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Active Portfolio Management With Cardinality Constraints: An Application Of Particle Swarm Optimization

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  • NIKOS S. THOMAIDIS

    ()
    (Decision and Management Engineering Laboratory, Department of Financial & Management Engineering, School of Business Studies University of the Aegean 31 Fostini Str., GR-821 00, Chios, Greece)

  • TIMOTHEOS ANGELIDIS

    ()
    (Department of Economics, University of Peloponnese GR 22100, Tripolis, Greece)

  • VASSILIOS VASSILIADIS

    ()
    (Decision and Management Engineering Laboratory, Department of Financial & Management Engineering, School of Business Studies, University of the Aegean, 31 Fostini Str., GR-821 00, Chios, Greece)

  • GEORGIOS DOUNIAS

    ()
    (Decision and Management Engineering Laboratory, Department of Financial & Management Engineering, School of Business Studies, University of the Aegean, 31 Fostini Str., GR-821 00, Chios, Greece)

Abstract

This paper considers the task of forming a portfolio of assets that outperforms a benchmark index, while imposing a constraint on the tracking error volatility. We examine three alternative formulations of active portfolio management. The first one is a typical setup in which the fund manager myopically maximizes excess return. The second formulation is an attempt to set a limit on the total risk exposure of the portfolio by adding a constraint that forces a priori the risk of the portfolio to be equal to the benchmark's. In this paper, we also propose a third formulation that directly maximizes the efficiency of active portfolios, while setting a limit on the maximum tracking error variance. In determining optimal active portfolios, we incorporate additional constraints on the optimization problem, such as a limit on the maximum number of assets included in the portfolio (i.e. the cardinality of the portfolio) as well as upper and lower bounds on asset weights. From a computational point of view, the incorporation of these complex, though realistic, constraints becomes a challenge for traditional numerical optimization methods, especially when one has to assemble a portfolio from a big universe of assets. To deal properly with the complexity and the "roughness" of the solution space, we use particle swarm optimization, a population-based evolutionary technique. As an empirical application of the methodology, we select portfolios of different cardinality that actively reproduce the performance of the FTSE/ATHEX 20 Index of the Athens Stock Exchange. Our empirical study reveals important results concerning the efficiency of common practices in active portfolio management and the incorporation of cardinality constraints.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

Volume (Year): 05 (2009)
Issue (Month): 03 ()
Pages: 535-555

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Handle: RePEc:wsi:nmncxx:v:05:y:2009:i:03:p:535-555

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Keywords: Active portfolio management; tracking error; particle swarm optimization;

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  1. Nadima El-Hassan & Paul Kofman, 2003. "Tracking Error and Active Portfolio Management," Australian Journal of Management, Australian School of Business, vol. 28(2), pages 183-207, September.
  2. 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.
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Cited by:
  1. Marco Corazza & Giovanni Fasano & Riccardo Gusso, 2011. "Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem," Working Papers 2011_10, Department of Economics, University of Venice "Ca' Foscari".
  2. Marco Corazza & Stefania Funari & Riccardo Gusso, 2012. "An evolutionary approach to preference disaggregation in a MURAME-based credit scoring problem," Working Papers 5, Department of Management, Università Ca' Foscari Venezia.

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