We propose a theory of banking in which banks cannot perfectly control deposit flows. Facing uninsurable loan and deposit shocks, banks dynamically manage lending, wholesale funding, deposits, and equity. Deposits create value by lowering funding costs. However, when the bank is undercapitalized and at risk of breaching leverage requirements, the marginal value of deposits can turn negative as deposit inflows, by raising leverage, increase the likelihood of costly equity issuance. Banks' inability to fully control leverage distinguishes them from nondepository intermediaries. Our model suggests a reevaluation of leverage regulations and offers new perspectives on banking in a low‐interest‐rate environment.

Corporate credit lines are drawn more heavily when funding markets are stressed. This elevates expected bank funding costs. We show that credit supply is dampened by the associated debt‐overhang cost to bank shareholders. Until 2022, this impact was reduced by linking the interest paid on lines to a credit‐sensitive reference rate like the London interbank offered rate (LIBOR). We show that transition to risk‐free reference rates may exacerbate this friction. The adverse impact on credit supply is offset if drawdowns are expected to be deposited at the same bank, which happened at some of the largest banks during the global financial crisis and COVID recession.