ACTIVE PORTFOLIO MANAGEMENT WITH CARDINALITY CONSTRAINTS: AN APPLICATION OF PARTICLE SWARM OPTIMIZATION

Nikos S. Thomaidis (), Timotheos Angelidis, Vassilios Vassiliadis () and Georgios Dounias ()
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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
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

New Mathematics and Natural Computation (NMNC), 2009, vol. 05, issue 03, 535-555

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 forcesa priorithe 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.

Keywords: Active portfolio management; tracking error; particle swarm optimization (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (4)

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Working Paper: Active Portfolio Management With Cardinality Constraints: An Application Of Particle Swarm Optimization (2008)
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DOI: 10.1142/S1793005709001519

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