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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
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    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.
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    Cited by:

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