Banking on Uninsured Deposits
We model the impact of interest rates on the liquidity risk of banks. Banks hedge the interest rate risk of their assets with their deposit franchise: when rates rise the value of their assets falls, but the value of their deposit franchise rises. Yet the deposit franchise is only valuable if deposits remain in the bank. This makes the deposit franchise runnable if deposits are uninsured. We show there is no run equilibrium at low interest rates, but a run equilibrium emerges as rates rise. This is because the value of the deposit franchise rises with rates, making a run more destructive, and hence more likely. To prevent a run, the bank needs to keep the value of its uninsured deposit franchise from exceeding its equity. It can do so by shortening the duration of its assets, so that their value falls less if rates rise. However, this undoes the bank’s interest rate hedge, which can make it insolvent if rates fall. The uninsured deposit franchise therefore poses a risk management dilemma: the bank cannot simultaneously hedge its interest rate and liquidity risk exposures. We show banks can address the dilemma by buying claims with option-like payoffs to interest rates, or by raising additional capital as interest rates rise. These strategies minimize the additional capital needed to prevent a run if rates rise and avoid insolvency if rates fall.