Exact and heuristic approaches for the index tracking problem with UCITS constraints

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,...

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Vydané v:Annals of operations research Ročník 205; číslo 1; s. 235 - 250
Hlavní autori: Scozzari, Andrea, Tardella, Fabio, Paterlini, Sandra, Krink, Thiemo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.05.2013
Springer
Springer Nature B.V
Predmet:
Algorithms
Benchmarks
Business and Management
Combinatorial analysis
Combinatorics
Constituents
Costs
Datasets
Heuristic
Heuristic methods
Heuristic programming
Investments
Investors
Linear programming
Mathematical economics
Mathematical models
Operations research
Operations Research/Decision Theory
Performance indices
Portfolio management
Quadratic programming
Securities markets
Stock exchanges
Studies
Theory of Computation
Tracking
Tracking problem
Italy
Differential evolution
Mixed integer quadratic programming
Index tracking
Cardinality constraints
Stochastic search heuristics
ISSN:0254-5330, 1572-9338
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Shrnutí: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-012-1207-1