IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789819813049_0003.html
   My bibliography  Save this book chapter

Overcoming Markowitz’s Instability with the Help of the Hierarchical Risk Parity (HRP): Theoretical Evidence

In: Transactions of ADIA Lab Interdisciplinary Advances in Data and Computational Science

Author

Listed:
  • Alexandre Antonov
  • Alexander Lipton
  • Marcos Lopez de Prado

Abstract

In this paper, we compare two methods of portfolio allocation: the classical Markowitz one and the hierarchical risk parity (HRP) approach. We derive analytical values for the noise of allocation weights coming from the estimated covariance. We demonstrate that the HRP is indeed less noisy (and thus more robust) w.r.t. the classical Markowitz. The second part of the paper is devoted to a detailed analysis of the optimal portfolio variance for which we derive analytical formulas and theoretically demonstrate the superiority of the HRP w.r.t. to the Markowitz optimization.We also address practical outcomes of our analytics. The first one is a fast estimation of the confidence level of the optimization weights calculated for a single (real-life) scenario. The second practical usefulness of analytics is an HRP portfolio construction criterion that selects assets and clusters, minimizing the analytical portfolio variance. We confirm our theoretical results with numerous numerical experiments.Our calculation technique can also be used in other areas of portfolio optimization.

Suggested Citation

  • Alexandre Antonov & Alexander Lipton & Marcos Lopez de Prado, 2025. "Overcoming Markowitz’s Instability with the Help of the Hierarchical Risk Parity (HRP): Theoretical Evidence," World Scientific Book Chapters, in: Horst Simon (ed.), Transactions of ADIA Lab Interdisciplinary Advances in Data and Computational Science, chapter 3, pages 87-121, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789819813049_0003
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/pdf/10.1142/9789819813049_0003
    Download Restriction: Ebook Access is available upon purchase.
    File URL: https://www.worldscientific.com/doi/abs/10.1142/9789819813049_0003
    Download Restriction: Ebook Access is available upon purchase.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Computational Science; Data Science; AI Applications; Climate Science; Medical Imaging; Sustainability; Interdisciplinary Research; Data Science; Mathematical and Quantitative Finance;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

    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:wsi:wschap:9789819813049_0003. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/page/worldscibooks .

    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.