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 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.
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Bibliographic InfoPaper provided by University of Peloponnese, Department of Economics in its series Working Papers with number 0016.
Length: 22 pages
Date of creation: 2008
Date of revision:
Active portfolio management; tracking error; particle swarm optimization.;
Other versions of this item:
- Nikos S. Thomaidis & Timotheos Angelidis & Vassilios Vassiliadis & Georgios Dounias, 2009. "Active Portfolio Management With Cardinality Constraints: An Application Of Particle Swarm Optimization," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 535-555.
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- 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.
- Nadima El-Hassan & Paul Kofman, 2003. "Tracking Error and Active Portfolio Management," Research Paper Series 98, Quantitative Finance Research Centre, University of Technology, Sydney.
- 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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