You are responsible for managing the following liability: 29-year bond, 6.5% annual coupon, when the market interest rate is 5%.
1. What is the present value of this liability?
2. What is the duration of this liability?
3. You want to consider immunizing the liability using 14- year and16-year zero-coupon bonds?
a. What are the investment weights needed for the two bonds?
b. What are the present values of the two bonds needed to immunize the liability?
c. What are the face values of the two bonds needed to immunize the liability?
d. Build a sensitivity table showing the results of changes in interest rates, with the following format:
|
Weight |
3% |
4% |
5% |
6% |
7% |
| Liability |
|
|
|
|
|
|
| Bond (14 years) |
|
|
|
|
|
|
| Bond (16 years) |
|
|
|
|
|
|
| Portfolio sum |
|
|
|
|
|
4. As an alternative, you want to consider immunizing the liability using 8-year and 30-year zero coupon-bonds.
a. What are the investment weights needed for the two bonds?
b. What are the present values of the two bonds needed to immunize the liability?
c. What are the face values of the two bonds needed to immunize the liability?
d. Build a sensitivity table showing the results of changes in interest rates, with the following format:
|
Weight |
3% |
4% |
5% |
6% |
7% |
| Liability |
|
|
|
|
|
|
| Bond (14 years) |
|
|
|
|
|
|
| Bond (16 years) |
|
|
|
|
|
|
| Portfolio sum |
|
|
|
|
|
5. Which strategy (from parts c and d) would you recommend, based solely on price sensitivity?
6. What additional factors might you want to consider before choosing between the two strategies?