A novel robust mixed integer linear programming model for index tracking problem under no rebalancing: heuristic optimization approach

Abstract

Passive management has increasingly won popularity over the past few years because of its advantages, such as lower management fees and transaction costs. Index tracking endeavors to reproduce the performance of an index with smaller sets of assets. In this paper, a novel formulation is proposed that is not only more robust than the existing ones but also performs better on out-of-sample data and tracks indices over long periods without any considerable deviation or the need for rebalancing. Solving index tracking problems in a polynomial time is a challenging task due to their NP-hard nature. To address this issue, a novel heuristic based on metaheuristic algorithms and local branching is also developed to solve the proposed model. The heuristic enjoys not only the exploration capabilities of a genetic algorithm but the characteristics of local search algorithms as well. The data from the OR library is used to verify the capabilities of the proposed heuristic in comparison with commercial solvers. Results indicate that not only is the heuristic able to converge to optimal solutions for not-so-large problem sizes, but the portfolios it generates also outperform those yielded by commercial solvers in terms of both in-sample and out-of-sample data.