均值-方差-近似偏度投资组合模型和实证分析

Mean-Variance-Approximate Skewness Portfolio Model and Empirical Analysis

均值-方差投资组合模型作为现代投资组合理论的基础,采用方差作为风险度量,但忽略了投资组合收益的非对称性.而考虑收益非对称性的基于偏度的投资组合模型由于非凸和非二次性使模型难以求解.本文提出用上下半方差的比值近似刻画偏度,建立了均值-方差-近似偏度(MVAS)模型,并利用该模型对中国证券市场主要股票指数进行实证分析.实证分析结果表明,在收益率非正态分布的市场中,考虑了收益率非对称性的投资组合模型较传统的MV和MAD模型具有更优的表现.

The classical Markowitz＇s mean-variance model in modern investment science uses variance as risk measure while it ignores the asymmetry of the return distri- bution. When skewness is adopted to measure the asymmetry, the portfolio optimization model becomes very difficult due to the nonconvex and non-quadratic features of skew- hess. In this paper, we propose a mean-variance-approximate skewness （MVAS） model which measures the asymmetry by the radio of positive semi-variance and negative semi- variance. Empirical analysis of Chinese stock market shows that the portfolio models which consider the asymmetry of the return distribution outperform MV and MAD mod- els when the market has non-normal feature.