A Theory of Systemic Risk and Design of Prudential Bank Regulation

Abstract

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.

Current regulation is based only on a bank's own risk and ignores the externalities of the bank's actions. Such regulation may leave the collective risk-shifting incentive unattended, and can, in fact, accentuate systemic risk. We show that a policy of unconditionally bailing out failed banks eliminates the strategic benefit to the surviving banks, and in turn, eliminates the ex-ante incentive of banks to make uncorrelated investments. Similarly, a policy that exhibits greater forbearance towards banks upon joint failure than in individual failures has a negative feedback effect and induces banks to undertake correlated investments.

Prudential regulation should thus operate at a collective level, and regulate each bank as a function of its joint risk with other banks as well. We show that optimal regulation consists of (i) a rescue policy that conducts bail out of only the 'essential' or 'too-big-to-fail' banks OR conducts bank sales upon individual failures and exhibits little forbearance (if any) upon joint failure; and (ii) a capital adequacy requirement that is increasing in the individual risk of each bank as well as in the correlation of banks' risks.

Keywords: Systemic risk, Risk-shifting, Capital adequacy, Bank regulation, Banking

JEL Classification: G21, G28, G38, E58, D62