摘 要
本文构建了基于矩特征的投资组合 DEA 评价模型，考虑了高阶矩风险对投
资决策的影响。文章根据投资组合优化模型，将二阶矩(方差)、三阶矩(偏度)和
四阶矩(峰度)特征作为 DEA 投入-产出指标构建生产可能集，使建立的评价模型
有理论根据与经济意义。在基于均值-方差的 DEA 评价模型的基础上，考虑偏度
风险，并以下半偏度指标代替偏度指标，使得一向存在非凸规划难题的三阶矩投
资组合模型成为凸规划问题，满足了投资组合模型生产可能集为凸集的要求，因
此可以建立起相应的基于均值-方差-下半偏度的 DEA 评价模型。并在此基础上
引入四阶矩(峰度)指标建立基于均值-方差-下半偏度-峰度的 DEA 评价模型。
实证部分文章对 27 个投资组合在 2009-2011 年度的表现进行评价对比分析。
实证分析表明投资组合收益率的非正态性特征非常明显且从不同评价模型的评
价结果对比分析中可以得到：每增加一个矩特征指标，被评投资组合相对有效性
都会发生变化，即效率排名发生变化。这意味着偏度、峰度对投资决策存在重要
影响，且影响程度不同。在矩特征框架下，有效投资组合数目会增多，那些具有
较大下半偏度、较低峰度的投资组合的效率排名得到提升，甚至从无效投资组合
变为有效投资组合；而那些具有较小下半偏度、高峰度的投资组合的效率排名不
变，甚至出现排名下降。文章最后采用配对资料的符号秩和检验有效说明了三种
评价模型下得到的效率排名存在显著差别。
总之，基于矩特征的投资组合 DEA 评价模型考虑了资产收益率分布特征和
收益-风险关系，符合投资者效用偏好，评价结果更全面、更科学、更符合实际，
对投资者的参考价值更大。
关键词：投资组合评价；数据包络分析；方差；下半偏度；峰度
Abstract
This thesis constructs DEA models to evaluate portfolio based on moment
characteristics, considering the effects of the moment characteristics on the
investment decisions. According to portfolio models, we select second
moment(variance), third moment(skewness) and fourth moment(kurtosis) as the
input-output indexes to build production probable sets and DEA models, making the
models with theoretical basises and economic significances. Based on mean-variance
DEA evaluation model, we put lower semi-third moment instead of skewness,
resolving the non convex programming problem that always exists and meeting the
third moment portfolio model’ frontier for concave function. So we can set up
corresponding DEA evaluation models based on third moment and fourth moment.
The empirical part, we evaluate and analysis the performance of 27 portfolio in
the 2009-2011. The empirical analysis shows that rate of return of portfolio is
non-normal distribution. From the evaluation results of three evaluation models, we
can get: moment characteristics have different effects on investors, namely,
skewness and kurtosis having important and different influences on the investment
decision-making. In the moment characteristics frameworks, the number of effective
portfolio will increase. Those with larger lower semi-third moment and lower
kurtosis portfolio rank ascend, even from invalid decision making units into the
effective decision makig units and vice versa. Finally, we use the Wilcoxon
signed-rank test to examine the differences of evaluation results.
In a word, the portfolio evaluation DEA models based on the moment
characteristics consider the distribution characteristics of rate of return, risk-return
relationship and the investors utility preference. The evaluation results are more
comprehensive, more scientific and more actual, and have larger reference value for
investors.
Key words: Portfolio evaluation; Data envelopment analysis; Variance; Lower
semi-third moment; Kurtosis