Question
An insurance company has the liabilities with the following payment pattern, each at the end of the respective year: Year 3: $2.5 million Year 7:
An insurance company has the liabilities with the following payment pattern, each at the end of the respective year:
Year 3: $2.5 million
Year 7: $4.2 million
Year 20: $6.0 million
There are no other liabilities for the insurance company to consider. The discount rate for the liabilities is 3%. The insurance company has the following investment opportunities in bonds and stocks:
Coupon Bonds
Maturity | Yield | Duration |
4 | 7.0% | 3 |
10 | 9.0% | 7 |
20 | 10.0% | 11 |
30 | 11.0% | 20 |
Common stocks
Stock | Dividend | Duration |
A | 5.0% | 20 |
B | 9.3% | 11 |
C | 10.0% | 10 |
D | 14.3% | 7 |
Zero Coupon Bonds
Maturity | Yield |
3 | 1.5% |
5 | 2.0% |
7 | 2.0% |
10 | 3.0% |
15 | 3.5% |
a. Using the information about the zero-coupon bonds, draw the yield curve and compute two forward rates of your choice.
b. Calculate the duration of the liability.
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