IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v213y2011i3p538-550.html
   My bibliography  Save this article

Heuristic algorithms for the cardinality constrained efficient frontier

Author

Listed:
  • Woodside-Oriakhi, M.
  • Lucas, C.
  • Beasley, J.E.

Abstract

This paper examines the application of genetic algorithm, tabu search and simulated annealing metaheuristic approaches to finding the cardinality constrained efficient frontier that arises in financial portfolio optimisation. We consider the mean-variance model of Markowitz as extended to include the discrete restrictions of buy-in thresholds and cardinality constraints. Computational results are reported for publicly available data sets drawn from seven major market indices involving up to 1318 assets. Our results are compared with previous results given in the literature illustrating the effectiveness of the proposed metaheuristics in terms of solution quality and computation time.

Suggested Citation

  • Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:3:p:538-550
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711002670
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ehrgott, Matthias & Klamroth, Kathrin & Schwehm, Christian, 2004. "An MCDM approach to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 155(3), pages 752-770, June.
    2. Schaerf, Andrea, 2002. "Local Search Techniques for Constrained Portfolio Selection Problems," Computational Economics, Springer;Society for Computational Economics, vol. 20(3), pages 177-190, December.
    3. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    4. Juan Pablo Vielma & Shabbir Ahmed & George L. Nemhauser, 2008. "A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 438-450, August.
    5. Dimitris Bertsimas & Romy Shioda, 2009. "Algorithm for cardinality-constrained quadratic optimization," Computational Optimization and Applications, Springer, vol. 43(1), pages 1-22, May.
    6. Crama, Y. & Schyns, M., 2003. "Simulated annealing for complex portfolio selection problems," European Journal of Operational Research, Elsevier, vol. 150(3), pages 546-571, November.
    7. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    8. Syam, Siddhartha S., 1998. "A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals," European Journal of Operational Research, Elsevier, vol. 108(1), pages 196-207, July.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    11. Corazza, Marco & Favaretto, Daniela, 2007. "On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1947-1960, February.
    12. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    13. Duan Li & Xiaoling Sun & Jun Wang, 2006. "Optimal Lot Solution To Cardinality Constrained Mean–Variance Formulation For Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 83-101, January.
    14. Ulrich Derigs & Nils-H. Nickel, 2004. "On a Local-Search Heuristic for a Class of Tracking Error Minimization Problems in Portfolio Management," Annals of Operations Research, Springer, vol. 131(1), pages 45-77, October.
    15. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
    16. Branke, J. & Scheckenbach, B. & Stein, M. & Deb, K. & Schmeck, H., 2009. "Portfolio optimization with an envelope-based multi-objective evolutionary algorithm," European Journal of Operational Research, Elsevier, vol. 199(3), pages 684-693, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    2. Zhou, Zhongbao & Jin, Qianying & Xiao, Helu & Wu, Qian & Liu, Wenbin, 2018. "Estimation of cardinality constrained portfolio efficiency via segmented DEA," Omega, Elsevier, vol. 76(C), pages 28-37.
    3. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2013. "A new method for mean-variance portfolio optimization with cardinality constraints," Annals of Operations Research, Springer, vol. 205(1), pages 213-234, May.
    4. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2015. "Linear vs. quadratic portfolio selection models with hard real-world constraints," Computational Management Science, Springer, vol. 12(3), pages 345-370, July.
    5. Xiaojin Zheng & Xiaoling Sun & Duan Li & Jie Sun, 2014. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 379-397, October.
    6. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    7. Gili Rosenberg & Poya Haghnegahdar & Phil Goddard & Peter Carr & Kesheng Wu & Marcos L'opez de Prado, 2015. "Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer," Papers 1508.06182, arXiv.org, revised Aug 2016.
    8. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    9. Xiaojin Zheng & Xiaoling Sun & Duan Li, 2014. "Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 690-703, November.
    10. Ralph Steuer & Markus Hirschberger & Kalyanmoy Deb, 2016. "Extracting from the relaxed for large-scale semi-continuous variable nondominated frontiers," Journal of Global Optimization, Springer, vol. 64(1), pages 33-48, January.
    11. Kyle Steinhauer & Takahisa Fukadai & Sho Yoshida, 2020. "Solving the Optimal Trading Trajectory Problem Using Simulated Bifurcation," Papers 2009.08412, arXiv.org.
    12. K. Liagkouras & K. Metaxiotis, 2018. "A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem," Annals of Operations Research, Springer, vol. 267(1), pages 281-319, August.
    13. Branke, J. & Scheckenbach, B. & Stein, M. & Deb, K. & Schmeck, H., 2009. "Portfolio optimization with an envelope-based multi-objective evolutionary algorithm," European Journal of Operational Research, Elsevier, vol. 199(3), pages 684-693, December.
    14. Dimitris Bertsimas & Ryan Cory-Wright, 2022. "A Scalable Algorithm for Sparse Portfolio Selection," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1489-1511, May.
    15. Buckley, Winston & Long, Hongwei & Marshall, Mario, 2016. "Numerical approximations of optimal portfolios in mispriced asymmetric Lévy markets," European Journal of Operational Research, Elsevier, vol. 252(2), pages 676-686.
    16. 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.
    17. E. Grizickas Sapkute & M. A. Sánchez-Granero & M. N. López García & J. E. Trinidad Segovia, 2022. "The impact of regulation-based constraints on portfolio selection: The Spanish case," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-14, December.
    18. Eduardo Bered Fernandes Vieira & Tiago Pascoal Filomena, 2020. "Liquidity Constraints for Portfolio Selection Based on Financial Volume," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 1055-1077, December.
    19. Massol, Olivier & Banal-Estañol, Albert, 2014. "Export diversification through resource-based industrialization: The case of natural gas," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1067-1082.
    20. Jan Jurczyk & Alexander Eckrot & Ingo Morgenstern, 2016. "Quantifying Systemic Risk by Solutions of the Mean-Variance Risk Model," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-12, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:213:y:2011:i:3:p:538-550. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.