Consider a 1,000,000 (for convenience) GNMA pass-through security consisting of fresh 30-year fixed rate, fully amortizing mortgages, with a WAC of 7%, and servicing/guarantee fees totaling 0.5%. Allow for a general PSA prepayment rate.
a. Construct an IO/PO stripped MBS from this MPT above, showing the total cash flows to investors of each piece. For simplicity, price each piece so that the IRR at PSA 165 equals the MPT coupon.
You must show your amortization table at a 165 PSA.
b. Suppose you bought the tranches at the rice obtained in part a., but that mortgage rates (MR) suddenly change just after the purchase (just after t=0). Make a graph of the market value of the MPT and each piece as the MR varies from 2% to 12% in steps of 1%. To simplify, use MR less fees as the discount rate (DR) in your calculation. Also, to make things a little more realistic, assume that prepayment PSA changes with MR as
PSA = 165*max(1,WAC/MR).
Hand in your amortization table for the case when MR=7%.
c. Explain the shape of each of the three curves you obtain in part b.