Is Strategy A really beating Strategy B?

Question

Over 250 trading days, Strategy A averages 3bp per day with a daily standard deviation of 40bp; Strategy B averages 1bp per day with a standard deviation of 35bp. The two are run on separate capital and their daily returns are effectively independent.

A colleague says "A earns three times as much, obviously ship A." Test whether the difference in mean daily return is statistically significant, and explain what the answer teaches about comparing strategies.

Accepted Answer

Frame it as a two-sample test. Let \muA, \muB be the true mean daily returns. Test H0: \muA = \muB against H1: \muA 
eq \muB. The observed difference is 3 - 1 = 2bp. Standard error of the difference. Because the samples are independent, variances add. Using each sample's own variance (a Welch-style standard error): 	ext{SE} = \sqrt{\frac{40^2}{250} + \frac{35^2}{250}} = \sqrt{\frac{1600 + 1225}{250}} = \sqrt{11.3} \approx 3.36\,	ext{bp}. The t-statistic. t = \frac{2}{3.36} \approx 0.60. With hundreds of degrees of freedom this behaves like a z, so the two-sided p-value is roughly 2[1 - \Ph…

Is Strategy A really beating Strategy B?

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