IDEAS home Printed from
   My bibliography  Save this paper

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


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


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Manfred Gilli and Evis Kellezi, 2001. "Threshold Accepting for Index Tracking," Computing in Economics and Finance 2001 72, Society for Computational Economics.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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".

    More about this item


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

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uop:wpaper:0016. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Kleanthis Gatziolis). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.