Motivated by the regional bank crisis of 2023, we model the impact of interest rates on the liquidity risk of banks. Prior work shows that banks hedge the interest rate risk of their assets with their deposit franchise: when interest rates rise, the value of the assets falls but the value of the deposit franchise rises. Yet the deposit franchise is only valuable if depositors remain in the bank. This creates run incentives for uninsured depositors. We show that a run equilibrium is absent at low interest rates but appears when rates rise because the deposit franchise comes to dominate the value of the bank. The liquidity risk of the bank thus increases with interest rates. We provide a formula for the bank’s optimal risk management policy. The bank should act as if its deposit rate is more sensitive to market rates than it really is, i.e., as if its “deposit beta” is higher. This leads the bank to shrink the duration of its assets. Shortening duration has a downside, however: it exposes the bank to insolvency if interest rates fall. The bank thus faces a dilemma: it cannot simultaneously hedge its interest rate risk and liquidity risk exposures. The dilemma disappears only if uninsured deposits do not contribute to the deposit franchise (if they have a deposit beta of one). The recent growth of low-beta uninsured checking and savings accounts thus poses stability risks to banks. The risks increase with interest rates and are amplified by other exposures such as credit risk. We show how they can be addressed with an optimal capital requirement that rises with interest rates.