Week 10 Problem Set Assume that the spot rate curve is flat at 5% (annual compounding). Consider the following two government bonds. The first is a 5-year bond with an annual coupon of 5%. The second is a 10-year bond with an annual coupon of 5%.

Part A: For each of the two bonds, calculate the price, Macaulay duration, and modified duration.

Part B: Now suppose that you have a $100 million long position in the 10-year bond. You are trying to hedge the interest rate exposure on this position by selling 5-year bonds. Assuming that you rely on modified duration, how much of the 5-year should you sell?

Part C: After putting on your hedge, the spot curve shifts down by 10 basis points across all maturities. What are the new prices of the two bonds? What is the profit/loss on your hedged portfolio?

Part D Now suppose that instead the spot curve shifts down by 100 basis points to 4% across all maturities. What are the prices of the two bonds and the profit/loss on your hedged portfolio in this case?

1) (Part A) Price of the 5-year bond:

a) $90

b) $95

c) $100

d) $105

c) $110

Question 2

1 Point

2) (Part A) Price of the 10-year bond:

a) $90

b) $95

c) $100

d) $105

c) $110

3) (Part A) Macaulay duration for the 5-year bond:

a) 4

b) 4.33

c) 4.55

d) 5

c) 5.10

d) 7.72

e) 8.11

4) (Part A) Macaulay duration for the 10-year bond:

a) 4

b) 4.33

c) 4.55

d) 5

e) 5.10

f) 7.72

g) 8.11

5) (Part A) Modified duration for the 5-year bond:

4

4.33

4.55

5

5.10

7.72

8.11

6) (Part A) Modified duration for the 10-year bond:

4

4.33

4.55

5

5.10

7.72

8.11

7) (Part B) Now suppose that you have a $100 million long position in the 10-year bond. You are trying to hedge

the interest rate exposure on this position by selling 5-year bonds. Assuming that you rely on modified

duration, how much of the 5-year bond should you sell?

150.55M

178.35M

194.50M

205.70

210.47M

8) (Part C) After you have put on your hedge, the spot curve shifts down by 10 basis points across all maturities. What is the new price of the 5-year bond?

$99.28

$99.79

$100.05

$100.10

$100.25

$100.43

$100.78

9) (Part C) After you have put on your hedge, the spot curve shifts down by 10 basis points across all maturities. What is the new price of the 10-year bond?

$99.28

$99.79

$100.05

$100.10

$100.25

$100.43

$100.78

10) (Part C) After you have put on your hedge, the spot curve shifts down by 10 basis points across all maturities. What is the profit/loss on the hedged portfolio?

-$1,758

-$1,624

-$1,554

$0

$1,554

$1,624

$1,758