Estimation of Theory-Implied Correlation Matrices

Abstract

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