基于矩特征的投资组合DEA评价模型及其应用研究

发布时间：2018-03-29 14:07

本文选题：投资组合评价　切入点：数据包络分析　出处：《湖南大学》2012年硕士论文

【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。
[Abstract]:This paper constructs a portfolio evaluation model based on DEA moment feature, considering the impact of higher moments risk on investment decision-making. According to the portfolio optimization model, the two order moment (variance), three moments (skewness) and four moments (kurtosis) features as the DEA input-output index construction production set the established evaluation model according to the theoretical and economic significance. Based on the evaluation of DEA mean variance model, considering the skewness risk and skewness index, below half instead of skewness index, the three order moment there has always been non convex programming problem portfolio model is a convex programming problem and meet the investment portfolio the model is a convex production possibility set requirements, so we can establish the corresponding evaluation DEA mean variance skewness model based on the second half. And on the basis of the introduction of the four order moment (kurtosis) index and mean variance skewness based on half - The DEA evaluation model of kurtosis.
The empirical part of the article on the performance of a portfolio of 27 in the year 2009-2011 to evaluate the comparative analysis. The empirical analysis shows that the portfolio return rate of non normality is very obvious and can be obtained from the comparative analysis of different evaluation model evaluation results: each additional moment feature index, was awarded the portfolio relative effectiveness will change, namely efficiency ranking changes. This means that the skewness, kurtosis have important influence on investment decisions, and the influence of different degree. In the moment features under the framework of the number of effective investment portfolio will increase, the second half of those with larger skewness, kurtosis of the low efficiency of investment portfolio ranking has improved, even from the invalid portfolio into the effective investment portfolio; while those with lower half peak efficiency of skewness portfolio ranking unchanged, even dropped. Finally, using the paired The symbolic rank sum test of the data effectively shows that there is a significant difference in the efficiency ranking obtained under the three evaluation models.
In a word, the DEA evaluation model based on moment characteristics considers the distribution characteristics and return risk relationship of assets return, which is consistent with the utility preference of investors. The evaluation result is more comprehensive, more scientific and practical, and has greater reference value for investors.

【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.59

【参考文献】