What configuration of asset returns will make the banking system most susceptible to a self-fulfilling run? 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 the returns on banks´ assets and financial fragility is often non-monotone: a higher return may make banks either more or less susceptible to a run by depositors. The same is true for changes in the liquidation cost and the term premium. I derive precise conditions under which changes in each of these returns increase or decrease financial fragility.