Metaheuristics for sparse index-tracking problem: A case study on FTSE 100

Passive management contributes a more stable return than an active management strategy over the long term. Index-tracking is one of the passive investment strategies that attempt to replicate market indexes to reproduce the performance. Sparse index-tracking considers a subset of market index stocks to minimize the difference between the market index and the replicated index. In this paper, two metaheuristics are applied to solve this problem. The sparse index-tracking problem formed by the objective function of the empirical tracking error with the penalty values that result in an NP-hard problem. The penalty value is used to restrict the numbers of the considered stocks. To show the performance of the metaheuristics, various penalty values are investigated, and they produce approximation solutions to the index-tracking problem. Among them, particle swarm optimization shows better or statistically similar performance to GA in solving the sparse index-tracking problem.