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An Intersection–Union Test for the Sharpe Ratio

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  • Gabriel Frahm

    (Chair of Applied Stochastics and Risk Management, Department of Mathematics and Statistics, Helmut Schmidt University, Holstenhofweg 85, D-22043 Hamburg, Germany)

Abstract

An intersection–union test for supporting the hypothesis that a given investment strategy is optimal among a set of alternatives is presented. It compares the Sharpe ratio of the benchmark with that of each other strategy. The intersection–union test takes serial dependence into account and does not presume that asset returns are multivariate normally distributed. An empirical study based on the G–7 countries demonstrates that it is hard to find significant results due to the lack of data, which confirms a general observation in empirical finance.

Suggested Citation

  • Gabriel Frahm, 2018. "An Intersection–Union Test for the Sharpe Ratio," Risks, MDPI, vol. 6(2), pages 1-13, April.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:40-:d:142032
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    References listed on IDEAS

    as
    1. Gabriel Frahm & Tobias Wickern & Christof Wiechers, 2012. "Multiple tests for the performance of different investment strategies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 343-383, July.
    2. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
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    8. Bartosz Sawik, 2012. "Downside Risk Approach for Multi-Objective Portfolio Optimization," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 191-196, Springer.
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    12. Hanke, Michael & Penev, Spiridon, 2018. "Comparing large-sample maximum Sharpe ratios and incremental variable testing," European Journal of Operational Research, Elsevier, vol. 265(2), pages 571-579.
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    Cited by:

    1. Gabriel Frahm & Ferdinand Huber, 2019. "The Outperformance Probability of Mutual Funds," JRFM, MDPI, vol. 12(3), pages 1-29, June.

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