A Theory of Systemic Risk and Design of Prudential Bank Regulation

We examine the regulatory design problem of a central bank whose objective is to ensure an optimal level of individual as well as systemic risk of bank failure in an economy with possibly heterogeneous banks. We model systemic risk as the endogenously chosen correlation of returns on assets held by different banks. We demonstrate that in the presence of a negative externality of one bank's failure on the health of other banks, there is a systemic risk-shifting incentive where all banks undertake correlated investments. Thus, there is risk-shifting at the individual bank level as well as at the aggregate level. The latter phenomenon leads to systemic risk in the economy.