This paper studies how central banks' asset purchases (APs) of nominal public debt affect perceived default-inflation risks when investors learn from market prices. We design a stylised model of monetary-fiscal interactions where taxes are distortionary and risk-neutral investors trade bonds subject to position bounds. In our framework, APs are either irrelevant or reduce social welfare in the absence of beliefs heterogeneity or position bounds. With heterogeneous beliefs and position bounds we show that a positive amount of APs is instead optimal and increases welfare. This happens through two main channels. First, by crowding out the asset demand of more pessimistic agents, APs have a positive price effect which lowers interest rates, debt service and tax distortions in all states. Second, APs have a negative effect because they increase the precision of market information in default states. We show that the net welfare effect of the two channels is positive when APs are small, and becomes negative as APs increase and the precision effect eventually overturns the benefits of leveraging on optimism.