Active Portfolio Management With Cardinality Constraints: An Application Of Particle Swarm Optimization
AbstractThis 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 InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.
Volume (Year): 05 (2009)
Issue (Month): 03 ()
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Web page: http://www.worldscinet.com/nmnc/nmnc.shtml
Other versions of this item:
- 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.
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- Nadima El-Hassan & Paul Kofman, 2003.
"Tracking Error and Active Portfolio Management,"
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- 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".
- 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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