CAS Exam 7 Spring 2015, Question 8
Study guide: Exam 7
An insurer writes the following lines of business and has derived the associated coefficients of variation (CoV) for claim liabilities for the purpose of determining a risk margin.
| Line of Business | Claim Liability Distribution | Internal Systemic Risk CoV | External Systemic Risk CoV | Independent Risk CoV |
|---|---|---|---|---|
| Personal Auto | 60% | 5% | 4% | 5% |
| Commercial Auto | 35% | 7% | 5% | 5% |
| Commercial Umbrella | 5% | 15% | 10% | 7% |
- The insurer will only write umbrella over its own commercial auto policies.
- The insurer used a balanced scorecard approach for internal systemic risk.
Part a (1.5 points)
Describe two sources of internal systemic risk. Briefly explain why each one might lead to a higher CoV selection for umbrella than for the other two lines of business.
Part b (0.75 points)
Identify a source of external systemic risk with a relatively high correlation between two of the above lines of business. Name the two lines and provide a brief reason for the high correlation.
Part c (0.75 points)
Identify a source of external systemic risk with a relatively low correlation between two of the above lines of business. Name the two lines and provide a brief reason for the low correlation.
Part d (0.5 points)
Assuming independence, calculate the independent risk CoV for the overall portfolio.
Answer this question and see the worked solution
Concepts tested
- Coefficient of Variation
- Correlation
- Internal Systemic Risk
- External Systemic Risk
- Independent Risk
- Risk Margin