Stochastic Efficiency Analysis using Relative Entropy and Empirical Likelihood
26 Pages Posted: 10 Feb 2017
Date Written: September 1, 2014
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 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.
Keywords: Stochastic Dominance, utility theory, Relative Entropy, Empirical Likelihood, Linear Programming, portfolio theory, asset pricing
JEL Classification: C22, C32, D81, G11, G12
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