CAS Exam 5 Spring 2013, Question 8
Study guide: Exam 5
Given the following information:
- All policies are annual and written on January 1.
- Rate change effective date is January 1, 2013.
- Rate level is reviewed annually.
- Underwriting guidelines were revised on January 1, 2011, substantially changing the composition of the book of business.
| Accident Year | Reported Loss & ALAE as of June 30, 2012 |
|---|---|
| 2010 | $10,000,000 |
| 2011 | $6,000,000 |
| 2012 | $1,500,000 |
Selected Reported Loss & ALAE Age-to-Ultimate Factors:
| Month | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |
|---|---|---|---|---|---|---|---|---|---|---|
| Factor | 6.50 | 2.00 | 1.55 | 1.20 | 1.12 | 1.08 | 1.05 | 1.02 | 1.01 | 1.00 |
Reported Loss & ALAE:
| Calendar Year Ending | Frequency | Severity | Pure Premium |
|---|---|---|---|
| Sep 2009 | 0.058 | $20,355 | $1,181 |
| Dec 2009 | 0.059 | $20,125 | $1,187 |
| Mar 2010 | 0.062 | $20,500 | $1,271 |
| Jun 2010 | 0.063 | $21,575 | $1,359 |
| Sep 2010 | 0.063 | $21,388 | $1,347 |
| Dec 2010 | 0.065 | $19,903 | $1,294 |
| Mar 2011 | 0.078 | $19,567 | $1,526 |
| Jun 2011 | 0.078 | $19,238 | $1,501 |
| Sep 2011 | 0.079 | $19,538 | $1,543 |
| Dec 2011 | 0.082 | $20,063 | $1,645 |
| Mar 2012 | 0.081 | $20,050 | $1,624 |
| Jun 2012 | 0.082 | $19,950 | $1,636 |
| # of Points | Annual Frequency Exponential Fit | Annual Severity Exponential Fit | Annual Pure Premium Exponential Fit |
|---|---|---|---|
| 12 | 15.9% | -1.7% | 13.9% |
| 8 | 16.0% | -1.7% | 14.0% |
| 6 | 4.7% | 2.9% | 7.7% |
| 4 | 4.1% | 2.5% | 6.7% |
Calculate the 2010 accident year trended ultimate losses & ALAE to be used in a rate change analysis. Justify any trend selections.
Part a (3 points)
Answer this question and see the worked solution