CAS Exam 9 Spring 2015, Question 18
Study guide: Exam 9
An insurance company writes three lines: Auto Liability (AL), Auto Physical Damage (PD) and Workers' Compensation (WC).
- The total required capital is $5,000,000.
- Capital is allocated based on a Co-CTE risk measure.
- The expense ratio is 27% for each line of business.
- The interest rate for discounting is 2.5%.
- The cost of capital is 15%.
- Expenses are paid at the beginning of the year and losses are paid at the end of each year.
| Line | Premium | Undiscounted Loss Ratio | Loss Reserve Duration | 99.5% Co-CTE |
|---|---|---|---|---|
| AL | 5,000,000 | 70.0% | 2.5 | 2,275,000 |
| PD | 2,000,000 | 62.5% | 0.8 | 1,625,000 |
| WC | 8,000,000 | 77.5% | 3.5 | 2,600,000 |
| Total | 15,000,000 | 73.0% | 2.8 | 6,500,000 |
Determine whether the Workers' Compensation line of business adds value to the company on a risk-adjusted basis.
Part a (2.25 points)
Answer this question and see the worked solution