Ex Ante Comparison of Maximum Sharpe Ratios and Incremental Variable Testing

European Journal of Operational Research, Volume 265, Issue 2, 1 March 2018, Pages 571-579

21 Pages Posted: 19 Jan 2016 Last revised: 30 Jan 2018

See all articles by Michael Hanke

Michael Hanke

University of Liechtenstein

Spiridon Penev

University of New South Wales (UNSW) - School of Mathematics

Date Written: January 19, 2016

Abstract

A typical decision problem faced by investors is whether or not to include additional asset classes or return drivers into their portfolios. In the context of classical portfolio theory and in the presence of a riskless asset, the relevant criterion is a significant increase in the maximum Sharpe ratio (the Sharpe ratio of the tangency portfolio) achievable when enlarging the investment opportunity set. Although not all assumptions of classical portfolio theory are always satisfied by empirical return distributions, the Sharpe ratio is widely used in practice as a risk-adjusted performance measure and a benchmark. Most existing results on the distribution of the maximum Sharpe ratio depend on the assumption of multivariate normal return distributions. We generalize results from the literature to provide an analytical representation of the distribution of the difference between two maximum Sharpe ratios for much less restrictive distributional assumptions, both with and without short sales. For the long-only case, we provide conditions that allow us to check whether any local optima that may be encountered indeed correspond to the global optimum. Knowing the distribution of the difference enables us to test ex ante whether or not the inclusion of additional variables leads to a significant improvement in the maximum Sharpe ratio. High estimation uncertainty regarding means of asset returns makes it difficult to distinguish statistically between tangency portfolios at conventional significance levels.

Keywords: Maximum Sharpe ratio, Incremental variables, Comparing tangency portfolios, Mean-variance spanning

JEL Classification: G11, G12

Suggested Citation

Hanke, Michael and Penev, Spiridon, Ex Ante Comparison of Maximum Sharpe Ratios and Incremental Variable Testing (January 19, 2016). European Journal of Operational Research, Volume 265, Issue 2, 1 March 2018, Pages 571-579, Available at SSRN: https://ssrn.com/abstract=2718033 or http://dx.doi.org/10.2139/ssrn.2718033

Michael Hanke (Contact Author)

University of Liechtenstein ( email )

Fuerst Franz Josef-Strasse
Vaduz, FL-9490
Liechtenstein

Spiridon Penev

University of New South Wales (UNSW) - School of Mathematics ( email )

Department of Statistics
Sydney, New South Wales
2053 Australia

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