Hierarchical PCA and Modeling Asset Correlations

Abstract

Modeling cross-sectional correlations between thousands of stocks, acrosscountries and industries, can be challenging. In this paper, we demonstratethe advantages of using Hierarchical Principal Component Analysis (HPCA)over the classic PCA. We also introduce a statistical clustering algorithmto identify homogeneous clusters of stocks or “synthetic sectors”. We applythese methods to study cross-sectional correlations in the US, Europe, China,and Emerging Markets.

Keywords: correlations, factor models, hierarchical PCA, statistical clusters

JEL Classification: C31, C32, C58, C01, C61