IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v80y2021i3d10.1007_s10898-021-01022-1.html
   My bibliography  Save this article

Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems

Author

Listed:
  • Janusz Miroforidis

    (Polish Academy of Sciences)

Abstract

When solving large-scale cardinality-constrained Markowitz mean–variance portfolio investment problems, exact solvers may be unable to derive some efficient portfolios, even within a reasonable time limit. In such cases, information on the distance from the best feasible solution, found before the optimization process has stopped, to the true efficient solution is unavailable. In this article, I demonstrate how to provide such information to the decision maker. I aim to use the concept of lower bounds and upper bounds on objective function values of an efficient portfolio, developed in my earlier works. I illustrate the proposed approach on a large-scale data set based upon real data. I address cases where a top-class commercial mixed-integer quadratic programming solver fails to provide efficient portfolios attempted to be derived by Chebyshev scalarization of the bi-objective optimization problem within a given time limit. In this case, I propose to transform purely technical information provided by the solver into information which can be used in navigation over the efficient frontier of the cardinality-constrained Markowitz mean–variance portfolio investment problem.

Suggested Citation

  • Janusz Miroforidis, 2021. "Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems," Journal of Global Optimization, Springer, vol. 80(3), pages 617-634, July.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-021-01022-1
    DOI: 10.1007/s10898-021-01022-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-021-01022-1
    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/s10898-021-01022-1?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. Ignacy Kaliszewski, 2006. "Soft Computing For Complex Multiple Criteria Decision Making," International Series in Operations Research and Management Science, Springer, number 978-0-387-30177-8, January.
    2. 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.
    3. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
    4. Solanki, Rajendra S. & Appino, Perry A. & Cohon, Jared L., 1993. "Approximating the noninferior set in multiobjective linear programming problems," European Journal of Operational Research, Elsevier, vol. 68(3), pages 356-373, August.
    5. X. Cui & X. Zheng & S. Zhu & X. Sun, 2013. "Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1409-1423, August.
    6. 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.
    7. 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.
    8. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, June.
    9. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.
    10. Kaliszewski, Ignacy & Miroforidis, Janusz & Podkopaev, Dmitry, 2012. "Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy," European Journal of Operational Research, Elsevier, vol. 216(1), pages 188-199.
    11. Kaliszewski, Ignacy, 2004. "Out of the mist--towards decision-maker-friendly multiple criteria decision making support," European Journal of Operational Research, Elsevier, vol. 158(2), pages 293-307, October.
    12. I. Kaliszewski & J. Miroforidis, 2014. "Two-Sided Pareto Front Approximations," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 845-855, September.
    13. Gijs Rennen & Edwin R. van Dam & Dick den Hertog, 2011. "Enhancement of Sandwich Algorithms for Approximating Higher-Dimensional Convex Pareto Sets," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 493-517, November.
    14. 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.
    15. 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.
    16. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    17. 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.
    18. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.
    19. Ignacy Kaliszewski & Janusz Miroforidis & Dmitry Podkopaev, 2016. "Multiple Criteria Decision Making by Multiobjective Optimization," International Series in Operations Research and Management Science, Springer, number 978-3-319-32756-3, January.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. I. Kaliszewski & J. Miroforidis, 2022. "Probing the Pareto front of a large-scale multiobjective problem with a MIP solver," Operational Research, Springer, vol. 22(5), pages 5617-5673, November.

    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. I. Kaliszewski & J. Miroforidis, 2022. "Probing the Pareto front of a large-scale multiobjective problem with a MIP solver," Operational Research, Springer, vol. 22(5), pages 5617-5673, November.
    2. Steuer, Ralph E. & Qi, Yue & Wimmer, Maximilian, 2024. "Computing cardinality constrained portfolio selection efficient frontiers via closest correlation matrices," European Journal of Operational Research, Elsevier, vol. 313(2), pages 628-636.
    3. I. Kaliszewski & J. Miroforidis, 2021. "Cooperative multiobjective optimization with bounds on objective functions," Journal of Global Optimization, Springer, vol. 79(2), pages 369-385, February.
    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. Salo, Ahti & Doumpos, Michalis & Liesiö, Juuso & Zopounidis, Constantin, 2024. "Fifty years of portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(1), pages 1-18.
    6. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.
    7. 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.
    8. Doering, Jana & Kizys, Renatas & Juan, Angel A. & Fitó, Àngels & Polat, Onur, 2019. "Metaheuristics for rich portfolio optimisation and risk management: Current state and future trends," Operations Research Perspectives, Elsevier, vol. 6(C).
    9. Alexander Nikiporenko, 2023. "Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation," Papers 2307.04045, arXiv.org.
    10. 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.
    11. 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.
    12. 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.
    13. Paolo Giudici & Gloria Polinesi & Alessandro Spelta, 2022. "Network models to improve robot advisory portfolios," Annals of Operations Research, Springer, vol. 313(2), pages 965-989, June.
    14. 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.
    15. 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.
    16. Ina Lammel & Karl-Heinz Küfer & Philipp Süss, 2024. "An approximation algorithm for multiobjective mixed-integer convex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 321-350, August.
    17. 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.
    18. Juan Francisco Monge, 2017. "Cardinality constrained portfolio selection via factor models," Papers 1708.02424, arXiv.org.
    19. Rasmus Bokrantz & Anders Forsgren, 2013. "An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 377-393, May.
    20. Rennen, G. & van Dam, E.R. & den Hertog, D., 2009. "Enhancement of Sandwich Algorithms for Approximating Higher Dimensional Convex Pareto Sets," Other publications TiSEM e2255959-6691-4ef1-88a4-5, Tilburg University, School of Economics and Management.

    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:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-021-01022-1. 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.