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Robust performance hypothesis testing with the variance

Author

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  • Olivier Ledoit
  • 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.

Suggested Citation

  • Olivier Ledoit & Michael Wolf, 2010. "Robust performance hypothesis testing with the variance," IEW - Working Papers 516, Institute for Empirical Research in Economics - University of Zurich.
  • Handle: RePEc:zur:iewwpx:516
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    File URL: http://www.econ.uzh.ch/static/wp_iew/iewwp516.pdf
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    Keywords

    Bootstrap; HAC inference; Variance;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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