CAS Exam 9 Spring 2017, Question 19
Study guide: Exam 9
An insurer is exploring purchasing an excess of loss reinsurance policy that attaches at $100,000. The insurer has simulated 1,000 different scenarios with the following results:
Expected Retained Loss:
| Gross of Reinsurance | Net of Reinsurance |
|---|---|
| $29,000 | $27,000 |
The largest scenarios for the insurer's retained losses are shown in the table below:
| Scenario Rank | Gross of Reinsurance ($) | Net of Reinsurance ($) |
|---|---|---|
| 1,000 | 127,000 | 100,000 |
| 999 | 120,000 | 100,000 |
| 998 | 118,000 | 100,000 |
| 997 | 117,000 | 100,000 |
| 996 | 115,000 | 100,000 |
| 995 | 115,000 | 100,000 |
Given the following:
- Direct premium is $50,000.
- Reinsurance premium is $2,500.
- Expense ratio (other than ceding commission) is 20%.
- Ceding commission is 20%.
- Investment yield is 5%.
- Cost of capital is 12.5%.
- Capital is set at the 99.5% conditional tail expectation (CTE).
- All losses are paid at the end of the year. All other amounts are paid or received at the beginning of the year.
Part a (2 points)
Using a risk-adjusted return approach, determine whether the insurer should purchase the reinsurance policy.
Part b (0.5 points)
Calculate the additional risk margin that would need to be charged by the direct writer on the ground-up policy to make the risk-adjusted returns on capital equal on a gross and net basis.
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