A genetic algorithm for the UCITS-constrained index-tracking problem

We consider the problem of replicating the returns of a financial index as accurately as possible by selecting a subset of the assets that constitute the index and determining the portfolio weight of each selected asset subject to various constraints that are relevant in practice, including the UCITS III (Undertakings for Collective Investments in Transferable Securities) 5/10/40 concentration rule. For this problem, we present a genetic algorithm, in which the individuals correspond to subsets of the index constituents. The fitness of the individuals is determined by applying mixed-integer quadratic programming. Two main features of the presented genetic algorithm are novel. First, we use a representation of subsets which is the first that exhibits all of the four desirable properties feasibility, efficiency, locality, and heritability. The representation also allows to incorporate problem-specific knowledge in a very simple way. Second, to reduce the CPU time for the fitness evaluations, we first estimate the fitness of the individuals in an efficient way and then evaluate the fitness of promising individuals only. The results of a computational experiment based on real-world data demonstrate that in particular for large instances, the presented genetic algorithm devises very good solutions in short CPU time.