Metaheuristics for Index-Tracking with Cardinality Constraints

As one of the passive investment strategies, index-tracking aims to replicate market indexes to reproduce market performance. It is widely used for long-term investment. Full replication and partial index-tracking are common approaches for index-tracking problems. Although full replication tracks the chosen market index perfectly, the transaction cost is relatively high in practice. Therefore, partial index-tracking is desired that can reduce the transaction cost and avoid illiquid assets. The partial index-tracking approach selects the subset of a benchmark index and applies restrictions for the numbers of stocks with cardinality constraints. The constrained problem is converted into an unconstrained problem by adding the penalty term. This paper is concerned with the sparse index-tracking problem with cardinality constraints by various metaheuristics. Various metaheuristics are used to deal with the sparse index-tracking problem, and their performances are compared. Also, various penalty values are adopted to test the performance of the compared algorithm.