Deposit Franchise Runs

Abstract

We model a new type of bank run, a deposit franchise run. Banks pay below-market rates on deposits, which makes the deposit franchise a valuable asset. For a bank to keep this value, deposits must stay in the bank; if they leave, their value is lost to the bank. This makes the deposit franchise a runnable asset. Unlike Diamond-Dybvig runs, deposit franchise runs can occur even if the bank's loans are fully liquid. Since the deposit franchise value increases with interest rates, a run is more harmful, and hence more likely, when rates are high. To avoid runs, banks can shorten the duration of their assets, but this can make them insolvent if interest rates fall. Avoiding both runs and insolvency requires additional capital in proportion to the value of the uninsured portion of the deposit franchise. We use our model to estimate deposit franchise values and show how to identify vulnerable banks in the context of the 2023 Regional Bank Crisis.