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

33 Pages Posted: 13 May 2005 Last revised: 25 Mar 2016

Thierry Post

Koc University - Graduate School of Business

Milos Kopa

Charles University in Prague - Faculty of Mathematics and Physics

Date Written: January 31, 2008

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 non-parametric alternative. However, these procedures have been limited to considering binary choices.In this paper we consider 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 US stock market portfolio is significantly FSD non-optimal 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.

Keywords: stochastic dominance, optimality, admissibility, portfolio diversification

JEL Classification: D81, G11

Suggested Citation

Post, Thierry and Kopa, Milos, A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion (January 31, 2008). Journal of Financial and Quantitative Analysis (JFQA), Vol. 44, No. 5, pp. 1103-1124, 2009. Available at SSRN: https://ssrn.com/abstract=720882

Thierry Post (Contact Author)

Koc University - Graduate School of Business ( email )

Rumelifeneri Yolu
34450 Sariyer
Istanbul
Turkey

Milos Kopa

Charles University in Prague - Faculty of Mathematics and Physics ( email )

Sokolovska 83
Prague, 186 75
Czech Republic

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