The Complexity of Bank Holding Companies: A Topological Approach

Abstract

We develop metrics to assess the complexity of a bank holding company (BHC), based on its ownership structure. Large BHCs have intricate ownership hierarchies involving hundreds or even thousands of legal entities that may contribute to increased operational risk and greater opacity. Our measures are mathematically grounded, intuitive, and easy to implement. They may be particularly useful in the context of resolution, where regulators often face significant time pressure and coordination challenges. We use regulatory filing data from the Federal Reserve to validate the measures, demonstrating that they provide a useful complement to balance sheet information in assessing BHC complexity. Notably, the proposed measures are highly correlated with existing complexity indicators that are not based on organizational structure and are less correlated with size than these existing complexity measures. We show that the proposed measures provide additional explanatory power for the regulatory indicators, even after controlling for size.

Keywords: Orderly Resolution, Supervisory Coordination, Opacity, Graph Quotient, Edge Contraction, Y-15

JEL Classification: G21, G28, G33, C81