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This paper analyses the effects of the European Central Bank's expanded asset purchase programme (APP) on yields and on the macroeconomy, and sheds some light on its transmission channels. It shows, first, that the January 2015 announcement of the programme has significantly and persistently reduced sovereign yields on long-term bonds and raised the share prices of banks that held more sovereign bonds in their portfolios. This evidence is consistent with versions of the portfolio rebalancing channel acting through the removal of duration risk and the relaxation of leverage constraints for financial intermediaries. It then presents a stylised macroeconomic model that incorporates the aforementioned transmission channels. The model suggests that the macroeconomic impact of the programme can be expected to be sizable.