Nonnegative Group Lasso on Modified Block-Wise Coordinate Decent Algorithm with an Application in Index Tracking

Index tracking is known to be a passive portfolio management strategy by replicating the performance of a real or virtual index. However, the full replication, which considers all the asserts consisted of the index, often suffers from small and illiquid positions and large transaction costs. Thus, it is preferred to purchase sparse portfolios. Besides, existing literatures pointed out the phenomenon of the co-movement in assert returns, indicating that the index tracking problems possibly contain group structures together with sparsity. Based on the consideration of the grouping effects and sparsity in index tracking problems, this paper proposes a grouping sparse index tracking model with nonnegative restrictions. We derive a modified version of coordinate decent algorithm for solving the model. The asymptotic properties are also discussed in detail. To show the effciency of the model, we apply it into the constrained index tracking problem in Shanghai stock market, i.e. tracking SSE 50 Index. By selecting about 10 stocks, the result shows that nonnegative group lasso outperforms nonnegative lasso in assert allocation.