Consider an agency MBS pool consisting of $300m of 15 year FRMs with a mortgage coupon rate of 4.5%. Mortgage payments are monthly. Assume a servicing and guarantee fee of 50bp per year (combined) for this pool.

Assume that this pool prepays at 200% PSA throughout its life.

A. What is the net coupon rate paid to MBS investors?

B. What is the SMM on this pool in the first month? What is the peak SMM for this pool over its life? Show your calculations. Also provide a brief conceptual explanation of what SMM means.

C. Based on the information described above, build a spreadsheet that completely builds out all the cashflows from this MBS pool. Your spreadsheet should clearly indicate the total amount of principal payments, interest payments, servicing and guarantee payments, and prepayments, for each month over the life of the pool.

D.Assuming a discount rate of 5% a year (4% / 12 per month), what is the NPV of this mortgage pool? Is this pool trading at a discount or a premium? Why?

E. If the discount rate falls to 4%, what is the new NPV of the pool, assuming there is no change in the SMM.

F. Do you think this assumption that the SMM does not change is realistic? Why?

G.Now (under original assumption of discount rate as in part D) assume that all borrowers that have not prepaid within the first five 5 years default on their mortgages at year 5 (i.e. after 60 months). What is the credit loss to you as an investor? Would these defaults be good news or bad news for you, or would you be indifferent? Explain intuitively (no calculations required).

H.[Optional Bonus Question] Calculate the new NPV of the pool under the assumption in part G, assuming a discount rate of 5% per year. Assume for simplicity that face value of the mortgages that default is returned to the investor without any time lag. Compare your answer to what you calculated in part D, and confirm that it is consistent with your answer and explanation from part G above.