 1.60 = 0.80, 	ext{upper} = 2(1.20) - 0.90 = 2.40 - 0.90 = 1.50. So the basic interval is [0.8, 1.5]. (The percentile interval here would be [0.90, 1.60]; the two differ because the bootstrap distribution is not perfectly symmetric around 1.20.) Takeaway. Same rule every time: lower limit uses the upper quantile, upper …

Basic bootstrap interval for a Sharpe ratio

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