The chart below shows fixed rate agency MBS issuance since the financial crisis. With the Fed taking out some half of this gross issuance (see post), one would think there should be paper left for other investors, right?
Wrong. The net (vs. the gross) issuance of fixed rate agency MBS has actually been negative. That's in part because the GSEs are shrinking their balance sheets. In fact they've been told to start shrinking mortgage portfolios by 15% a year (see discussion). The GSEs issue new bonds slower than the old bonds amortize due to mortgage prepayments, producing a negative net.
As agency bond issuance declines, the Fed purchases are picking up (locking these securities away - probably to maturity). The amount of MBS bonds in the market will begin contracting rapidly going forward.