基于POET方法的投资组合选择模型  

Portfolio Selection Model Based on POET Method

作　　者：李宗铭 房勇[1,2] LI Zong-ming;FANG Yong(Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Economics and Management,University of Chinese Academy of Science,Beijing 100190,China)

机构地区：[1]中国科学院数学与系统科学研究院,北京100190 [2]中国科学院大学经济与管理学院,北京100190

出　　处：《数学的实践与认识》2020年第9期78-88,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71631008)。

摘　　要：Markowitz开创了现代投资组合理论的先河,他提出的均值方差模型为后来投资组合选择模型的研究奠定了基础.然而,许多学者的研究表明,均值方差模型对参数非常敏感,当模型参数的估计存在较大的误差时,模型并不是在配置风险和收益,而是在配置误差.模型的误差分别来自收益端和风险端,为了改善收益端的参数估计,学者们提出了更具有实际应用价值的Black-Litterman模型,而如何改善风险端的估计误差还有待进一步的研究.在实际应用中,有效的数据样本往往较少,当资产数量较大时,样本协方差矩阵存在很大的估计误差,因此,引入POET方法估计协方差矩阵提高协方差矩阵的估计精度,从风险端改善投资组合选择模型的配置效率.将构建的投资组合选择模型分别应用在申万一级行业指数和二级行业指数上,算例分析的结果表明,引入POET方法后模型有更好的表现.Markowitz pioneered the modern portfolio theory.His proposed mean variance model laid the foundation for the later research on portfolio selection model.However,many scholars have shown that the mean variance model is very sensitive to parameters.When there is a large error in the estimation of model parameters,the model is not in the configuration risk and benefit,but in the configuration error.The error of the model comes from the income side and the risk side respectively.In order to improve the parameter estimation of the income side,the scholars put forward the Black-Litterman model with more practical application value.How to improve the estimation error of the risk side remains to be further studied.In practical applications,effective data samples tend to be less.When the number of assets is large,the sample covariance matrix has a large estimation error.Therefore,the POET method is introduced to estimate the covariance matrix to improve the estimation accuracy of the covariance matrix.The risk side improves the allocation efficiency of the portfolio selection model.The portfolio selection model constructed in this paper is applied to the Shenwan first-level industry index and the second-level industry index respectively.The results of the example analysis show that the model has better performance after the introduction of the POET method.

关 键 词：均值方差模型 POET方法 行业资产配置 

分 类 号：F224[经济管理—国民经济] F830.91