General Linear Formulations of Stochastic Dominance Criteria: With an Analysis of Stock Market Portfolio Efficiency

29 Pages Posted: 4 Feb 2012 Last revised: 15 May 2018

See all articles by Thierry Post

Thierry Post

Graduate School of Business of Nazarbayev University

Milos Kopa

Charles University in Prague - Faculty of Mathematics and Physics

Date Written: February 2, 2012

Abstract

We develop and implement linear formulations of general N-th order Stochastic Dominance criteria for discrete probability distributions. Our approach is based on a piece-wise polynomial representation of utility and its derivatives and can be implemented by solving a relatively small system of linear inequalities. This approach allows for comparing a given prospect with a discrete set of alternative prospects as well as for comparison with a polyhedral set of linear combinations of prospects. We also derive a linear dual formulation in terms of lower partial moments and co-lower partial moments. An empirical application to historical stock market data suggests that the passive stock market portfolio is highly inefficient relative to actively managed portfolios for all investment horizons and for nearly all investors. The results also illustrate that the mean-variance rule and second-order stochastic dominance rule may not detect market portfolio inefficiency because of non-trivial violations of non-satiation and prudence.

Keywords: Stochastic dominance, utility theory, non-satiation, risk aversion, prudence, temperance, linear programming, mean-variance analysis, market portfolio efficiency, lower partial moments

JEL Classification: C22, C32, D81, G11, G12

Suggested Citation

Post, Thierry and Kopa, Milos, General Linear Formulations of Stochastic Dominance Criteria: With an Analysis of Stock Market Portfolio Efficiency (February 2, 2012). Available at SSRN: https://ssrn.com/abstract=1997521 or http://dx.doi.org/10.2139/ssrn.1997521

Thierry Post (Contact Author)

Graduate School of Business of Nazarbayev University ( email )

53 Kabanbay Batyra Avenue
Astana, 010000
Kazakhstan

Milos Kopa

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

Czech Republic

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