基于因子载荷二叉树的高维投资组合优化  

High-Dimensional Portfolio Optimization Based on Binary Tree of Factor Loadings

作　　者：倪宣明 陈檬檬 钱龙 赵慧敏[3] NI Xuanming;CHEN Mengmeng;QIAN Long;ZHAO Huimin(School of Software and Microelectronics,Peking University,Beijing 100871;School of Economics and Management,Tsinghua University,Beijing 100084;School of Business,Sun Yat-Sen University,Guangzhou 510275)

机构地区：[1]北京大学软件与微电子学院,北京100871 [2]清华大学经济管理学院,北京100084 [3]中山大学管理学院,广州510275

出　　处：《系统科学与数学》2022年第9期2312-2326,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(71991474)资助课题。

摘　　要：二叉树结构有助于张成复杂的资产空间.针对个股,文章使用多种不同的划分依据生成了多层的二叉树,并对所有节点组合张成的高维资产空间进行了投资组合优化.具体的,文章首先选取三种适用于A股的因子:价值、规模和换手率,在此基础上上生成4种不同的二叉树组合(TS)数据集进行高维投资组合优化.随后,基于A股2000年至2020年所有股票数据,文章的实证结果显示,相比直接基于个股,基于树组合进行投资组合优化能够显著改善全局最小方差(GMV)和均值-方差(MV)策略以及带稀疏惩罚项GMV和MV策略的样本外夏普率、标准差和最大回撤率表现.最后,基于前新冠疫情数据集的结果表明本文结论具有很好的稳健性.Binary tree can help generate complicated asset space.Using varied sorting basis,this paper generates multi-layer binary trees of individual stocks and conducts portfolio optimization on the high-dimensional asset space spanned by treenode portfolios.Specifically,this paper firstly selects three factors that are suitable for A-share market:Value,size and turnover,and generates four different binary treesorted(TS)portfolio datasets to conduct high-dimensional portfolio optimization.Then,the empirical results based on all stock data from A-share market ranging from year 2000 to year 2020 show that,compared to direct optimization on individual stocks,optimizing on TS portfolios can significantly improve the out-of-sample Sharpe ratio,standard error and maximum drawdown performance of global minimum variance(GMV)and mean-variance(MV)strategies,and also GMV and MV with sparsity regularization.Finally,the results based on pre-COVID-19 dataset can indicate the fine robustness of our conclusions.

关 键 词：高维投资组合优化 二叉树 资产定价 

分 类 号：F224[经济管理—国民经济] F832.51