CAS Exam 5 Fall 2019, Question 11
Study guide: Exam 5
The graph below shows frequency model results for industry types. The same data and assumptions are used in both models.
Model Results — bars show the number of exposures by industry type (left axis, 0 to 250,000); two lines show the estimated frequency relativity (right axis, "Factor", 0 to 1.6): a dotted line with round markers for the One-Way Result, and a dashed line with square markers for the Generalized Linear Model Result.
Reading the chart approximately:
| Industry Type | Exposures | One-Way Result | GLM Result |
|---|---|---|---|
| 1 | ~75,000 | ~0.50 | ~0.35 |
| 2 | ~85,000 | ~0.60 | ~0.40 |
| 3 | ~90,000 | ~0.80 | ~0.65 |
| 4 | ~128,000 | ~0.90 | ~0.82 |
| 5 | ~230,000 | 1.00 | 1.00 |
| 6 | ~217,000 | ~1.08 | ~1.12 |
| 7 | ~113,000 | ~1.10 | ~1.20 |
| 8 | ~80,000 | ~1.20 | ~1.48 |
Industry type 5 carries the most exposures, and the two lines coincide there. Below industry 5 the GLM factors sit below the one-way factors; above it they sit above.
Part a (0.25 points)
Briefly discuss why the relativity for both line graphs match for industry 5.
Part b (0.5 points)
Explain why the models in part a. above produce different results.
Part c (0.5 points)
Describe how the use of one-way results might impact profitability for an insurance company.
Answer this question and see the worked solution