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Question

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)

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