CAS Exam 6C Fall 2013, Question 19
Study guide: Exam 6C
A company began writing personal property and liability lines of business on January 1, 2012. The personal property line of business had the following losses at December 31, 2012:
Property Line of Business – 2012 Loss Year:
| Gross Layer: Paid Loss ($000s) | Gross Layer: Incurred Loss ($000s) | Gross Layer: Ultimate Loss ($000s) | Net Layer: Paid Loss ($000s) | Net Layer: Incurred Loss ($000s) | Net Layer: Ultimate Loss ($000s) |
|---|---|---|---|---|---|
| $2,000 | $7,500 | $10,000 | $1,200 | $4,500 | $6,000 |
Notes on the property line of business:
- The claims development Margin for Adverse Deviation (MfAD) is twice as large as the reinsurance recovery MfAD.
- The company uses the same margins and payment pattern for their gross, ceded, and net reserve layers.
- The ceded claims discounted at 5% are $3,012.23.
- The net claims discounted at 5% are $4,518.35.
- The net claims discounted at 4% are $4,571.88.
- The net claim liability including margins is $5,023.72.
- The cumulative accident year payment pattern for the property line of business is as follows:
| Months | Percentage paid |
|---|---|
| 12 | 20% |
| 24 | 50% |
| 36 | 90% |
| 48 | 100% |
- Assume that all payments are made in the middle of the year.
Other information:
- The portfolio yield rate on the assets that are assumed to be backing all claims liabilities is 6%.
- The portfolio of investment assets contains only zero-coupon bonds maturing in 3 to 5 years with a modified duration of 3.5 years.
- The liability line of business has a 10-year assumed payment pattern with a modified duration of 6.5 years.
Part a (1 point)
Identify and briefly explain two considerations that would cause the actuary to consider a discount rate other than the assumed portfolio yield rate of 6% for the liability line of business.
Part b (2.5 points)
Assuming that the actuary decides that a 5% discount rate and a 1% investment return MfAD is appropriate, calculate the gross discounted claims liability, including margins, for the property line of business.
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