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A local relaxation method for the cardinality constrained portfolio optimization problem

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  • Walter Murray
  • Howard Shek

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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  • Walter Murray & Howard Shek, 2012. "A local relaxation method for the cardinality constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 53(3), pages 681-709, December.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:681-709
    DOI: 10.1007/s10589-012-9471-1
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    References listed on IDEAS

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    Cited by:

    1. Alexander Nikiporenko, 2023. "Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation," Papers 2307.04045, arXiv.org.
    2. Christian Kanzow & Andreas B. Raharja & Alexandra Schwartz, 2021. "Sequential optimality conditions for cardinality-constrained optimization problems with applications," Computational Optimization and Applications, Springer, vol. 80(1), pages 185-211, September.
    3. Chen, Qi-an & Hu, Qingyu & Yang, Hu & Qi, Kai, 2022. "A kind of new time-weighted nonnegative lasso index-tracking model and its application," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    4. Leonardo Riegel Sant’Anna & Tiago Pascoal Filomena & Pablo Cristini Guedes & Denis Borenstein, 2017. "Index tracking with controlled number of assets using a hybrid heuristic combining genetic algorithm and non-linear programming," Annals of Operations Research, Springer, vol. 258(2), pages 849-867, November.
    5. Madani Bezoui & Mustapha Moulaï & Ahcène Bounceur & Reinhardt Euler, 2019. "An iterative method for solving a bi-objective constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 72(2), pages 479-498, March.
    6. Jize Zhang & Tim Leung & Aleksandr Aravkin, 2018. "A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization," Papers 1810.10563, arXiv.org.
    7. Max Bucher & Alexandra Schwartz, 2018. "Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 383-410, August.
    8. Martin Branda & Max Bucher & Michal Červinka & Alexandra Schwartz, 2018. "Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization," Computational Optimization and Applications, Springer, vol. 70(2), pages 503-530, June.
    9. Nasim Dehghan Hardoroudi & Abolfazl Keshvari & Markku Kallio & Pekka Korhonen, 2017. "Solving cardinality constrained mean-variance portfolio problems via MILP," Annals of Operations Research, Springer, vol. 254(1), pages 47-59, July.

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