CAS Exam 8 Fall 2014, Question 1
Study guide: Exam 8
An actuary has devised a new method to assign credibility to observations of severity relativities by state. In order to test the validity of the method, the following quintile test has been prepared. The actuary has split the data into two distinct partitions: Test and Holdout. Test data was used to predict the credibility-adjusted relativities of the holdout data.
| Quintile | Holdout Relativity | Prediction Based on Countrywide Average | Prediction Based on Raw Test Data | Prediction Based on New Credibility Procedure |
|---|---|---|---|---|
| 1 | 0.55 | 1.00 | 0.25 | 0.90 |
| 2 | 0.75 | 1.00 | 0.40 | 0.95 |
| 3 | 0.90 | 1.00 | 0.85 | 0.99 |
| 4 | 1.30 | 1.00 | 1.40 | 1.05 |
| 5 | 1.50 | 1.00 | 2.10 | 1.10 |
| Mean | 1.00 | 1.00 | 1.00 | 1.00 |
| Sum of Squared Errors | 0.6150 | 0.5850 | 0.3931 |
Part a (0.75 points)
Describe whether this new method overstates or understates the credibility of the state relativities.
Part b (0.5 points)
Discuss whether the new method or the countrywide average should be used to determine state relativities.
Answer this question and see the worked solution