A Revamped Sparse Index Tracker Leveraging K-Sparsity and Reduced Portfolio Reshuffling

Yiu Yu Chan, Chi-Sing Leung

Abstract: In financial engineering, sparse index tracking (SIT) serves as a specialized and cost-effective passive strategy that seeks to replicate a financial index using a representative subset of its constituents. However, many existing SIT algorithms have two imperfections: (1) they do not allow investors to explicitly control the number of assets held in the portfolio, and (2) these algorithms often result in excess purchasing and selling activities during the rebalancing process. To address these deficiencies, this paper first proposes a practical constrained optimization problem. Afterwards, the paper develops the corresponding algorithm, termed the index tracker with four portfolio constraints via projected gradient descent (IT4-PGD). With IT4-PGD, investors can freely define the settings of a portfolio, including the number of holding assets, the maximum holding position, and the maximum turnover ratio of each constituent. Simulation results using real-world data demonstrate that IT4-PGD outperforms existing methods by its lower magnitude of daily tracking error (MDTE) and lower accumulative turnover ratio (ATR).