1. Suppose you were offered a choice between a 30-year mortgage at 6% with zero points or a 5.5% mortgage with 2 discount points. Assume you want to borrow $200,000. How many months will you have to live in the house to make it worthwhile to take the 5.5% mortgage with the 2 points?
2. Given two mortgage options: 1) 30-year fixed at 6% with zero points, and 2) 30-year fixed at 5.5% with points. Assume a $200,000 mortgage. If you intend to live in your house for 10 years, what is the maximum amount of points that you would be willing to pay?
3. a) Compute the monthly payment on a $300,000 30-year mortgage at a rate of 5%. b) What is the first monthly principal payment in (a)?
4. c) What is the first monthly interest payment in (a)?
5. Again, assume you have a 300,000 30-year mortgage at a rate of 5%. a) What are the total principal payments for first year?
6. b) What are the total interest payments for the first year?
7. Now assume you have a 300,000 15-year mortgage at a rate of 4.5%. a) What are the total principal payments for the first year?
8. b) What are the total interest payments for the first year?
9. Given the amortization schedule in the table below, compute the weighted average life.

Time

Principal

1

5

2

10

3

20

4

40

5

80

Total

155

7. Given the below single month mortality rates for a mortgage security. What are the corresponding conditional prepayment rates?

Age

SMM

CPR

5

0.6

(a)

6

1.0

(b)

7

2.0

(c)

8

5.0

(d)

1. Given the below par-yield curve, what is the spot curve?
2. Suppose you have a 8.5% coupon paying mortgage bond. Given the information in question 8 above, suppose the weighted average life is 2.25. What is the WAL yield spread to par?
3. Suppose you have a 8.5% coupon paying mortgage bond. Given the information in question 8 above, and the below bond cash flows, what is the yield curve spread to the spot curve?
4. Given the information in question 8, what are the 1-year forward rates based upon the spot curve?
5. Given the cash flows from question 10 and the 1-year forward rates in question 11, what is the yield curve spread when using the forward rates?
6. Compute the effective durations and effective convexities of the securities in the below table.

Year

1

2

3

4

5

Par Curve

3.0%

5.0%

8.0%

9.0%

9.5%

Spot Curve

(a)

(b)

(c)

(d)

(e)

Year

Cash Flow

1

39.50

2

31.65

3

24.28

4

17.38

5

10.98

Year

1

2

3

4

5

1-Year Forward Rates

(a)

(b)

(c)

(d)

Bond 1

Bond 2

Bond 3

-50 bp

55.83

105.19

23.03

Base

45.00

104.22

26.75

+ 50 bp

36.38

103.03

29.92

Effective Duration

(a)

(b)

(c)

Effective Convexity

(d)

(e)

(f)

14. Using the calculated durations and convexities in question 13, what would be the new prices of Bonds 1, 2 and 3 if interest rates rose by 25 basis points?

Bond 1

Bond 2

Bond 3

Price + 25 bp

(a)

(b)

(c)