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A local relaxation method for the cardinality constrained portfolio optimization problem

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  • Walter Murray

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  • Howard Shek

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    Abstract

    The NP-hard nature of cardinality constrained mean-variance portfolio optimization problems has led to a number of different algorithms with varying degrees of success in reaching optimality given limited computational resources and under the presence of strict time constraints present in practice. The proposed local relaxation algorithm explores the inherent structure of the objective function. It solves a sequence of small, local, quadratic-programs by first projecting asset returns onto a reduced metric space, followed by clustering in this space to identify sub-groups of assets that best accentuate a suitable measure of similarity amongst different assets. The algorithm can either be cold started using a suitable heuristic method such as the centroids of initial clusters or be warm started based on the last output. Results, using a basket of up to 3,000 stocks and with different cardinality constraints, indicates that the proposed algorithm can lead to significant performance gain over popular branch-and-cut methods. One key application of this algorithm is in dealing with large scale cardinality constrained portfolio optimization under tight time constraint, such as for the purpose of index tracking or index arbitrage at high frequency. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9471-1
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 53 (2012)
    Issue (Month): 3 (December)
    Pages: 681-709

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:681-709

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Portfolio optimization; Local relaxation method; Nonlinear programming; Cardinality constrained optimization;

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    1. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    2. Hiroshi Konno & Rei Yamamoto, 2005. "Integer programming approaches in mean-risk models," Computational Management Science, Springer, vol. 4(4), pages 339-351, November.
    3. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    4. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-85, March.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
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