2006 Fixed Income Final
Fixed Income Final
April 3, 1996
1. (3 points)When rates increase by 2%, the net economic surplus of a corporation
reaches $300 million. The duration of the liabilities is 10. Assets stand at $800 million
and liabilities at $300 Million.
a. What is the assets’ duration?
2. (6 points) You borrow $1 million at 5.00% for three month (92 days) and deposit $1
million for one month (31 days)at 4.75%. The 2-month rate is at 4.90%.You wish to
hedge the mismatched position, based on the following FRA prices quoted to you:
1 x 3 : 5.00% /5.10%
1 x 4: 5.07%/5.09%
3 x 4 : 5.10% / 5.15%
a. Do you buy or sell the FRA?
b. At what price ?
c. For a complete hedge, what amount do you deal?
When it comes to fixing the FRA, the corresponding Eurodollar futures contract
trades at 94.40.
d. What is the settlement amount ? Who pays whom? The 2-month rate is
at 4.90%.
e. What is the overall profit or loss of the book and the end of the 3
month?
3. (5 points) A structured note guarantees its clients a 6% yearly return (annual payment)
on a 4-year period. Interest for this note attracts $50 million.
The structurer immunized rate is 8%.
At what rate must the structurer start immunizing his portfolio if he invests all the
funds a 10-year corporate zero coupon bond yielding 8% ? (Hint: you must first
calculate the duration of the zero coupon bond)
Once the rate reached , what must the structurer do? Be precise in your answer.
4. (6 points)Use Handout1 (2 sheets) for this question. You have the following position:
Long $3,000,000 Face value of the Exxon (XOM)bond
Long $1,500,000 face value of the Wal-Mart (WMT) bond
Long $2,000,000 face value of the Procter & Gamble (PG) bond
a) What is the market value of your portfolio including
accrued interest?
b) What is the average duration and convexity of your
portfolio?
c) You wish to decrease the average duration of your
portfolio by 20% using the futures market. How many
contracts must you buy/sell to reach that duration?
d) You wish to swap the Exxon and PG bonds for the
WMT bond while keeping the same duration. How
many WMT bond must you buy or sell to maintain the
duration found in question c)
e) You now hold only WMT bonds (volatility= 17%) and
wish to hedge against an increase in interest rates.
What futures contracts will you use and why,
How many contracts must you buy/sell to hedge?
5. (5 points)Use Handout 2 for this question. Determine the probability of default the 5year Natural Rural Utilities corporate bond. Assume a 40% recovery rate. Suppose
that the probability of default is Q per year and that defaults always happens halfway
through a year. Use the ask price for both bonds in your calculations.
TIME
(years)
P(default)
0.5
1.5
2.5
3.5
4.5
Q
Q
Q
Q
Q
Recovery
amount
Risk free
value ($)
99.84
101.94
102.04
102.20
102.31
Loss given
default ($)
PV of
expected
loss
April 3, 1996
1. (3 points)When rates increase by 2%, the net economic surplus of a corporation
reaches $300 million. The duration of the liabilities is 10. Assets stand at $800 million
and liabilities at $300 Million.
a. What is the assets’ duration?
2. (6 points) You borrow $1 million at 5.00% for three month (92 days) and deposit $1
million for one month (31 days)at 4.75%. The 2-month rate is at 4.90%.You wish to
hedge the mismatched position, based on the following FRA prices quoted to you:
1 x 3 : 5.00% /5.10%
1 x 4: 5.07%/5.09%
3 x 4 : 5.10% / 5.15%
a. Do you buy or sell the FRA?
b. At what price ?
c. For a complete hedge, what amount do you deal?
When it comes to fixing the FRA, the corresponding Eurodollar futures contract
trades at 94.40.
d. What is the settlement amount ? Who pays whom? The 2-month rate is
at 4.90%.
e. What is the overall profit or loss of the book and the end of the 3
month?
3. (5 points) A structured note guarantees its clients a 6% yearly return (annual payment)
on a 4-year period. Interest for this note attracts $50 million.
The structurer immunized rate is 8%.
At what rate must the structurer start immunizing his portfolio if he invests all the
funds a 10-year corporate zero coupon bond yielding 8% ? (Hint: you must first
calculate the duration of the zero coupon bond)
Once the rate reached , what must the structurer do? Be precise in your answer.
4. (6 points)Use Handout1 (2 sheets) for this question. You have the following position:
Long $3,000,000 Face value of the Exxon (XOM)bond
Long $1,500,000 face value of the Wal-Mart (WMT) bond
Long $2,000,000 face value of the Procter & Gamble (PG) bond
a) What is the market value of your portfolio including
accrued interest?
b) What is the average duration and convexity of your
portfolio?
c) You wish to decrease the average duration of your
portfolio by 20% using the futures market. How many
contracts must you buy/sell to reach that duration?
d) You wish to swap the Exxon and PG bonds for the
WMT bond while keeping the same duration. How
many WMT bond must you buy or sell to maintain the
duration found in question c)
e) You now hold only WMT bonds (volatility= 17%) and
wish to hedge against an increase in interest rates.
What futures contracts will you use and why,
How many contracts must you buy/sell to hedge?
5. (5 points)Use Handout 2 for this question. Determine the probability of default the 5year Natural Rural Utilities corporate bond. Assume a 40% recovery rate. Suppose
that the probability of default is Q per year and that defaults always happens halfway
through a year. Use the ask price for both bonds in your calculations.
TIME
(years)
P(default)
0.5
1.5
2.5
3.5
4.5
Q
Q
Q
Q
Q
Recovery
amount
Risk free
value ($)
99.84
101.94
102.04
102.20
102.31
Loss given
default ($)
PV of
expected
loss