How many days for a t-stat of 2?

Question

A strategy's daily mean return is one-tenth of its daily standard deviation (a per-day ratio of $0.1$ ). You will call the edge significant when its t-statistic reaches $2$ .

How many trading days of data do you need, and what role does $\sqrt{n}$ play?

Accepted Answer

The t-statistic for the mean divides the estimate by its standard error: t = \frac{\bar X}{\operatorname{SE}(\bar X)} = \frac{\bar X}{\sigma / \sqrt{n}} = \frac{\bar X}{\sigma}\sqrt{n}. The ratio \bar X / \sigma is the per-day signal-to-noise (a daily Sharpe ratio), here equal to 0.1. The \sqrt{n} is what turns a small per-day edge into a detectable one: the mean estimate's precision improves as 1/\sqrt{n}, so the t-stat grows as \sqrt{n}. Set t = 2 and solve: 0.1 	imes \sqrt{n} = 2 \implies \sqrt{n} = 20 \implies n = 400 	ext{ days}. So about 400 trading days, roughly a year and a half, be…

How many days for a t-stat of 2?

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