基于随机矩阵理论的市场信息识别与高维投资组合研究  

Quantitative Research on Market Information Identification and High-Dimensional Portfolio Based on Random Matrix Theory

作　　者：杨红伟 王励励 YANG Hong-wei;WANG Li-li(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China;China Institute of Regulation Research,Zhejiang University of Finance and Economics,Hangzhou 310018,China;Collaborative Innovation Center of Statistical Data Engineering,Technology&Application,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018 [2]浙江财经大学中国政府管制研究院,浙江杭州310018 [3]浙江工商大学统计数据工程技术与应用协同创新中心,浙江杭州310018

出　　处：《数理统计与管理》2021年第6期1113-1126,共14页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学研究项目(21YJC91009);国家自然科学基金青年科学基金项目(11701509);浙江省属高校基本业务费专项资金.

摘　　要：协方差矩阵的准确估计是有效开展高维Markowitz最优投资组合的基础,随机矩阵理论为改进高维协方差矩阵的估计提供了有效的手段.基于对Spiked矩阵极限谱性质的研究,能够更有效地识别样本协方差矩阵中的"市场信息",并基于样本自协方差矩阵最小特征值比值确定因子数量,进一步估计高维样本协方差矩阵,通过对S&P500成份股1988-2017年的超额收益率的实证研究,得到了更高夏普率和更低风险的投资组合.The accurate estimation of the covariance matrix is the basis for effectively developing the high-dimensional Markowitz“mean-variance”(MV)optimal portfolio.The random matrix theory(RMT)and methodology provide an effective approach for improving the estimation of the high-dimensional co-variance matrix.Based on the study of the limiting spectral properties of the Spiked covariance matrix,the“market information”in the sample covariance matrix can be more effectively identified.Moreover,through the minimum eigenvalue ratio are proposed to determine the number of factors for improving the estimation of sample covariance matrix.The empirical study of the proposed methods on the excess return of stocks data which are S&P500 components during 1988 to 2017 shows a higher Sharpe ratio and lower risk with the covariance estimation methods stated in this paper.

关 键 词：高维协方差矩阵 投资组合 Spiked矩阵 市场信息识别 

分 类 号：C812[社会学—统计学] O212.4[理学—概率论与数理统计]