Diversification, protection of liability holders and regulatory arbitrage

Any solvency regime for financial institutions should be aligned with the two fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. From these objectives we derive two normative requirements for capital adequacy tests, called surplus and num\'{e}raire invariance, respectively. We characterize capital adequacy tests that satisfy surplus and num\'{e}raire invariance, establish an intimate link between these requirements, and highlight an inherent tension between the ability to meet them and the desire to give credit for diversification.