CAS Exam 9 Spring 2018, Question 2
Study guide: Exam 9
Given the following information regarding an insurance company and the market:
- Loss and Loss Adjustment Expense (LAE) is $75 million.
- Loss and LAE are paid at the following times:
| Time (years) | % of Loss and LAE Paid |
|---|---|
| 1 | 50% |
| 2 | 30% |
| 3 | 20% |
- 100% of assets are invested at the investment income yield of 5.5%.
- Investment income is paid annually at the end of the year.
- The beta value for this company is 1.5.
- Expenses (other than LAE) are $39 million.
- Premium is collected and expenses (other than LAE) are paid at time 0.
- Premium is immediately earned, so there is no unearned premium reserve.
- Loss reserves are established at time 0.
- An undiscounted reserves-to-surplus ratio of 2:1 is maintained at all times.
- A Treasury Bill is selling for the following price:
| Treasury Bill | Price |
|---|---|
| Face value $1,000, 2-yr maturity, 4% annual coupon | $1,048.90 |
- The expected market return is 8.5%.
- The risk-free rate is constant over time.
- Ignore taxes and inflation.
There are two profit requirements:
- Regulators require the present value of underwriting cash flows to be no greater than 7% of premium.
- Shareholders require a minimum internal rate of return consistent with CAPM.
Assuming the same business is written every year (steady-state), the Product Manager has requested the business to be priced to achieve a total steady-state calendar year return on surplus of 30%.
Recommend a premium the company should charge. Describe how the recommended premium relates to the premiums needed to satisfy the regulators, the shareholders, and the Product Manager.
Part a (7.25 points)
No current syllabus covers this question; it is kept for the record.
Answer this question and see the worked solution