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Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints

18 Pages Posted: 26 May 2012  

Andrea Scozzari

University of Rome Niccolo' Cusano

Fabio Tardella

Faculty of Economics - Sapienza University of Rome

Sandra Paterlini

EBS Universität für Wirtschaft und Recht

Thiemo Krink

affiliation not provided to SSRN

Date Written: May 25, 2012

Abstract

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far.

The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches

Keywords: Index tracking, mixed integer quadratic programming, stochastic search heuristics, differential evolution, cardinality constraints

JEL Classification: C15, C61, G11

Suggested Citation

Scozzari, Andrea and Tardella, Fabio and Paterlini, Sandra and Krink, Thiemo, Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints (May 25, 2012). Available at SSRN: https://ssrn.com/abstract=2066672 or http://dx.doi.org/10.2139/ssrn.2066672

Andrea Scozzari

University of Rome Niccolo' Cusano ( email )

Via Don Carlo Gnocchi, 3
Roma, 00166
Italy

Fabio Tardella

Faculty of Economics - Sapienza University of Rome ( email )

Via del Castro Laurenziano, 9
Roma, Rome 00161
Italy

Sandra Paterlini (Contact Author)

EBS Universität für Wirtschaft und Recht ( email )

Gustav-Stresemann-Ring 3
Wiesbaden, Hessen 65189
Germany

Thiemo Krink

affiliation not provided to SSRN ( email )

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