Halving the Error

Question

You estimate a strategy's edge from n independent samples and your confidence interval is twice as wide as you need. How many samples do you need in total, and why exactly that many?

Accepted Answer

The standard error of a sample mean is textSE = fracsigmasqrtn, so precision improves with the square root of the sample size. Halving the SE (and hence the CI width) requires fracsigmasqrtn' = frac12 cdot fracsigmasqrt n implies n' = mathbf4n. Four times the data for twice the precision, and ten-thousand times the data for a 100× sharper estimate. This brutal scaling is why: - backtests need long histories before small edges are statistically real (a Sharpe-1 strategy needs roughly n approx 4 years of daily data for a 2σ signal: textSRsqrtT = 2); - high-frequency firms can evaluate strategies in days (millions of samples) while macro funds argue for decades; - "we doubled the data and the error barely moved" is expected, not a bug. If the samples are correlated, replace n with the effective sample size n_texteff < n, autocorrelated P&L gives you fewer independent looks than you think, the standard trap in evaluating trading records.

Halving the Error

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