Estimation of Theory-Implied Correlation Matrices

18 Pages Posted: 20 Nov 2019

See all articles by Marcos Lopez de Prado

Marcos Lopez de Prado

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

Date Written: November 9, 2019


Correlation matrices are ubiquitous in finance. Some key applications include portfolio construction, risk management, and factor/style analysis. Correlation matrices are usually estimated from historical empirical observations or derived from historically estimated factors. It is widely acknowledged that empirical correlation matrices: (a) have poor numerical properties that lead to unreliable estimators; and (b) have poor predictive power. Additionally, factor-based correlation matrices have their own caveats. In particular, estimated factors are typically non-hierarchical and do not allow for interactions at different levels. This contravenes the fact that financial instruments typically exhibit a nested cluster structure (e.g., MSCI’s GICS levels 1-4).

This paper introduces a machine learning (ML) algorithm to estimate forward-looking correlation matrices implied by economic theory. Given a particular theoretical representation of the hierarchical structure that governs a universe of securities, the method fits the correlation matrix that complies with that theoretical representation of the future. This particular use case demonstrates how, contrary to popular perception, ML solutions are not black-boxes, and can be applied effectively to develop and test economic theories.

Keywords: hierarchical clustering, economic classification, correlation estimation, knowledge graph

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

Suggested Citation

López de Prado, Marcos and López de Prado, Marcos, Estimation of Theory-Implied Correlation Matrices (November 9, 2019). Available at SSRN: or

Marcos López de Prado (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States


Abu Dhabi Investment Authority ( email )

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


True Positive Technologies ( email )

United States


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