We introduce a model of the banking sector that formally incorporates a buffer function of capital. Heterogeneous banks choose their portfolio risk, bank size, and capital holdings. Banks voluntarily hold equity when the buffer effect against the risk of default outweighs the cost advantages of debt financing. In this setting, banks with lower monitoring costs are larger, choose riskier portfolios, and have less equity. Moreover, binding capital requirements or levies on bank borrowing are shown to make higher-risk portfolios more attractive. Accounting for banks' interior capital choices can thus explain why higher capital ratios incentivize banks to undertake riskier projects
