Sparse Index Tracking Portfolio with Sector Neutrality

As a popular passive investment strategy, a sparse index tracking strategy has advantages over a full index replication strategy because of higher liquidity and lower transaction costs. Sparsity and nonnegativity constraints are usually assumed in the construction of portfolios in sparse index tracking. However, none of the existing studies considered sector risk exposure of the portfolios that prices of stocks in one sector may fall at the same time due to sudden changes in policy or unexpected events that may affect the whole sector. Therefore, sector neutrality appeals to be critical when building a sparse index tracking portfolio if not using full replication. The statistical approach to sparse index tracking is a constrained variable selection problem. However, the constrained variable selection procedure using Lasso fails to produce a sparse portfolio under sector neutrality constraints. In this paper, we propose a high-dimensional constrained variable selection method using TLP for building index tracking portfolios under sparsity, sector neutrality and nonnegativity constraints. Selection consistency is established for the proposed method, and the asymptotic distribution is obtained for the sparse portfolio weights estimator. We also develop an efficient iteration algorithm for the weight estimation. We examine the performance of the proposed methodology through simulations and an application to the CSI 300 index of China. The results demonstrate the validity and advantages of our methodology.