Question

Introduction to Mortgage Mathematics and Mortgage-Backed Securities

(I ONLY NEED THE SOLUTIONS FOR 5,6,7 and 8, the previous exercises are given as a reference) 4 SOLUTIONS IN TOTAL

1.(Level-Payment Mortgages) Compute the monthly payment on a 30-year level payment mortgage assuming an annual mortgage rate of 5% and an initial mortgage principal of $400,000. Submission Guideline: Give your answer rounded to two decimal places. For example, if you compute the answer to be $73.2367, submit 73.24.

2 (Mortgage Pass-Throughs) Consider a $400 million pass-through MBS that has just been created (so the 'seasoning' of the pass-through is equal to 0). The underlying pool of mortgages each has a maturity of 20 years and an annual mortgage coupon rate of 6%. The pass-through rate of the mortgage pool is 5%. Assuming a prepayment multiplier of 100 PSA what is the total amount of interest paid to the pass-through investors? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

3 (Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

4 (Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments if the rate of prepayments increases to 200 PSA? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

5 (Principal-Only MBS and Interest-Only MBS) Suppose we construct principal-only (PO) and interest-only (IO) mortgage-backed securities (MBS) using the mortgage pass-through of the previous questions. Assume a prepayment multiplier of 100 PSA. What is the present value of the PO MBS if we use an annual risk-free rate of 4.5% to value the cash-flows? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

6. (Principal-Only MBS and Interest-Only MBS) Referring to the previous question, what is the value of the IO MBS? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

7. (Principal-Only MBS and Interest-Only MBS) Referring to the previous question, what is the average life of the IO MBS? Submission Guideline: Give your answer in years rounded to two decimal places. For example, if you compute the answer to be 12.1234 years, submit 12.12.

8. (Principal-Only MBS and Interest-Only MBS) Suppose now that you purchased the IO MBS of the previous question and that the price you paid was the same price that you calculated in the previous question. The risk-free interest rate suddenly changes from 4.5% to 3.5%. Everything else stays the same. How much money have you made or lost on your investment? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

Answer 1

Solution
Outstanding Balance of Mortgage			400 millions
Coupon rate			6%
Pass through Rate			5%
Term of loan			20 years
As 100 PSA therefore rounding is to be done
year	Prinicpal at the end	Monthly Intt paid 6%	Pass through intt@5%	Closing Balance for prepayments
1	400	24	20	376
2	376	23	19	353
3	353	21	18	332
4	332	20	17	312
5	312	19	16	294
6	294	18	15	276
7	276	17	14	259
8	259	16	13	244
9	244	15	12	229
10	229	14	11	215
11	215	13	11	203
12	203	12	10	190
13	190	11	10	179
14	179	11	9	168
15	168	10	8	158
16	158	9	8	149
17	149	9	7	140
18	140	8	7	131
19	131	8	7	123
20	123	7	6	116
		284	237
Answer (a)	Total interest to pass through investors		237	millions
Answer (b)	Total Amount of prepayments		Total Intt + Principal
			400 + 284
			684	millions

Brother this answer is too long try to ask one by one