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Abstract:
I model the capital-risk-profit relation in a simultaneous three-equation model. The results show no systematic relation between risk and profit which is consistent with the view that risk is chosen optimally. Taking this as given, the equilibrium relation between capital and profit depends on the definition of capital. First, the evidence suggests that banks manage regulatory capital to maximise profit - leading to no systematic relation between regulatory capital and profit. Second, capital regulations divert banks' attention away from and/or limit their ability to manage economic capital - leading to a significant negative relation between economic capital and profit. Taken together, these findings explain why banks begrudge regulators for setting capital limits yet continue to hold regulatory capital well in excess of minimum requirements.

Banking, profitability, capital, risk, endogeneity

Abstract:
The orthodox assumption in the banking literature is that capital requirements are a binding constraint on banking behavior. This is in conflict with the empirical observation that banks hold a buffer of capital well in excess of the minimum requirements. This paper develops a model where capital is endogenously determined within a profit-maximizing equilibrium. Optimality involves balancing the reduction in expected costs associated with regulatory breach with the excess cost of financing from increasing capital. We demonstrate that when the equilibrium probability of regulatory breach is less than one-half, banks are expected to hold precautionary capital.