Banking and Optimal Capital Ratio in an Equilibrium Model∗

I address the question of optimal capital ratio in banking, particularly the fact that banks’ riskweighted capital are substantially larger than the stipulated reserve requirements by Bank of International Settlements. My contribution is to show that when the underlying values of borrowers are correlated, banks should hold positive risk-weighted capital, regardless of the regulation. I use a derived distribution for debt portfolios to show that intermediation in a debt market will outperform direct lending, even if intermediaries are allowed to default. The model used is a generalization of Williamson (1986), with Costly State Verification as asymmetric information. By using a factor model for the value of entrepreneurs’ projects, I introduce a positive probability for banks to default. It is shown that, in equilibrium, banks choose to hold capital reserves that are almost large enough to eliminate the expected auditing cost for their depositors. The reason is that auditing does not provide any utility and hence, the cake to be split between banks and depositors is enlarged by capital as an insurance against bad outcomes. It is also shown that the more correlation there is in the debt portfolio, the larger is the optimal share of risk-weighted capital. This could explain why small regional banks in Sweden often have more than twice the capital ratio of their nation-wide competitors. I am grateful for comments and suggestion by Hans Wijkander, Jean-Charles Rochet, Martin Holmén, and Ola Hammarlid. Financial support from Sparbankernas Forskningsstiftelse is gratefully acknowledged. Borlänge, Sweden, Tel: +46-8-786 9000, e-mail: [email protected]