CAS Exam 8 Fall 2014, Question 17
Study guide: Exam 8
A large insured is considering a retrospectively rated policy for its workers compensation coverage with the following characteristics:
| Characteristic | Value |
|---|---|
| Standard premium | $1,000,000 |
| Unlimited expected loss ratio | 65% |
| Expense ratio | 20% |
| Loss conversion factor | 1.10 |
| Premium tax rate | 4.0% |
| Maximum premium | $1,200,000 |
| Minimum premium | $750,000 |
The actuary will use the following tables for rating:
| Entry Ratio | ELG 31 | ELG 30 | ELG 29 | ELG 28 | ELG 27 | ELG 26 |
|---|---|---|---|---|---|---|
| 0.70 | 0.4026 | 0.4000 | 0.3975 | 0.3949 | 0.3924 | 0.3898 |
| 0.80 | 0.3912 | 0.3826 | 0.3740 | 0.3656 | 0.3581 | 0.3489 |
| 0.90 | 0.3519 | 0.3426 | 0.3334 | 0.3242 | 0.3189 | 0.3060 |
| 1.00 | 0.3135 | 0.3037 | 0.2938 | 0.2839 | 0.2809 | 0.2642 |
| 1.10 | 0.2777 | 0.2673 | 0.2570 | 0.2464 | 0.2416 | 0.2254 |
| 1.20 | 0.2519 | 0.2413 | 0.2307 | 0.2200 | 0.2093 | 0.1986 |
| 1.30 | 0.2300 | 0.2194 | 0.2088 | 0.1981 | 0.1874 | 0.1766 |
| 1.40 | 0.2081 | 0.1975 | 0.1868 | 0.1761 | 0.1654 | 0.1547 |
| 1.50 | 0.1863 | 0.1756 | 0.1649 | 0.1542 | 0.1435 | 0.1327 |
| 1.60 | 0.1644 | 0.1537 | 0.1429 | 0.1322 | 0.1215 | 0.1107 |
| ELG | Expected Loss Range |
|---|---|
| 31 | 630,000 - 720,000 |
| 30 | 720,001 - 830,000 |
| 29 | 830,001 - 990,000 |
| 28 | 990,001 - 1,180,000 |
| 27 | 1,180,001 - 1,415,000 |
| 26 | 1,415,001 - 1,744,000 |
| Per Occurrence Limit | Excess Loss Factor |
|---|---|
| $50,000 | 0.214 |
Part a (0.5 points)
Determine the guaranteed cost premium.
Part b (2.25 points)
Determine the basic premium for a $50,000 per occurrence limit.
Part c (0.75 points)
The insured's risk manager believes the retrospective premium can be reduced by selecting a higher per occurrence limit because the insured will assume a greater portion of the losses.
Evaluate the risk manager's assertion.
Answer this question and see the worked solution