Assessing Portfolio Efficiency Tests: Theory, Simulations, and Applications

29 Pages Posted: 8 Mar 2011 Last revised: 14 Mar 2011

See all articles by Marie Briere

Marie Briere

Amundi Asset Management; Paris Dauphine University; Université Libre de Bruxelles

Bastien Drut

Université Libre de Bruxelles (ULB) - Solvay Brussels School of Economics and Management; Université Paris Ouest - Nanterre, La Défense - EconomiX

Valérie Mignon

EconomiX-CNRS, University of Paris Ouest; Centre d'Etudes Prospectives et d'Info. Internationales (CEPII)

Kim Oosterlinck

Université Libre de Bruxelles - SBS-EM, CEB

Ariane Szafarz

Université Libre de Bruxelles, Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB) & CERMi

Date Written: March 5, 2011

Abstract

The recent turmoil in the financial markets has highlighted that no asset is really free of risk. Indeed, even the supposedly safest assets, namely sovereign bonds issued by developed countries, are exposed to default risk. Despite this observation most mean-variance efficiency tests are designed for universes that include a riskless asset. This paper develops a new mean-variance efficiency test based on the “vertical distance” to the efficient frontier. This test acknowledges the possibility that all assets are risky. The paper presents the asymptotic properties of our test which is then compared with two alternative mean-variance efficiency tests (Basak, Jagannathan and Sun 2002, and Levy and Roll 2010). Simulations show that our test outperforms its competitors for large samples since it exhibits lower size distortions for a comparable power. An empirical application to the US equity market shows that whatever the considered number of stocks, the market portfolio is never mean-variance efficient according to our test and the one developed by Basak, Jagannathan and Sun (2002). For the Levy and Roll (2010) test the conclusion depends on the choice of the coefficient used to assess the mean-variance trade-off. Eventually, since nowadays samples tend to be large, our test is particularly well-suited for portfolio managers.

Keywords: Efficient Portfolio, Mean-Variance Efficiency, Efficiency Test

JEL Classification: G11, G12, C12

Suggested Citation

Briere, Marie and Drut, Bastien and Mignon, Valérie and Oosterlinck, Kim and Szafarz, Ariane, Assessing Portfolio Efficiency Tests: Theory, Simulations, and Applications (March 5, 2011). Available at SSRN: https://ssrn.com/abstract=1780514 or http://dx.doi.org/10.2139/ssrn.1780514

Marie Briere

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Paris Dauphine University ( email )

Université Libre de Bruxelles ( email )

Brussels
Belgium

Bastien Drut

Université Libre de Bruxelles (ULB) - Solvay Brussels School of Economics and Management ( email )

19 Av Franklin Roosevelt
1050
Brussels
Belgium

Université Paris Ouest - Nanterre, La Défense - EconomiX

200 Avenue de la République
Nanterre cedex, Nanterre Cedex 92000
France

Valérie Mignon

EconomiX-CNRS, University of Paris Ouest ( email )

200 Avenue de la République
Nanterre, Nanterre Cedex 92001
France

Centre d'Etudes Prospectives et d'Info. Internationales (CEPII) ( email )

113 rue de Grenelle
Paris, F-75007
France

Kim Oosterlinck

Université Libre de Bruxelles - SBS-EM, CEB ( email )

50 Avenue Roosevelt, CP114/03
Brussels 1050
Belgium

Ariane Szafarz (Contact Author)

Université Libre de Bruxelles, Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB) & CERMi ( email )

50 Avenue Roosevelt
Brussels 1050
Belgium

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