CAS Exam 8 Fall 2018, Question 9
Study guide: Exam 8
Three insurers are using experience rating to determine premiums for a specific class of business. The same ten risks were rated using the experience plan of each insurer. Information related to each rating plan is given below:
Insurer 1's Plan
| Risk # | Manual Premium | Loss | Mod | Standard Premium |
|---|---|---|---|---|
| 1 | $810 | $750 | 0.97 | $786 |
| 2 | $900 | $490 | 0.68 | $612 |
| 3 | $950 | $1,075 | 1.13 | $1,074 |
| 4 | $975 | $650 | 0.78 | $761 |
| 5 | $1,075 | $850 | 0.88 | $946 |
| 6 | $1,100 | $1,000 | 0.96 | $1,056 |
| 7 | $1,225 | $1,300 | 1.06 | $1,299 |
| 8 | $1,300 | $800 | 0.72 | $936 |
| 9 | $1,450 | $1,175 | 0.90 | $1,305 |
| 10 | $1,500 | $975 | 0.76 | $1,140 |
Insurer 2's Plan
| Quintile | Manual Loss Ratio | Standard Loss Ratio |
|---|---|---|
| 1 | 58.6% | 94.5% |
| 2 | 65.7% | 90.0% |
| 3 | 80.2% | 85.3% |
| 4 | 91.6% | 79.7% |
| 5 | 109.2% | 75.3% |
| Sample Variance | 0.0411 | 0.0059 |
Insurer 3's Plan
| Efficiency Test Statistic |
|---|
| 0.0000 |
Part a (2.75 points)
Rank each of the insurers' rating plans from most to least equitable using the Efficiency Test as described by Fisher et al.
Part b (1.5 points)
Explain how adverse selection may affect each of the three insurers in a well-functioning insurance market. Assume that no adjustments are made to the experience rating plans over time.
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