A two-stage approach to the UCITS-constrained index-tracking problem. (March 2019)

• Record Type: Journal Article
• Authors: Strub, O.; Trautmann, N.
• Is Part Of: Computers & operations research. Volume 103(2019)
• Page Start: 167
• Page End: 183
• Publication Date: 2019-03
• Subjects: Portfolio management -- Index tracking -- Mixed-integer quadratic programming -- Heuristics; Operations research -- Periodicals; Electronic digital computers -- Periodicals; 004.05
• DOI: 10.1016/j.cor.2018.10.002
• Languages: English
• ISSNs: 0305-0548

Abstract

Highlights: We study the index-tracking problem subject to UCITS regulations. We propose a new mixed-integer quadratic programming formulation of this problem. We develop a heuristic based on a genetic algorithm and local branching. We present a new representation of individuals for the genetic algorithm. We find that the UCITS regulations reduce the out-of-sample portfolio risk. 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.