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

Bossaerts, Peter and Hillion, Pierre (1993) Testing The Mean-Variance Efficiency of Well-Diversified Portfolios in Very Large Cross-Sections. Social Science Working Paper, 854. California Institute of Technology , Pasadena, CA. (Unpublished)

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We propose a new way of testing the mean-variance efficiency of well-diversified portfolios that exploits the cross-sectional size of typical financial datasets. 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:Report or Paper (Working Paper)
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URLURL TypeDescription ItemPublished Version
Bossaerts, Peter0000-0003-2308-2603
Additional Information:Published as Bossaerts, Peter, and Pierre Hillion. "Testing the mean-variance efficiency of well-diversified portfolios in very large cross-sections." Annales d'Economie et de Statistique (1995): 93-124.
Group:Social Science Working Papers
Subject Keywords:Mean-Variance Efficiency, Well-diversified Portfolios, Exchangeable Random Variables, De Finetti's Theorem, Central Limit Theorem, Law of the Iterated Logarithm
Series Name:Social Science Working Paper
Issue or Number:854
Record Number:CaltechAUTHORS:20170824-150038586
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80772
Deposited By: Jacquelyn Bussone
Deposited On:30 Aug 2017 18:38
Last Modified:03 Oct 2019 18:34

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