Index tracking model through an enhanced GRASP approach for the financial portfolio problem

Abstract

Financial portfolio optimization problems may become computationally infeasible when some practical constraints are considered in the model. In these circumstances, it is difficult to find an optimal solution in a reasonable time. An investment strategy that aims to replicate the performance of a stock market index, whose model solution is included in this class of difficult problems, is called index tracking. This work brings an analysis, spanning the last decade, about the advances in solution approaches for index tracking. The systematic literature review covered important issues, such as the most relevant research areas, solution methods, and model structures. Also, the author presents a novel application of Greedy Randomized Adaptive Search Procedure (GRASP) for index tracking. It was sought to implement and adapt a heuristic that was not yet applied to the index tracking problem and evaluate its performance relative to a commercial solver. It was necessary to develop a new greedy function and to compare the results after greedy and random solution construction. Besides, a way is proposed to improve a local search component in the selected GRASP metaheuristic. By conducting computational experiments, GRASP and a general-purpose solver have been compared using benchmark instances. The results showed that GRASP found solutions with almost the same quality as those of CPLEX solver in a smaller time. Moreover, it was observed that the proposed local search component implied in obtaining better solutions relative to those of the reference GRASP metaheuristic. Not performing statistical tests when comparing solution methods, using only benchmark instances and one index tracking model can be considered as limitations of this work. The practical implication of this research is the achievement of good solutions for the index tracking problem in a smaller time and new perspectives for building GRASP heuristics for portfolio optimization problems. As far as we know, this is the first time that a GRASP heuristic was used in this type of problem. GRASP has a great potential in portfolio optimization, more specifically in solving index tracking problems. With a simple parameter tuning procedure, it was possible to obtain good solutions in a smaller time.