On the relationship between borrower and bank risk

We use tools from survival analysis to study the equilibrium probability of bank failure in a model with imperfect correlation in loan defaults where a systematic risk factor and idiosyncratic frailty factors govern borrower credit worth. We derive several surprising results: in equilibrium, a bank can be more likely to fail with less risky than with more risky borrowers. In addition, the equilibrium relationship between borrower and bank risk can be fundamentally altered by a greater dispersion of the frailty factors, similar to how mixing items of different durability can fundamentally change the overall aging pattern.