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Robust performance hypothesis testing with the variance


Ledoit, Olivier; Wolf, Michael (2011). Robust performance hypothesis testing with the variance. Wilmott Magazine, 2011(55):86-89.

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.

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.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Date:September 2011
Deposited On:23 Jan 2012 15:28
Last Modified:03 Aug 2016 08:39
Publisher:Wiley-Blackwell
ISSN:1540-6962
Publisher DOI:https://doi.org/10.1002/wilm.10036
Related URLs:http://www.iew.uzh.ch/wp/iewwp516.pdf

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