Bank Capital Standards for Market Risk: A Welfare Analysis

We propose a simple model that is suitable for evaluating alternative bank capital regulatory proposals for market risk. Our model formalizes the conflict between bank objectives and regulatory goals. Banks' decisions represent a tension between their desire to exploit the deposit-insurance put option and their desire to preserve franchise value. Regulators seek to balance the social value of deposits in mediating transactions against the deadweight costs of failure resolution. Our social welfare criterion is standard: a weighted average agents' utilities.We demonstrate that banks do not incrementally alter their portfolio risk as the economic environment changes. Rather, banks either choose the minimal feasible risk or the maximal feasible risk. This pattern, in turn, drives regulatory decisions: The first goal of the regulator is to induce banks to choose the minimal risk level. For all nontrivial cases, unregulated banks fail to choose the first-best allocations. Traditional ex-ante capital requirements can induce banks to choose the socially-optimal level of portfolio risk, but the required capital is often inefficiently high. In contrast, variants of the Federal Reserve Board's precommitment proposal imply far smaller efficiency losses, and achieve allocations at or near the first-best for most reasonable model specifications. The ex-post penalties required for the optimal implementation of precommitment are not excessively large. The welfare gains from precommitment are even higher when the precommitment penalty function is precluded from sending banks into default. We conclude that state-contingent regulatory mechanisms, of which the precommitment approach is an example, offer the possibility of substantial gains in regulatory efficiency, relative to traditional state non-contingent regulation.