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

Alexandre Antonov, Alexander Lipton and Marcos Lopez de Prado

Chapter 3 in Transactions of ADIA Lab:Interdisciplinary Advances in Data and Computational Science, 2025, pp 87-121 from World Scientific Publishing Co. Pte. Ltd.

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.

Keywords: Computational Science; Data Science; AI Applications; Climate Science; Medical Imaging; Sustainability; Interdisciplinary Research; Data Science; Mathematical and Quantitative Finance (search for similar items in EconPapers)
JEL-codes: C45 C63 G11 Q54 (search for similar items in EconPapers)
Date: 2025
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