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基于Sparse-Group Lasso 的指数跟踪

王国长1,高桃璇1,徐世荣2   

  1. 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, 香港  999077
  • 出版日期:2019-12-25 发布日期:2020-03-20

王国长,高桃璇,徐世荣. 基于Sparse-Group Lasso 的指数跟踪[J]. 系统科学与数学, 2019, 39(12): 2025-2040.

WANG Guochang,GAO Taoxuan,XU Shirong. Index Tracking Based on Sparse-Group Lasso[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(12): 2025-2040.

Index Tracking Based on Sparse-Group Lasso

WANG Guochang1 ,GAO Taoxuan1 ,XU Shirong2   

  1. 1. School of Economy, Jinan University, Guangzhou 510632; 2. School of Science and Engineering, City University of Hong Kong, Hong Kong 999077
  • Online:2019-12-25 Published:2020-03-20

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.

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