CAS Exam 5 Fall 2015, Question 10
Study guide: Exam 5
An automobile insurer has calculated indicated rating plan factors using both a loss ratio analysis and a generalized linear model (GLM). Data from years 2012-2014 was used in both analyses. Given the following output for the proposed Annual Mileage rating variable:
GLM Relativities by Year — a combination chart with two vertical axes. The horizontal axis is "Annual Mileage Group" with three levels, Below 2,000, 2,000-10,000 and Above 10,000. The left axis is "Indicated Relativities" (0.70 to 1.20) and is read by three plotted series, one per model year 2012, 2013 and 2014; the right axis is "Number of Policies" (0 to 600,000) and is read by the open bars.
Exposure volume behind each level (bars, read off the right axis):
| Annual Mileage Group | Number of Policies (approximate) |
|---|---|
| Below 2,000 | ~50,000 |
| 2,000-10,000 | ~300,000 |
| Above 10,000 | ~500,000 |
Fitted relativities (three series, read off the left axis):
| Annual Mileage Group | 2012 | 2013 | 2014 |
|---|---|---|---|
| Below 2,000 | ~0.75 | ~0.77 | ~0.80 |
| 2,000-10,000 | ~1.00 | ~1.00 | ~1.00 |
| Above 10,000 | ~1.08 | ~1.10 | ~1.11 |
All three year-lines slope upward across the three mileage groups and lie close to one another, with 2012 running slightly below 2013 and 2014 at the highest mileage group.
GLM and Loss Ratio Method Relativities — a second combination chart over the same three mileage groups and the same bars. The left axis is "Indicated Relativities" (0.00 to 2.00); the right axis is "Number of Policies" (0 to 600,000). Four series are plotted against the left axis: the Loss Ratio Result, the GLM Result, and the GLM's +2 SE and -2 SE bounds.
| Annual Mileage Group | Loss Ratio Result | GLM Result | +2 SE | -2 SE |
|---|---|---|---|---|
| Below 2,000 | ~0.90 | ~0.80 | ~1.30 | ~0.60 |
| 2,000-10,000 | ~1.00 | ~1.00 | ~1.10 | ~0.90 |
| Above 10,000 | ~1.50 | ~1.10 | ~1.20 | ~0.95 |
The standard error band around the GLM result is widest at the lowest-volume mileage group and narrows as exposure volume increases; the loss ratio result sits inside the band at the two lower mileage groups and well above it at Above 10,000.
Part a (1 point)
Using the data in each graph above, discuss whether annual mileage would be a good rating variable.
Part b (0.5 points)
Taking into account two other criteria of a good rating variable, discuss whether annual mileage would be a good rating variable.
Part c (0.5 points)
Recommend whether the insurer should add annual mileage to their rating plan.
Answer this question and see the worked solution