CAS Exam 7 Spring 2013, Question 20
Study guide: Exam 9
Given the following 2013 information for an insurance company:
| Gross premiums | $250 million |
| Gross loss ratio | 60% |
| Gross expense ratio | 32% |
| Risk-free interest rate | 1.5% |
| Investment yield | 3.5% |
| Beginning surplus | $1 billion |
| Probability of distress without reinsurance | 2% |
The insurance company is considering a reinsurance treaty with the following characteristics:
| Proposed reinsurance | 20% quota share |
| Ceding commission | 10% of reinsurance premiums |
| Probability of distress with reinsurance | 0.4% |
- All premiums, expenses and commissions are collected or paid at the beginning of the year.
- All claims are paid at the end of the year.
- The insurance portfolio composition is not expected to grow or change in future years.
Part a (4 points)
Using the risk-adjusted present value of future earnings, quantify the effect on the firm's value of purchasing the quota share reinsurance.
Part b (1 point)
Identify and briefly describe two alternative approaches to quantifying the value of risk transfer to the insurance company.
Answer this question and see the worked solution