A two-stage approach to the UCITS-constrained index-tracking problem

Abstract

Undertakings for Collective Investments in Transferable Securities (UCITS) are investment funds that are regulated by the European Union. UCITS have become increasingly popular, resulting in a total corresponding amount of assets under management of € 8.5 trillion by the end of 2016. We present a two-stage approach to the problem of how to construct a portfolio of assets for a UCITS that aims to replicate the returns of a financial index subject to the constraints imposed by the UCITS regulations. In the first stage, we apply a genetic algorithm that treats subsets of the index constituents as individuals to construct a good feasible solution in a short CPU time. In this genetic algorithm, we use a new representation of subsets, which is the first to exhibit all of the following four desirable properties: feasibility, efficiency, locality, and heritability. In the second stage, we apply local branching based on a new mixed-integer quadratic programming formulation to improve the best solution obtained in the first stage. In a numerical experiment on real-world data, the approach yields very good feasible solutions in a short CPU time.