8.

In this question, you will create a CMO structure, price 2 tranches and compare each tranches exposure to prepayment risk.

Assume that the WAC is 3.50%, the WAM is 360, and that the PSA is 150.

Payment rules:

1. For payment of periodic coupon interest: Disburse periodic coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the period.

2. For disbursement of principal payments: Disburse principal payments to tranche A until it is paid off completely. After tranche A is paid off completely, disburse principal payments to tranche B until it is paid off completely. After tranche B is paid off completely, disburse principal payments to tranche C until it is paid off completely. After tranche C is paid off completely, disburse principal payments to tranche D until it is paid off completely.

1. Provide the balance and complete set of cash flows to Tranches A and D over the lifetime of the CMO. Be sure to separate Principal payment from Interest payment. (15 points)

Your answer should look like the following.

	TRANCHE A			TRANCHE D
Month	Balance	Principal Payment	Interest Payment	Balance	Principal Payment	Interest Payment
1
2

2. We will now value Tranche A and Tranche D. We have the cash flows. We need the discount rates. For this, we are creating a yield curve for these cash flows.

1 Mo	2 Mo	3 Mo	6 Mo	1 Yr	2 Yr	3 Yr	5 Yr	7 Yr	10 Yr	20 Yr	30 Yr
4.61%	4.62%	4.56%	4.52%	4.35%	4.22%	4.17%	4.16%	4.25%	4.36%	4.66%	4.89%

Since we need a discount rate for each cash flow, we need 360 discount rates. We will do this by interpolation as we did when we bootstrapped the yield curve. For example, we need the rate for cash flows at times 4-month and 5-month. Since, in my case, the 3-month rate and the 6-month rate are equal, I would simply use 4.85%. If the rates had been different, say the 6-month rate had been 4.88%. The rate on the 4-month rate would then be: Rate of 3-month + 1 equal step = 4.85% + (4.88% - 4.85%) / 3 = 4.85% + 0.03% / 3 = 4.86%. The rate on the 5-month rate would then be: Rate of 3-month + 2 equal steps = 4.85% + 2 * (4.88% - 4.85%) / 3 = 4.85% + 2 * 0.03% / 3 = 4.87%. To check you understand the process, heres the 7-month rate using the correct 6-month rate of 4.85%. 7-month rate is 4.85% + 1 * (4.71% - 4.85%) / 6 = 4.8267% (where 4.71% is the 1-Year rate, i.e., the next known rate). Similarly, the rate on the 11-month will be 4.85% + 5 * (4.71% - 4.85%) / 6 = 4.7333%. Note that the number of months the rates are apart later on in the series can be large. There are, for example, 120 months between the 10-year rate and the 20-year rate.

You should create these 360 rates in a column so that they can be easily used in combination with the CMO tranches cash flows that are already in columns.

Now, we can compute the present values of each of the cash flows paid to the tranches. The cash flow received is the sum of any principal and interest received in that month by the tranche. Remember that the rates you computed above are APRs so the proper way to discount, say, $1,000 received in Month 6 where the 6-month rate is 4.85% is to compute: $1,000 / (1 + 0.0485 / 12) ^ 6. Same, $5,000 received in 2 years where the 2-year rate is 4.45% has a present value of $5,000 / (1 + 0.0445 / 12) ^ 24.

What is the Present Value of Tranche A? What is the Present Value of Tranche D? (15 points)

3. Lets assume now that market conditions change and a more appropriate PSA level for these tranches is 100 PSA according to the chief economist of your group. Recompute the present values for Tranche A and Tranche D. Of course, the change in PSA will have changed the cash flows. We assume here that the discount rates do not change. Since you now have the new present values, compute the percentage changes in value for both tranches. The percentage change is set up as: (PV @ 100 PSA PV @ 150 PSA) / PV @ 150 PSA. (10 points)

4. Compare the percentage returns of Tranche A and Tranche D. Is this what you expected? How is this related to prepayment risk and how the CMO structure shifts prepayment risk? What type of prepayment risk is shifted in this example? (10 points)

5. In this question, we will transform Tranche D into an accrual Z Tranche. For this, you will have to change the cash flows to reflect that the Z Tranche transforms the interest it should receive into additional principal payment to the early tranches.

Specifically, you should 1) assign any foregone interest that would have been received by Tranche Z to Tranche A, then B and then C until Tranche C is gone. KEEP the value of principal to Tranche Z equal to its original value (this will help you compute the amount of interest to assign to the early tranches), and 2) once Tranche C is gone, give all the cash flows from the MBS to Tranche Z. Do not keep track of the principal going to Tranche Z. Tranche Z will receive more principal than is listed because it exchanged interests early to receive more principal later.

Provide the balance and complete set of cash flows to Tranches A and Z over the lifetime of the MBS. Be sure to separate Principal payment from Interest payment. (15 points)

Your answer should look like the following.

	TRANCHE A			TRANCHE Z
Month	Balance	Principal Payment	Interest Payment	Balance	Principal Payment	Interest Payment
1
2

6. Using the yield curve you created earlier, please compute the following (10 points):
   1. The present value of Tranche A and the Z Tranche @ 150 PSA [The PV of Tranche A is not the same as in b. since the cash flows have changed]
   2. The present value of Tranche A and the Z Tranche @ 100 PSA
   3. The percentage change in value in both tranches
   4. How are these percentage changes different from your answer in part c. How does changing Tranche D into a Z Tranche affect the redistribution of prepayment risk?

7. BONUS points Replicate parts c and d but this time instead of changing the PSA, change the yield curve. You should assume that each rate in the yield curve increases by 1%. What are the percentage price changes for Tranche A and Tranche D? What does this say about their respective interest rate risk? Is that what you expected? (15 points)