Bootstrapping
Standard errors exist in closed form for a few statistics. For most of the ones traders care about, they do not.
What is the standard error of a Sharpe ratio? A maximum drawdown? A 95th percentile? The formulas are unpleasant, rest on assumptions that returns violate, or do not exist.
The bootstrap sidesteps all of it.
The procedure
- Resample your data with replacement to get a new dataset of the same size.
- Compute the statistic on it.
- Repeat many times.
- The spread of those values approximates the sampling distribution.
From that you read off a standard error, or take the 2.5th and 97.5th percentiles for a 95% confidence interval.
Why it works
The idea is a substitution: use the empirical distribution of your sample as a stand-in for the true distribution.
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