Testing whether two strategies are equally volatile

Question

Two strategies have similar average returns, but you suspect one is meaningfully more volatile than the other. Strategy A has sample variance $0.0009$ (3% daily vol) over 60 days; Strategy B has $0.0004$ (2% daily vol) over 60 days.

Set up the F-test for equal variances, compute the statistic, and explain the big caveat that makes practitioners distrust it.

Accepted Answer

The test. To compare two variances, test H0: \sigmaA^2 = \sigmaB^2 using the ratio of sample variances: F = \frac{sA^2}{sB^2} = \frac{0.0009}{0.0004} = 2.25. Under the null (and the assumptions below), F follows an F-distribution with (nA - 1, nB - 1) = (59, 59) degrees of freedom. Put the larger variance on top so F \geq 1 and use the upper tail (two-sided, so compare against the \alpha/2 critical value). For (59, 59) df the two-sided 5% upper critical value is roughly 1.67. Since 2.25 1.67, we reject: Strategy A is significantly more volatile. The big caveat: non-normality wrecks it. The F-…

Testing whether two strategies are equally volatile

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