This work proposes a framework to study the risk-benefit trade-off of quantitative easing (QE) for the consolidated government, integrating the central bank and treasury department. In a simple model with distortionary taxes, nominal frictions, and a zero lower bound, we characterize the optimal size of a QE program as equalizing the marginal benefit from stimulating output to the marginal cost of induced rollover risk for taxpayers. A conservative quantification of this trade-off suggests that QE programs in the US made a positive net present contribution to welfare.