SOA Exam ASTAM Spring 2023, Question 5
Study guide: Exam ASTAM
You are conducting a ratemaking analysis for a line of business that is sold in only two geographical areas, Territory A and Territory B.
You are given the following information:
(i) The current base rate for Territory A and Age Group 1 is 200.
(ii) Age Group differentials will not change.
| Territory | Age Group | Calendar Year 2022 Earned Exposures | Accident Year 2022 Losses as of December 31, 2022 |
|---|---|---|---|
| A | 1 | 5,000 | 600,000 |
| A | 2 | 2,200 | 242,000 |
| B | 1 | 3,100 | 434,000 |
| B | 2 | 1,300 | 169,000 |
| Territory | Current Differential |
|---|---|
| A | 1.00 |
| B | 1.20 |
| Age Group | Current Differential |
|---|---|
| 1 | 1.00 |
| 2 | 0.95 |
Part a (2 points)
Show that the new differential for Territory B is 1.17 to the nearest 0.01, using the loss ratio method. You should calculate the value to the nearest 0.001.
Part b (1 point)
State why losses do not need to be developed to ultimate values when calculating indicated differentials in part (a).
Part c (2 points)
The company has decided to implement the following new territory differentials:
| Territory | New Differential |
|---|---|
| A | 1.00 |
| B | 1.15 |
Calculate the new Territory A, Age Group 1 base rate needed to give an overall rate increase of 7%.
Part d (2 points)
- (i) Calculate the percentage increase in premiums in Territory B.
- (ii) State with reasons whether you would expect the proportion of policies sold in Territory A to increase, decrease, or stay the same, as a result of the rate changes.
Answer this question and see the worked solution