Assessing Portfolio Efficiency Tests: Theory, Simulations, and Applications

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.