CAS Exam 9 Spring 2014, Question 11
Study guide: Exam 9
Given the following:
Coupon Bonds
| Term | Yield | Duration (Years) |
|---|---|---|
| 4-year | 7% | 3 |
| 10-year | 9% | 7 |
| 20-year | 10% | 11 |
| 30-year | 11% | 20 |
Common Stocks
| Stocks | Annual Dividend | Duration (Years) |
|---|---|---|
| A | 5.00% | 20 |
| B | 9.30% | 11 |
| C | 10.00% | 10 |
| D | 14.30% | 7 |
Zero Coupon Bonds
| Term | Yield |
|---|---|
| 3-year | 1.50% |
| 5-year | 2.00% |
| 7-year | 2.50% |
| 10-year | 3.00% |
| 15-year | 3.50% |
| 20-year | 4.00% |
An insurance company has liabilities with the following payment pattern:
| Development Year | Payment |
|---|---|
| 0 to 2 | 0 |
| 3 | 2.8 million |
| 4 to 6 | 0 |
| 7 | 5.2 million |
| 8 to 19 | 0 |
| 20 | 7.0 million |
- The liability discount rate is 3.0%.
- Assume all payments occur at the end of the year.
Part a (0.5 points)
Calculate the Macaulay Duration of the liability.
Part b (1.5 points)
The target rate of return on investments is 11.6%.
Using the securities listed above, design an investment portfolio that is immunized from small changes in interest rates and has an expected return greater than or equal to the target rate of return on investments.
Part c (0.5 points)
Explain which investments from those listed above should be included in the portfolio to be completely immunized from all interest rate changes.
No current syllabus covers this question; it is kept for the record.
Answer this question and see the worked solution