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...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 literature 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 efficiency 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.展开更多
基金supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202400514)the Foundation Project of Chongqing Normal University(Grand No.23XLB020)+1 种基金partly supported by Chongqing Social Science Planning Doctoral Program(Grant No.2022BS064)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202301541)。
文摘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 literature 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 efficiency 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.
