Liquidity production is a central role of banks. We show that, under idealized conditions, high leverage is optimal for banks when there is a market premium for (socially valuable) liquid financial claims and no deviations from Modigliani and Miller (1958) due to agency problems, deposit insurance, taxes, or any other distortions. Our model can explain (i) why bank leverage increased over the last 150 years or so, (ii) why high bank leverage per se does not necessarily cause systemic risk, and (iii) why limits on the leverage of regulated banks impede their ability to compete with unregulated shadow banks. Our model indicates that MM’s debt-equity neutrality principle is inapplicable to banks. Because debt-equity neutrality assigns zero weight to the social value of liquidity, it is an inappropriately equity-biased baseline for assessing whether the high leverage ratios of real-world banks are excessive.