*** The average paydown rate of the GSEs' portfolios from 1997 to 2004 was about 25 percent. Even if outright sales of MBS were required to shrink portfolios, the proceeds would presumably be employed to redeem GSE debt.
In effect, a private investor whose holding of GSE debt has been redeemed receives, in exchange, either the mortgage-backed security sold by the GSE or other assets sold by those who acquire the mortgage-backed security.