This paper explores the impacts on an economy of a central bank changing the size and composition of its balance sheet. One of the ways in which such asset purchases could influence prices and demand is via portfolio balance effects. We develop and calibrate a simple OLG model in which risk-averse households hold money and bonds to insure against risk. Central bank asset purchases have the potential to affect households' choices by changing the composition and return of their asset portfolios. We find that the effect is weak, and that its size depends on how fiscal policy is conducted. That is not to say that the big expansion of central bank balance sheets in recent years has been ineffective. Our finding is rather that the portfolio balance channel evaluated in an environment of normally functioning (though nonetheless incomplete) asset markets is weak. That is not inconsistent with the evidence that large-scale asset purchases by central banks since 2008 have had significant effects, because those purchases were made when financial markets were, to varying extents, dysfunctional. Nonetheless our results are relevant to those purchases because they may be unwound in an environment where financial markets are no longer dysfunctional.