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Testing the Mean-Variance Efficiency of Well-Diversified Portfolios in Very Large Cross-Sections

Bossaerts, Peter and Hillion, Pierre (1995) Testing the Mean-Variance Efficiency of Well-Diversified Portfolios in Very Large Cross-Sections. Annales d'Économie et de Statistique, 40 . pp. 93-124. ISSN 2115-4430.

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We propose a new way of testing the mean-variance efficiency of well-diversified portfolios on large cross-sections of extremely short return histories. The methodology consists of a sequence of simple tests, the results of which are aggregated in a statistic. This statistic is shown to be asymptotically standard normally distributed, despite dependence, in cross-section and over time, of the idiosyncratic risk. We investigate theoretically the asymptotic power of our test against the alternative that the well-diversified portfolio is not mean-variance efficient. By construction, our procedure is more powerful than standard tests of mean-variance efficiency that combine the assets in the cross-section into a limited set of (arguably) arbitrary portfolios. Even in cases where the latter has zero power, it can have unit asymptotic power. The incremental power is evidenced in tests of the mean-variance efficiency of the value weighted portfolio of common stock listed on the NYSE and AMEX. Unlike previously thought, however, the selection bias caused by including only continuously traded securities in the test is found to be important. By running the test in a case where it is known to have zero power, we are able to empirically confirm the correctness of the theoretical asymptotic properties of our statistic.

Item Type:Article
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URLURL TypeDescription ItemSSWP 854
Bossaerts, Peter0000-0003-2308-2603
Additional Information:© 1995 GENES. We are grateful for comments and suggestions from the referee, participants at seminars at Carnegie Mellon University, U.C. Riverside, the Center for Economic Research (Tilburg University), and the 1993 Conference in Paris on Financial Market Dynamics and Forecasting. We thank Jet Propulsion Laboratory for access to their CRAY. Formerly SSWP 854.
Subject Keywords:Arbitrage, Financial portfolios, Securities trading, Time series, Value weighted index, Security portfolios, Selection bias, Power efficiency, Asymptotic properties, Statistical variance
Record Number:CaltechAUTHORS:20171107-171504417
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83051
Deposited By: Jacquelyn Bussone
Deposited On:08 Nov 2017 18:30
Last Modified:03 Oct 2019 19:01

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