We show that maturity transformation does not expose banks to significant interest rate risk—it actually hedges banks’ interest rate risk. We argue that this is driven by banks’ deposit franchise. Banks incur large operating costs to maintain their deposit franchise, and in return get substantial market power. Market power allows banks to charge depositors a spread by paying deposit rates that are low and insensitive to market rates. The deposit franchise therefore works like an interest rate swap where banks pay the fixed-rate leg (the operating costs) and receive the floating-rate leg (the deposit spread). To hedge the deposit franchise, banks must therefore hold long-term fixed-rate assets; i.e., they must engage in maturity transformation. Consistent with this view, we show that banks’ aggregate net interest margins have been highly stable and insensitive to interest rates over the past six decades, and that banks’ equity values are largely insulated from monetary policy shocks. Moreover, in the cross section we find that banks match the interest-rate sensitivities of their income and expenses one- for-one, and that banks with less sensitive interest expenses hold substantially more long-term assets. Our results imply that forcing banks to hold only short-term assets (“narrow banking”) would make banks unhedged and, more broadly, that the deposit franchise is what allows banks to lend long term.