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Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood

Thierry Post () and Valerio Potì ()
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Thierry Post: Graduate School of Business, Koç University, 34450 Sarıyer/Istanbul, Turkey

Management Science, 2017, vol. 63, issue 1, 153-165

Abstract: This study formulates portfolio analysis in terms of stochastic dominance, relative entropy, and empirical likelihood. We define a portfolio inefficiency measure based on the divergence between given probabilities and the nearest probabilities that rationalize a given portfolio for some admissible utility function. When applied to a sample of time-series observations in a blockwise fashion, the inefficiency measure becomes a likelihood ratio statistic for testing inequality moment conditions. The limiting distribution of the test statistic is bounded by a chi-squared distribution under general sampling schemes, allowing for conservative large-sample testing. We develop a tight numerical approximation for the test statistic based on a two-stage optimization procedure and piecewise linearization techniques. A Monte Carlo simulation study of the empirical likelihood ratio test shows superior small-sample properties compared with various generalized method of moments tests. An application analyzes the efficiency of a passive stock market index in data sets from the empirical asset pricing literature. This paper was accepted by Manel Baucells, decision analysis .

Keywords: stochastic dominance; relative entropy; empirical likelihood; convex programming; utility theory; portfolio theory; asset pricing (search for similar items in EconPapers)
Date: 2017
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