Interest rates and financial fragility

How do the interest rates banks earn on their assets affect the susceptibility of the banking system to a self-fulfilling run by depositors? I study this question in a version of the model of Diamond and Dybvig (1983) with limited commitment and a non-trivial portfolio choice. I show that the relationship between these interest rates and financial fragility is often non-monotone. For example, a small increase in the return on illiquid investment (or a small increase in the term premium) may raise banks' susceptibility to a run, while a larger increase would make the banking system more stable. The same is true for changes in short-term rates, holding the longer-term rates fixed. I provide a precise characterization of these comparative statics of financial fragility.