The Cyclical Behavior of Optimal Bank Capital

This paper presents a dynamic model of optimal bank capital in which the bank optimizes over costs associated with failure, holding capital, and flows of external capital. The solution to the infinite-horizon optimization problem is related to period-by-period value-at-risk (var) in which the optimal probability of failure is endogenously determined. Over a cycle, var is positively correlated with optimal flows of external capital, but negatively correlated with optimal net changes in capital and the optimal level of total capital. Thus, a regulatory minimum requirement based on var, if binding, is likely to be procyclical. The model suggests several ways of reducing this problem. For example, a var-based requirement makes more sense if it is applied to external capital flows than if it is applied to the total level of capital. Call report data suggest that U.S. commercial bank behavior since 1984 is consistent with the model. JEL Codes: G-21, G-28 *Federal Reserve Bank of New York, 33 Liberty Street, New York, NY 10045, USA, e-mail [email protected]. The views expressed are the author’s and do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System. I thank seminar participants at the Federal Reserve Bank of New York and the Sveriges Riksbank, and Gijoon Hong for excellent research support.