IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v72y2019i2d10.1007_s10589-018-0052-9.html
   My bibliography  Save this article

An iterative method for solving a bi-objective constrained portfolio optimization problem

Author

Listed:
  • Madani Bezoui

    (University M’hamed Bougara of Boumerdes
    LaROMad, Faculty of Mathematics (USTHB))

  • Mustapha Moulaï

    (LaROMad, Faculty of Mathematics (USTHB))

  • Ahcène Bounceur

    (Lab-STICC - UMR CNRS 6285, UBO)

  • Reinhardt Euler

    (Lab-STICC - UMR CNRS 6285, UBO)

Abstract

In this work, we consider the problem of portfolio optimization under cardinality and quantity constraints. We use the standard model of mean-variance in its bi-objective form which is presented here as a bi-objective quadratic programming problem under cardinality and quantity constraints. This problem is NP-hard, which is why the majority of methods proposed in the literature use metaheuristics for its resolution. In this paper, we propose an iterative method for solving constrained portfolio optimization problems. Experiments are performed with major market indices, such as the Hang Seng, DAX, FTSE, S&P 100, Nikkei, S&P 500 and Nasdaq using real-world datasets involving up to 2196 assets. Comparisons with two exact methods and a metaheuristic are performed. These results show that the new method allows to find efficient portfolio fronts in reasonable time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0052-9
    DOI: 10.1007/s10589-018-0052-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-018-0052-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-018-0052-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Luca Gaspero & Giacomo Tollo & Andrea Roli & Andrea Schaerf, 2011. "Hybrid metaheuristics for constrained portfolio selection problems," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1473-1487.
    2. Mehdi Beyhaghi & James P. Hawley, 2013. "Modern portfolio theory and risk management: assumptions and unintended consequences," Journal of Sustainable Finance & Investment, Taylor & Francis Journals, vol. 3(1), pages 17-37, January.
    3. 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.
    4. 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.
    5. 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.
    6. de Almeida, Adiel Teixeira & Vetschera, Rudolf, 2012. "A note on scale transformations in the PROMETHEE V method," European Journal of Operational Research, Elsevier, vol. 219(1), pages 198-200.
    7. Dimitris Bertsimas & Romy Shioda, 2009. "Algorithm for cardinality-constrained quadratic optimization," Computational Optimization and Applications, Springer, vol. 43(1), pages 1-22, May.
    8. 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.
    9. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Zhi-Long Dong & Fengmin Xu & Yu-Hong Dai, 2020. "Fast algorithms for sparse portfolio selection considering industries and investment styles," Journal of Global Optimization, Springer, vol. 78(4), pages 763-789, December.
    8. Wei Xu & Jie Tang & Ka Fai Cedric Yiu & Jian Wen Peng, 2024. "An Efficient Global Optimal Method for Cardinality Constrained Portfolio Optimization," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 690-704, March.
    9. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Tahereh Khodamoradi & Maziar Salahi & Ali Reza Najafi, 2021. "Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 197-214, June.
    15. 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.
    16. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    17. Jize Zhang & Tim Leung & Aleksandr Aravkin, 2018. "A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization," Papers 1810.10563, arXiv.org.
    18. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2015. "Portfolio Management With Higher Moments: The Cardinality Impact," GEMF Working Papers 2015-15, GEMF, Faculty of Economics, University of Coimbra.
    19. 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.
    20. Alexander Nikiporenko, 2023. "Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation," Papers 2307.04045, arXiv.org.

    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:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0052-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.