CAS Exam 6C Spring 2016, Question 13
Study guide: Exam 6C
The following information is available for a property and casualty insurance company that only writes auto insurance as at December 31, 2015. All amounts are in thousands of dollars ($000s).
The cumulative accident year payment pattern is as follows:
| Age (months) | % cumulative paid |
|---|---|
| 12 | 25.0% |
| 24 | 50.0% |
| 36 | 75.0% |
| 48 | 100.0% |
The following additional information is also available:
- Assume all claim payments are made in the middle of the year.
- The company started writing business on January 1, 2015.
- The exposures, 12 months policies, are uniformly written throughout the year.
- There is no reinsurance.
- Annual Gross Written Premium in 2015 = $10,000
- Net undiscounted unpaid claims at the end of 2015 = $5,250
- Margin for Adverse Deviation (MfAD) Claims development: 10.0%
- MfAD Investment return rates: 0.5%
- The budgeted loss ratio for 2016 is equal to 65.0%.
- Maintenance expenses are equal to 3.0% of gross written premiums.
- Assume that maintenance expenses are paid during the time the unearned premium is earned.
- Interest rate shock factor = 1.25%.
The composition of the company's bond portfolio is as follows:
| Description | Bond #1 | Bond #2 |
|---|---|---|
| Maturity Date | 31/12/2016 | 31/12/2017 |
| Annual Coupon Rate | 2.60% | 3.50% |
| # of coupons per year | 2 | 2 |
| Par value | $10,000 | $10,000 |
| Coupons value ($) | $130 | $175 |
| Annual effective yield | 2.31% | 3.23% |
| Modified Duration | 0.972 | 1.888 |
| Market Value | $10,030 | $10,060 |
Note that there are no other invested assets other than Bond #1 and Bond #2 and that the combined market yield of the investment portfolio is used to discount losses.
Calculate the margin required for interest rate risk for the current year.
Part a (7.75 points)
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