How does heterogeneity in banks’ interest-rate risk exposure shape monetary policy transmission? We develop a quantitative macroeconomic model of heterogeneous banks to answer this question. We establish an irrelevance result: differences in interest-rate risk exposure between fixed- and variable-rate banking systems matter for transmission only when bank solvency concerns become relevant. Calibrating the model to the euro area, we show that idiosyncratic default risk pushes a substantial share