Stochastic Efficiency Analysis using Relative Entropy and Empirical Likelihood

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 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