Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints
AbstractIndex 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 Di_erential 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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Bibliographic InfoPaper provided by University of Modena and Reggio E., Faculty of Economics "Marco Biagi" in its series Department of Economics with number 0685.
Length: pages 22
Date of creation: Jun 2012
Date of revision:
Index tracking; mixed integer quadratic programming; stochastic search heuristics; differential evolution; cardinality constraints;
Other versions of this item:
- Andrea Scozzari & Fabio Tardella & Sandra Paterlini & Thiemo Krink, 2012. "Exact and heuristic approaches for the index tracking problem with UCITS constraints," Center for Economic Research (RECent) 081, University of Modena and Reggio E., Dept. of Economics.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-03 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Andriosopoulos, Kostas & Doumpos, Michael & Papapostolou, Nikos C. & Pouliasis, Panos K., 2013. "Portfolio optimization and index tracking for the shipping stock and freight markets using evolutionary algorithms," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 52(C), pages 16-34.
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