CAS Exam 5 Spring 2019, Question 5
Study guide: Exam 5
Given the following loss data as of December 31, 2018 for an insurer:
Cumulative Reported Losses ($000s)
| Accident Year | 12 | 24 | 36 | 48 |
|---|---|---|---|---|
| 2012 | 169,000 | |||
| 2013 | 181,000 | |||
| 2014 | 180,000 | |||
| 2015 | 169,000 | |||
| 2016 | 161,000 | |||
| 2017 | 150,000 | |||
| 2018 | 121,000 |
Shock Losses
| Accident Year | Claim Count | Reported Ground-Up Losses ($000s) |
|---|---|---|
| 2012 | 3 | 3,000 |
| 2013 | 4 | 5,000 |
| 2014 | 3 | 3,000 |
| 2015 | 1 | 600 |
| 2016 | 1 | 900 |
| 2017 | 0 | 0 |
| 2018 | 1 | 900 |
Selected Age-to-Age Development Factors:
| 12 - 24 | 24 - 36 | 36 - 48 |
|---|---|---|
| 1.2 | 1.1 | 1.05 |
| $500,000 | Excess loss threshold used by the insurer for individual reported losses |
The annual frequency and severity exponential trend fits based on data for the 12 months ending each quarter evaluated through December 31, 2018 are as follows:
| Exponential Trend | Frequency | Total Severity |
|---|---|---|
| 20 point | 1.7% | 5.0% |
| 16 point | 1.4% | 5.4% |
| 12 point | 1.8% | 5.1% |
| 8 point | 1.5% | 2.0% |
| 6 point | 1.3% | 0.1% |
| 4 point | 1.6% | 0.0% |
- All policies are annual.
- Rates will be in effect for one year.
- There is no development after 48 months.
- Loss development is the same for basic and excess losses.
- Accident years 2012 through 2015 are used to estimate the shock loss adjustment.
Part a (3.75 points)
Calculate the projected trended ultimate losses for accident year 2018 to be used to determine a rate change effective January 1, 2020. Briefly justify the trend selections.
Part b (0.5 points)
Briefly describe two approaches for selecting an excess loss threshold used for capping shock losses.
Answer this question and see the worked solution