Optimal Capital Requirement with Noisy Signals on Banking Risk

In this paper we analyze the optimal capital requirement in a model of banks with heterogeneous investment risks and asymmetric information. Asymmetric information prevents depositors from charging an actuarially-fair interest rate based on banking risk, and leads to cross-subsidization across banks. A capital requirement in the form of a leverage constraint reduces the investment of riskier banks and partially mitigates the pecuniary externality on deposit rates. When depositors and the policymaker have no information about banking risk, only a uniform leverage constraint is possible. In this case, the optimal leverage constraint is tighter than the first-best leverage ratio and strictly improves social welfare. When depositors and the policymaker observe a noisy signal of banking risk, a signal-based leverage constraint is possible. We demonstrate that the optimal signal-based leverage constraint is tighter when the signal has worse precision, rather than a larger level of expected risk.