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

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  • Nikos Thomaidis
  • Timotheos Angelidis
  • Vassilios Vassiliadis
  • Georgios Dounias

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 set up 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. The third formulation, presented in this paper, 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 numeric 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 application, 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 as concerns the efficiency of common practices in active portfolio management and the incorporation of cardinality constraints.

Suggested Citation

  • Nikos Thomaidis & Timotheos Angelidis & Vassilios Vassiliadis & Georgios Dounias, 2008. "Active Portfolio Management With Cardinality Constraints: An Application Of Particle Swarm Optimization," Working Papers 0016, University of Peloponnese, Department of Economics.
  • Handle: RePEc:uop:wpaper:0016
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    References listed on IDEAS

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    1. Manfred Gilli and Evis Kellezi, 2001. "Threshold Accepting for Index Tracking," Computing in Economics and Finance 2001 72, Society for Computational Economics.
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    Cited by:

    1. 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.
    2. 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".

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    Keywords

    Active portfolio management; tracking error; particle swarm optimization.;

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