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A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion

Published online by Cambridge University Press:  01 October 2009

Miloš Kopa  and
Thierry Post
Miloš Kopa
Affiliation:
Charles University in Prague, Faculty of Mathematics and Physics, Sokolovska 83, 186 75 Prague, Czech Republic. kopa@karlin.mff.cuni.cz
Thierry Post
Affiliation:
HAPO Center for Financial Research, Spoorstraat 38, Deventer 7412VE, The Netherlands. thierrypost@hotmail.com
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Abstract

Existing approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance-based procedures promise a useful nonparametric alternative. However, these procedures have been limited to considering binary choices. In this paper we take a new approach that considers all diversified portfolios and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. Using our new test, we show that the U.S. stock market portfolio is significantly FSD nonoptimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no nonsatiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 44 , Issue 5 , October 2009 , pp. 1103 - 1124
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2009

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