The Complexity of Bank Holding Companies: A Topological Approach

Working Paper: NBER ID: w23755

Authors: Mark D. Flood; Dror Y. Kenett; Robin L. Lumsdaine; Jonathan K. Simon

Abstract: Large bank holding companies (BHCs) are structured into intricate ownership hierarchies involving hundreds or even thousands of legal entities. Each subsidiary in these hierarchies has its own legal form, assets, liabilities, managerial goals, and supervisory authorities. In the event of BHC default or insolvency, regulators may need to resolve the BHC and its constituent entities. Each entity individually will require some mix of cash infusion, outside purchase, consolidation with other subsidiaries, legal guarantees, and outright dissolution. The subsidiaries are not resolved in isolation, of course, but in the context of resolving the consolidated BHC at the top of the hierarchy. The number, diversity, and distribution of subsidiaries within the hierarchy can therefore significantly ease or complicate the resolution process. We propose a set of related metrics intended to assess the complexity of the BHC ownership graph. These proposed metrics focus on the graph quotient relative to certain well identified partitions on the set of subsidiaries, such as charter type and regulatory jurisdiction. The intended measures are mathematically grounded, intuitively sensible, and easy to implement. We illustrate the process with a case study of one large U.S. BHC.

Keywords: bank holding companies; complexity; resolution; network analysis; graph theory

JEL Codes: C02; C81; D85; G21; G28; G3; L22


Causal Claims Network Graph

Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.


Causal Claims

CauseEffect
Complexity of BHC ownership structure (L22)Resolution process complexity (C69)
Number of links of ownership and control (G32)Complexity of resolution (D74)
Complexity of BHC ownership structure (L22)Effectiveness of resolution strategies (D74)

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