M估计在单指数投资组合模型中的应用  

Application of M-estimation in Single-index Investment Portfolio Model

作　　者：陈亚男 刘月娟 朱睿 CHEN Yanan;LIU Yuejuan;ZHU Rui(School of Mathematics and Statistics,Chaohu University,Hefei 238000,China;The Seventh Affiliated Hospital of Sun Yat-Sen University,Shenzhen 518000,China)

机构地区：[1]巢湖学院数学与统计学院,安徽合肥238000 [2]中山大学附属第七医院,广东深圳518000

出　　处：《宿州学院学报》2021年第6期13-19,共7页Journal of Suzhou University

基　　金：巢湖学院人文社会科学研究项目(XLY-202006);巢湖学院教学团队项目(ch20-jxtd02)。

摘　　要：股票收益率中离群值的存在导致股票收益率并不完全服从正态分布,传统的单指数模型使用的最小二乘法(OLS)对回归参数的估计误差十分敏感,且不稳定的权重随时间推移大幅波动。鲁棒估计(M-Huber估计和MTukey估计)具有一定的稳健性,将其引入单指数模型中,构建鲁棒估计单指数投资组合模型,以便减小离群值对回归结果的影响,提高权重的稳定性,增加模型的可操作性和实用性。实证结果表明:相对于最小二乘法(OLS)的单指数模型,改进的鲁棒估计单指数投资组合模型对股票收益率偏离正态分布的程度不太敏感,具有更好的稳健性。The existence of outliers in stock returns results in that they do not follow the normal distribution completely.The least square method(OLS)used in the traditional single-index model is very sensitive to the estimation error of the regression parameters,and the unstable weight fluctuates greatly over time.The article introduces two kinds of robust estimation(M-Huber estimation and M-Tukey estimation)into the single-index model,and constructs a single-index portfolio model in order to reduce the influence of outliers on the regression results and improve the stability of the weights and increase the operability and practicality of the model.The empirical results show that,compared with the single index model of the least square method(OLS),the improved single index portfolio model based on robust estimation is less sensitive to the degree of stock return deviation from the normal distribution,and has better robustness.

关 键 词：单指数模型 M估计 Tukey损失函数 离群值 

分 类 号：F224[经济管理—国民经济] F832.51