IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2307.04045.html
   My bibliography  Save this paper

Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation

Author

Listed:
  • Alexander Nikiporenko

Abstract

A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm.

Suggested Citation

  • Alexander Nikiporenko, 2023. "Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation," Papers 2307.04045, arXiv.org.
    • Handle: RePEc:arx:papers:2307.04045
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2307.04045
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Wanda J. Orlikowski & Jack J. Baroudi, 1991. "Studying Information Technology in Organizations: Research Approaches and Assumptions," Information Systems Research, INFORMS, vol. 2(1), pages 1-28, March.
    3. Niszczota, Paweł & Białek, Michał, 2021. "Women oppose sin stocks more than men do," Finance Research Letters, Elsevier, vol. 41(C).
    4. 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.
    5. Hendershott, Terrence & Moulton, Pamela C., 2011. "Automation, speed, and stock market quality: The NYSE's Hybrid," Journal of Financial Markets, Elsevier, vol. 14(4), pages 568-604, November.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. 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).
    8. 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.
    9. Hong, Harrison & Kacperczyk, Marcin, 2009. "The price of sin: The effects of social norms on markets," Journal of Financial Economics, Elsevier, vol. 93(1), pages 15-36, July.
    10. Mark Buchanan, 2015. "Physics in finance: Trading at the speed of light," Nature, Nature, vol. 518(7538), pages 161-163, February.
    11. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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).
    5. Gupta, Pankaj & Mittal, Garima & Mehlawat, Mukesh Kumar, 2013. "Expected value multiobjective portfolio rebalancing model with fuzzy parameters," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 190-203.
    6. Luis Ferruz & Fernando Muñoz & María Vargas, 2012. "Managerial Abilities: Evidence from Religious Mutual Fund Managers," Journal of Business Ethics, Springer, vol. 105(4), pages 503-517, February.
    7. 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.
    8. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    9. Wang, Shaolin & Cheng, Ho Cheung & Wang, Jianli & Yick, Ho Yin, 2025. "The performance of ESG portfolios: Evidence from the Chinese market under COVID-19," Economic Modelling, Elsevier, vol. 143(C).
    10. A. Garcia-Bernabeu & J. V. Salcedo & A. Hilario & D. Pla-Santamaria & Juan M. Herrero, 2019. "Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA," Complexity, Hindawi, vol. 2019, pages 1-12, December.
    11. Engau, Alexander, 2009. "Tradeoff-based decomposition and decision-making in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 199(3), pages 883-891, December.
    12. Benita, Francisco & López-Ramos, Francisco & Nasini, Stefano, 2019. "A bi-level programming approach for global investment strategies with financial intermediation," European Journal of Operational Research, Elsevier, vol. 274(1), pages 375-390.
    13. Shumi Akhtar & Maria Jahromi & Tom Smith, 2017. "Risk, return and mean-variance efficiency of Islamic and non-Islamic stocks: evidence from a unique Malaysian data set," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 57(1), pages 3-46, March.
    14. 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.
    15. Bilbao-Terol, Amelia & Arenas-Parra, Mar & Cañal-Fernández, Verónica, 2016. "A model based on Copula Theory for sustainable and social responsible investments," Revista de Contabilidad - Spanish Accounting Review, Elsevier, vol. 19(1), pages 55-76.
    16. Yue Qi & Ralph E. Steuer, 2020. "On the analytical derivation of efficient sets in quad-and-higher criterion portfolio selection," Annals of Operations Research, Springer, vol. 293(2), pages 521-538, October.
    17. 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).
    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. Niszczota, Paweł & Błaszczyński, Jakub, 2024. "Hard to digest investments: People oppose investment in both conventional and cultured meat producers," Ecological Economics, Elsevier, vol. 218(C).
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2307.04045. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.