Robust performance hypothesis testing with the variance

Olivier Ledoit and Michael Wolf

Abstract

Applied researchers often test for the difference of the variance of two investment strategies; in particular, when the investment strategies under consideration aim to implement the global minimum variance portfolio. A popular tool to this end is the F-test for the equality of variances. Unfortunately, this test is not valid when the returns are correlated, have tails heavier than the normal distribution, or are of time series nature. Instead, we propose the use of robust inference methods. In particular, we suggest to construct a studentized time series bootstrap confidence interval for the ratio of the two variances and to declare the two variances different if the value one is not contained in the obtained interval. This approach has the advantage that one can simply resample from the observed data as opposed to some null-restricted data. A simulation study demonstrates the improved finite-sample performance compared to existing methods.


The code in Matlab and in R for the estimator proposed in the paper can be downloaded for free from the website of my co-author Michael Wolf in the Department of Economics of the University of Zurich.


Wilmott Magazine, Issue 55, September 2011, pages 86-89


Download full paper (Acrobat PDF - 116KB)


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