Building Diversified Portfolios that Outperform Out-of-Sample

31 Pages Posted: 28 Dec 2015 Last revised: 24 May 2016

See all articles by Marcos Lopez de Prado

Marcos Lopez de Prado

AQR Capital Management, LLC; Cornell University - Operations Research & Industrial Engineering; RCC - Harvard University

Date Written: May 23, 2016


This paper introduces the Hierarchical Risk Parity (HRP) approach. HRP portfolios address three major concerns of quadratic optimizers in general and Markowitz’s CLA in particular: Instability, concentration and underperformance.

HRP applies modern mathematics (graph theory and machine learning techniques) to build a diversified portfolio based on the information contained in the covariance matrix. However, unlike quadratic optimizers, HRP does not require the invertibility of the covariance matrix. In fact, HRP can compute a portfolio on an ill-degenerated or even a singular covariance matrix, an impossible feat for quadratic optimizers. Monte Carlo experiments show that HRP delivers lower out-of-sample variance than CLA, even though minimum-variance is CLA’s optimization objective. HRP also produces less risky portfolios out-of-sample compared to traditional risk parity methods.

A presentation can be found at

Keywords: Risk parity, tree graph, cluster, dendogram, linkage, metric space

JEL Classification: G0, G1, G2, G15, G24, E44

Suggested Citation

López de Prado, Marcos, Building Diversified Portfolios that Outperform Out-of-Sample (May 23, 2016). Journal of Portfolio Management, 2016, Forthcoming. Available at SSRN: or

Marcos López de Prado (Contact Author)

AQR Capital Management, LLC ( email )

One Greenwich Plaza
Greenwich, CT 06830
United States


Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States


RCC - Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States


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