The cyclical behavior of optimal bank capital - Estrella, Arturo (Journal of Banking & Finance, 2004)
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 stochastic 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. Analysis of this pattern suggests that a regulatory minimum requirement based on var, if binding, is likely to be procyclical. The model points to 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. US commercial bank data since 1984 are generally consistent with the model.