CAS Exam 7 Spring 2013, Question 8

Study guide: Exam 7

Given the following information for an insurance company's outstanding claim liabilities as of December 31, 2012:

Line of business	Central Estimate	Independent risk CoV	Internal systemic risk CoV	External systemic risk CoV
Workers compensation	$110,000,000	7.2%	7.5%	3.4%
Auto	95,000,000	5.2%	4.5%	4.3%
Homeowners	45,000,000	5.8%	5.0%	6.7%
Total	250,000,000			4.7%

Assume that the claim liabilities are normally distributed.
The z-value for the $75^{\text{th}}$ percentile of the normal distribution is: 0.674
The selected correlation between each pair of lines of business for internal systemic risk is: 0.25
Assume that each source of independent risk is uncorrelated with any other source of risk.

Part a (0.5 points)

Calculate the independent risk CoV for all lines combined.

Part b (0.5 points)

Describe why it is reasonable to assume that there is positive correlation between lines of business for internal systemic risk.

Part c (1 point)

Calculate the internal systemic risk CoV for all lines combined.

Part d (0.5 points)

Calculate the consolidated CoV for all sources of risk.

Part e (0.5 points)

Calculate the risk margin (in dollars) for the overall book of business that provides a 75% probability of reserve adequacy.

Part f (0.5 points)

Discuss how the risk margin in e. above would change if the selected pair-wise correlation between each pair of lines of business for internal systemic risk were higher than 0.25.

Part g (1.5 points)

Analyze the consistency of the selected CoVs by line of business using internal benchmarking checks. Discuss all three main sources of risk.

Part h (0.75 points)

Discuss an external systemic risk for which the assumption of constant correlation between lines of business across their loss distributions does not hold. Suggest a method to incorporate variable correlation into the risk margin.

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