CAS Exam 5 Fall 2013, Question 4
Study guide: Exam 5
Given the following information:
- The insurance company entered the market in State X at the beginning of 2008.
- All policies are annual.
- Rates will be in effect for 12 months beginning on July 1, 2014.
- Rate change history:
- +5% effective July 1, 2010.
- +7% effective April 1, 2012.
- Premiums are expected to increase at an inflationary rate of 2% annually.
- Annual loss cost trend = +4%.
- ULAE provision = 12% of loss and ALAE.
- Fixed expense ratio = 7%.
- Variable expense ratio = 21%.
- Underwriting profit and contingencies provision = 8%.
- To simplify calculations, assume premium is earned evenly throughout the year.
- Assume no loss development after 48 months.
| Calendar Year | State X Earned Premium | State X Earned Exposures | State X Written Premium | State X Written Exposures |
|---|---|---|---|---|
| 2010 | $400,000 | 400 | $630,000 | 600 |
| 2011 | $2,200,000 | 2,000 | $3,105,000 | 2,700 |
| 2012 | $16,800,000 | 14,000 | $18,750,000 | 15,000 |
State X Incurred Losses and ALAE
| Accident Year | 12 Months | 24 Months | 36 Months | 48 Months |
|---|---|---|---|---|
| 2008 | $0 | $200 | $800 | $1,000 |
| 2009 | $50,000 | $61,300 | $78,200 | $80,000 |
| 2010 | $380,500 | $587,000 | $624,486 | |
| 2011 | $671,600 | $1,316,239 | ||
| 2012 | $9,706,667 |
Countrywide Incurred Losses and ALAE
| Accident Year | 12 Months | 24 Months | 36 Months | 48 Months |
|---|---|---|---|---|
| 2007 | $123,600,000 | $125,000,000 | ||
| 2008 | $62,700,000 | $68,600,000 | $70,000,000 | |
| 2009 | $75,000,000 | $83,300,000 | $88,200,000 | $90,000,000 |
| 2010 | $80,500,000 | $87,000,000 | $93,000,000 | |
| 2011 | $71,600,000 | $78,800,000 | ||
| 2012 | $86,900,000 |
Part a (6.25 points)
Calculate the indicated rate level change for State X using the loss ratio method. Use two-step trending to project premiums.
Part b (0.5 points)
The assumption that the premium is earned evenly should not hold for State X given that it is a new book of business. Briefly describe two alternatives to the traditional parallelogram method that would improve the accuracy of the estimated projected premiums.
Part c (0.75 points)
Fully discuss the impact to the rate level indication for State X by assuming the premium is earned evenly. Include the directional change to the rate level indication that would result if adjusting for the actual earning of the premium.
Answer this question and see the worked solution
Concepts tested
- Overall Rate Level Indication
- On Level Premium
- Loss Trend
- Premium Trend
- Parallelogram Method
- Loss Ratio Method
- Extension of Exposures