IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p557-d746988.html
   My bibliography  Save this article

Tracking a Well Diversified Portfolio with Maximum Entropy in the Mean

Author

Listed:
  • Argimiro Arratia

    (Computer Science, Universitat Politècnica de Catalunya (UPC), 08024 Barcelona, Spain
    These authors contributed equally to this work.)

  • Henryk Gzyl

    (Centro de Finanzas IESA, Caracas 1010, Venezuela
    These authors contributed equally to this work.)

  • Silvia Mayoral

    (Business Administration, Universidad Carlos III de Madrid, 28903 Madrid, Spain
    These authors contributed equally to this work.)

Abstract

In this work we address the following problem: Having chosen a well diversified portfolio, we show how to improve on its return, maintaining the diversification. In order to achieve this boost on return we construct a neighborhood of the well diversified portfolio and find a portfolio that maximizes the return in that neighborhood. For that we use the method of maximum entropy in the mean to find a portfolio that yields any possible return up to the maximum return within the neighborhood. The implicit bonus of the method is that if the benchmark portfolio has acceptable risk and diversification, the portfolio of maximum return in that neighborhood will also have acceptable risk and diversification.

Suggested Citation

  • Argimiro Arratia & Henryk Gzyl & Silvia Mayoral, 2022. "Tracking a Well Diversified Portfolio with Maximum Entropy in the Mean," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:557-:d:746988
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/557/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/557/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    2. David Moreno & Rosa Rodr�guez, 2013. "Optimal diversification across mutual funds," Applied Financial Economics, Taylor & Francis Journals, vol. 23(2), pages 119-122, January.
    3. Anil Bera & Sung Park, 2008. "Optimal Portfolio Diversification Using the Maximum Entropy Principle," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 484-512.
    4. Desmoulins-Lebeault, François & Kharoubi-Rakotomalala, Cécile, 2012. "Non-Gaussian diversification: When size matters," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1987-1996.
    5. Azra Zaimovic & Adna Omanovic & Almira Arnaut-Berilo, 2021. "How Many Stocks Are Sufficient for Equity Portfolio Diversification? A Review of the Literature," JRFM, MDPI, vol. 14(11), pages 1-30, November.
    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. Al-Nassar, Nassar S. & Yousaf, Imran & Makram, Beljid, 2023. "Spillovers between positively and negatively affected service sectors from the COVID-19 health crisis: Implications for portfolio management," Pacific-Basin Finance Journal, Elsevier, vol. 79(C).

    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. Lassance, Nathan & Vrins, Frédéric, 2023. "Portfolio selection: A target-distribution approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 302-314.
    2. Yuri Salazar Flores & Adan Diaz‐Hernandez & Oralia Nolasco‐Jauregui & Luis Alberto Quezada‐Tellez, 2025. "A portfolio diversification measure in the unit interval: A coherent and practical approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 2771-2785, July.
    3. Francesco Cesarone & Rosella Giacometti & Manuel Luis Martino & Fabio Tardella, 2023. "A return-diversification approach to portfolio selection," Papers 2312.09707, arXiv.org.
    4. Reis, Pedro Nogueira & Pinto, António Pedro Soares, 2024. "Unlocking portfolio resilient and persistent risk: A holistic approach to unveiling potential grounds," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    5. Peralta, Gustavo & Zareei, Abalfazl, 2016. "A network approach to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 157-180.
    6. Kang, Yan-li & Tian, Jing-Song & Chen, Chen & Zhao, Gui-Yu & Li, Yuan-fu & Wei, Yu, 2021. "Entropy based robust portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    7. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    8. Georg Mainik & Georgi Mitov & Ludger Ruschendorf, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Papers 1505.04045, arXiv.org.
    9. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The RQE-CAPM : New insights about the pricing of idiosyncratic risk," CIRANO Working Papers 2021s-28, CIRANO.
    10. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2023. "Unifying Portfolio Diversification Measures Using Rao’s Quadratic Entropy," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(4), pages 769-802, December.
    11. Prateek SHARMA, 2017. "Economic value of portfolio diversification: Evidence from international multi-asset portfolios," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(613), W), pages 33-42, Winter.
    12. Wahid, Abdul & Kowalewski, Oskar, 2025. "Sustainable portfolio optimization: A multi-class framework for eco-friendly stocks," Research in International Business and Finance, Elsevier, vol. 76(C).
    13. Simbarashe Brandon MATANHIKE & Newman WADESANGO & Lovemore SITSHA, 2025. "The Impact of Gold Coin Investments on Portfolio Diversification and Risk Management in the Zimbabwean Financial Markets," CECCAR Business Review, Body of Expert and Licensed Accountants of Romania (CECCAR), vol. 6(8), pages 69-82, August.
    14. Alfonso Valero, 2024. "Diversification strategies for indirect real estate. Intersection of business, economics, and society in shanghai mixed-use developments," SN Business & Economics, Springer, vol. 4(10), pages 1-26, October.
    15. Dilip B. Madan & King Wang, 2023. "Measuring Dependence in a Set of Asset Returns," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 363-385, June.
    16. Alessandro Avellone & Ilaria Foroni & Chiara Pederzoli, 2025. "Minimum capital requirement portfolios according to the new Basel framework for market risk," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 39(2), pages 171-192, June.
    17. David E. Allen & Michael McAleer & Robert Powell & Abhay K. Singh, 2013. "A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500," JRFM, MDPI, vol. 6(1), pages 1-25, October.
    18. Hatemi-J, Abdulnasser & Hajji, Mohamed Ali & El-Khatib, Youssef, 2022. "Exact solution for the portfolio diversification problem based on maximizing the risk adjusted return," Research in International Business and Finance, Elsevier, vol. 59(C).
    19. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Econometrics and Statistics 2/11, University of Cologne, Institute of Econometrics and Statistics.
    20. Xia Han & Liyuan Lin & Ruodu Wang, 2022. "Diversification quotients: Quantifying diversification via risk measures," Papers 2206.13679, arXiv.org, revised Jul 2024.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:gam:jmathe:v:10:y:2022:i:4:p:557-:d:746988. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.