Sample size to compare two portfolios' returns

Question

You want to compare the mean periodic return of two portfolios. Each portfolio's per-period return has a standard deviation of about $\sigma = 8\%$ . You want to detect a true mean difference of $\Delta = 4\%$ , using a two-sided test at $\alpha = 0.05$ with $80\%$ power.

Roughly how many periods per group do you need?

Accepted Answer

The formula. Per group, for two independent means with equal variance, n \approx \frac{2\,\sigma^2 \left(z{\alpha/2} + z\betaight)^2}{\Delta^2}. Constants. (z{\alpha/2} + z\beta)^2 = (1.96 + 0.84)^2 = 7.84. Plug in. \sigma^2 = 64, \Delta^2 = 16: n \approx \frac{2 	imes 64 	imes 7.84}{16} = \frac{1004.7}{16} \approx 63. So about 63 periods per group. The relative signal here (a 4-point gap against 8 points of noise) is larger than in many trading comparisons, which is why the required count is modest. Takeaway. With the difference set to half the standard deviation, you need roughly 63 per…

Sample size to compare two portfolios' returns

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