基于Sparse-Group Lasso的指数跟踪  

Index Tracking Based on Sparse-Group Lasso

作　　者：王国长[1] 高桃璇 徐世荣 WANG Guochang;GAO Taoxuan;XU Shirong(School of Economy,Jinan University,Guangzhou 510632;School of Science and Engineering,City University of Hong Kong,Hong Kong 999077)

机构地区：[1]暨南大学经济学院,广州510632 [2]香港城市大学科学与工程学院,中国香港999077

出　　处：《系统科学与数学》2019年第12期2025-2040,共16页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11501248);广州市科技计划项目(201804010276);广州市科技计划项目(2018070100047)资助课题。

摘　　要：在指数跟踪问题中,股票指数与行业板块的相关性往往是集中在某些特定的行业,且行业走向通常由几个有影响力的公司决定,因此如何选取具有代表性的行业和公司是提高跟踪精度的一个很好的切入点.在以往的研究方法中,Lasso等变量选择方法忽略了行业因素的影响,而分层抽样则忽略了不同行业和股票指数关联性大小的不同.文章引入Sparse-Group Lasso方法,实现了对行业及行业内部单一股票的筛选,同时对跟踪误差的定义进行扩展,综合考虑线性和非线性两种跟踪误差的优点对股票组合的权重进行优化.实证表明,基于Sparse-Group Lasso方法筛选的股票组合的稳健性一致优于依据市值筛选的股票组合,当股票组合规模较小时,基于Sparse-Group Lasso方法筛选的股票组合的跟踪误差也要优于依据市值进行筛选股票的方法.In the process of index tracking,since the correlation between industry groups and stock index is only significant in some particular industries,and there are often several influential companies that determine the direction of the industry,how to select industries and companies within the industries that are closely related to the stock index is a good point for more accurate index tracking.In the previous studies,Lasso and other variable selection methods ignore the influence of industry,while stratified sampling ignores the difference of correlation between different industries and stock index.In this paper,a Sparse-Group Lasso method is introduced to filter the industries and the stocks within the industries.At the same time,the definition of tracking error is extended,and the advantages of linear and nonlinear tracking errors are considered to optimize the weight of stock portfolio.The empirical shows that:The robustness of the portfolio based on Sparse-Group Lasso outperforms consistently portfolio based on market value.Also,when the scale of stock portfolio is small,the tracking error based on Sparse-Group Lasso outperforms that based on market value.

关 键 词：指数跟踪 Sparse-Group Lasso 跟踪误差 行业筛选 

分 类 号：F832.51[经济管理—金融学] O212[理学—概率论与数理统计]