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

26 Pages Posted: 22 Mar 2024

See all articles by Alexandre Antonov

Alexandre Antonov

Abu Dhabi Investment Authority; ADIA

Alex Lipton

Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT)

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; Abu Dhabi Investment Authority; True Positive Technologies

Date Written: March 5, 2024

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 the analytics is an HRP portfolio construction criterion which selects assets and clusters minimizing the analytical portfolio variance. We confirm our theoretical results with numerous numerical experiments. Our calculation technique can be also used in other areas of portfolio optimization.

Keywords: Trading strategy, portfolio allocation, Markowitz optimisation, Hierarchical Risk Parity, Clustered Optimisation, optimisation weights noise

JEL Classification: G0, G1, G2, G11, E44, E47

Suggested Citation

Antonov, Alexandre and Lipton, Alex and López de Prado, Marcos and López de Prado, Marcos, Overcoming Markowitz's Instability with the Help of the Hierarchical Risk Parity (HRP): Theoretical Evidence (March 5, 2024). Available at SSRN: https://ssrn.com/abstract=4748151 or http://dx.doi.org/10.2139/ssrn.4748151

Alexandre Antonov (Contact Author)

Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates

ADIA ( email )

211 Corniche
abu Dhabi
United Arab Emirates

Alex Lipton

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, Jerusalem 91905
Israel

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Marcos López de Prado

Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates

HOME PAGE: http://www.adia.ae

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

HOME PAGE: http://www.orie.cornell.edu

True Positive Technologies ( email )

NY
United States

HOME PAGE: http://www.truepositive.com

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