CAS Exam 5 Fall 2018, Question 7
Study guide: Exam 5
Given the following information as of December 31, 2017:
Cumulative Reported Claim Counts as of (months)
| Accident Year | 12 | 24 | 36 |
|---|---|---|---|
| 2015 | 480 | 456 | 447 |
| 2016 | 560 | 532 | |
| 2017 | 590 |
Cumulative Reported Loss + ALAE ($) as of (months)
| Accident Year | 12 | 24 | 36 |
|---|---|---|---|
| 2015 | 7,200,000 | 8,208,000 | 8,850,600 |
| 2016 | 8,120,000 | 9,256,800 | |
| 2017 | 9,145,000 |
| $98,000 | Expected reinsurance recoveries |
| $318,000 | Cost of reinsurance (expected ceded premium) |
| 3% | Expected annual exposure increase |
| Calendar Year | Earned Exposures |
|---|---|
| 2015 | 14,000 |
| 2016 | 15,000 |
| 2017 | 17,000 |
| 5% | ULAE provision as a percent of loss and ALAE |
| 3% | Annual pure premium trend |
| $21 | Projected fixed expenses per exposure |
| 15% | Variable expense ratio |
| 10% | Profit provision |
| 2% | Contingency provision |
| $950 | On-leveled and projected earned premium per exposure |
- Exposures are written evenly throughout each year.
- All policies are annual.
- There is no loss development or claim count development beyond 36 months.
- The reinsurance contract has a 12 month term length and an effective date of January 1, 2019.
- Rates are to be in effect for one year.
- Rate revision is planned to be effective April 1, 2019.
Part a (1 point)
Calculate the projected net reinsurance cost per exposure using a 12-month term for the reinsurance contract.
Part b (2 points)
Calculate the ultimate losses and ALAE for each accident year using an appropriate frequency-severity technique.
Part c (1.75 points)
Calculate the projected pure premium per exposure using even weights across the three accident years.
Part d (1 point)
Calculate the indicated rate change.
Answer this question and see the worked solution