The largest bank holding companies (BHCs) have hundreds (or thousands) of subsidiaries, with multiple kinds of businesses, in multiple states or countries. Diversity can be a strength in successful operations, but that same kind of complexity can present challenges in situations of distress. In the event of BHC default or insolvency, regulators may need to resolve the BHC and its constituent entities. Each entity individually could require some mix of cash infusion, outside purchase, consolidation with other subsidiaries, legal guarantees, or outright dissolution, all done in the context of resolving the whole BHC. The number, diversity, and distribution of subsidiaries within the hierarchy can therefore significantly complicate the resolution process.
We propose a set of related metrics intended to assess the structural complexity of the BHC. These proposed metrics focus on quotient spaces of the ownership hierarchy graph relative to partitions of the set of subsidiaries into categories such as charter type and regulatory jurisdiction.