Diversification, protection of liability holders and regulatory arbitrage

TL;DR

This paper characterizes surplus-invariant capital adequacy tests for financial institutions, highlighting the tension with diversification and the importance of invariance across jurisdictions to ensure stability and protection of liability holders.

Contribution

It provides a complete characterization of surplus-invariant, convex capital adequacy tests and explores their relationship with numéraire invariance, addressing key regulatory objectives.

Findings

Characterization of surplus-invariant, convex capital adequacy tests

Identification of tension between surplus-invariance and diversification

Link between surplus-invariance and numéraire invariance

Abstract

Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider surplus-invariant capital adequacy tests, i.e. tests that do not depend on the surplus of a financial institution. We provide a complete characterization of closed, convex, surplus-invariant capital adequacy tests that highlights an inherent tension between surplus-invariance and the desire to give credit for diversification. The second objective leads to requiring consistency of capital adequacy tests across jurisdictions. Of particular importance in this respect are capital adequacy tests that remain invariant under a change of num\'{e}raire. We establish an intimate link between surplus- and num\'{e}raire invariant tests.