基于 Sparse-Group Lasso 的指数跟踪

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.