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Portfolio analysis using stochastic dominance, relative entropy, and empirical likelihood

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GRADUATE SCHOOL OF BUSINESS
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Poti, Valerio

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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.

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The Institute for Operations Research and the Management Sciences (INFORMS)

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Management, Operations research, Management science

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Management Science

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DOI

10.1287/mnsc.2015.2325

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