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 $1,500,000 face value of the Wal-Mart (WMT) bond
a) What is the market value of your portfolio including accrued interest?
b) What is the average duration and convexity of your portfolio?
c) You wish to decrease the average duration of your portfolio by 20% using the futures market. How many contracts must you buy/sell to reach that duration? d) You wish to swap the Exxon and PG bonds for the
WMT bond while keeping the same duration. How many WMT bond must you buy or sell to maintain the duration found in question c)
e) You now hold only WMT bonds (volatility= 17%) and wish to hedge against an increase in interest rates.
What futures contracts will you use and why,
How many contracts must you buy/sell to hedge?
5. (5 points)Use Handout 2 for this question. Determine the probability of default the 5-year Natural Rural Utilities corporate bond. Assume a 40% recovery rate. Suppose that the probability of default is Q per year and that defaults always happens halfway through a year. Use the ask price for both bonds in your calculations.
TIME (years)
P(default) Recovery amount
Risk free value ($)
Loss given default ($)
PV of expected
loss
0.5 Q 99.84
1.5 Q 101.94
2.5 Q 102.04
3.5 Q 102.20
