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Differential Evolution and Combinatorial Search for Constrained Index Tracking

Author

Listed:
  • Thiemo Krink
  • Stefan Mittnik
  • Sandra Paterlini
Abstract
Index tracking is a valuable low-cost alternative to active portfolio management. The implementation of a quantitative approach, however, is a major challenge from an optimization perspective. The optimal selection of a group of assets that can replicate the index of a much larger portfolio requires both to find the optimal subset of assets and to fine-tune their weights. The former is a combinatorial, the latter a continuous numerical problem. Both problems need to be addressed simultaneously, because whether or not a selection of assets is promising depends on the allocation weights and vice versa. Moreover, the problem is usually of high dimension. Typically, an optimal subset of 30-150 positions out of 100-600 need to be selected and their weights determined. Search heuristics can be a viable and valuable alternative to traditional methods, which often cannot deal with the problem. In this paper, we propose a new optimization method, which is partly based on Differential Evolution (DE) and on combinatorial search. The main advantage of our method is that it can tackle index tracking problem as complex as it is, generating accurate and robust results.

Suggested Citation

  • Thiemo Krink & Stefan Mittnik & Sandra Paterlini, 2009. "Differential Evolution and Combinatorial Search for Constrained Index Tracking," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0016, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    • Handle: RePEc:mod:wcefin:0016
    as

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    References listed on IDEAS

    as
    1. Thiemo Krink & Sandra Paterlini, 2008. "Differential Evolution for Multiobjective Portfolio Optimization," Center for Economic Research (RECent) 021, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    2. Gunter Dueck & Peter Winker, 1992. "New concepts and algorithms for portfolio choice," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 8(3), pages 159-178, September.
    3. Beasley, J. E. & Meade, N. & Chang, T. -J., 2003. "An evolutionary heuristic for the index tracking problem," European Journal of Operational Research, Elsevier, vol. 148(3), pages 621-643, August.
    4. Sergio Focardi & Frank Fabozzi, 2004. "A methodology for index tracking based on time-series clustering," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 417-425.
    5. Paterlini, Sandra & Krink, Thiemo, 2006. "Differential evolution and particle swarm optimisation in partitional clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1220-1247, March.
    6. Krink, Thiemo & Paterlini, Sandra & Resti, Andrea, 2007. "Using differential evolution to improve the accuracy of bank rating systems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 68-87, September.
    7. Rudolf, Markus & Wolter, Hans-Jurgen & Zimmermann, Heinz, 1999. "A linear model for tracking error minimization," Journal of Banking & Finance, Elsevier, vol. 23(1), pages 85-103, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Index Tracking; Passive Asset Management; Differential Evolution; Combinatorial Search;
    All these keywords.

    JEL classification:

    • 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

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