Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood
提出一种基于随机占优和相对熵的投资组合无效性度量，将其转化为似然比统计量，通过数值近似和蒙特卡洛模拟验证其优于广义矩方法，并用于检验股票市场指数的有效性。
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.