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Confidence interval

A range that would contain the true value in a stated share of repeated samples, usually 95%. It is the sane way to report any backtest statistic.

Reporting one number for expected return hides everything that matters. Reporting an interval makes the reader see how thin the evidence is, which is exactly why most strategy write-ups avoid it.

The common construction is estimate +/- 1.96 standard errors, valid when the sampling distribution is roughly normal. For skewed or fat-tailed trade returns the bootstrap gives a better interval because it makes no shape assumption: resample the trades 10,000 times, compute the statistic each time, and read off the 2.5th and 97.5th percentiles.

Interpretation trap: a 95% interval does not mean 95% probability that the true value is inside this particular interval. It means the procedure captures the truth 95% of the time. In practice the distinction rarely changes a trading decision, but it does stop people writing nonsense.

Related: standard-error, bootstrap, p-value, probabilistic-sharpe-ratio

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