I study optimal monetary policy in a simple New Keynesian model with portfolio adjustment costs. Purchases of long-term debt by the central bank (quantitative easing; ‘QE’) alter the average portfolio return and hence influence aggregate demand and inflation. The central bank chooses the short-term policy rate and QE to minimise a welfare-based loss function under discretion. Adoption of QE is rapid, with large-scale asset purchases triggered when the policy rate hits the zero bound, consistent with observed policy responses to the Global Financial Crisis. Optimal exit is gradual. Despite the presence of portfolio adjustment costs, a policy of ‘permanent QE’ in which the central bank holds a constant stock of long-term bonds does not improve welfare.