CAS Exam 5 Fall 2014, Question 12
Study guide: Exam 5
Given the following information:
| Policy Year | Premium | Present Value of Losses | Variable Expenses: New | Variable Expenses: Renewal | Fixed Expenses: New | Fixed Expenses: Renewal | Income |
|---|---|---|---|---|---|---|---|
| 1 | $800 | $656 | $242 | - | $142 | - | $(240) |
| 2 | $872 | $701 | - | $54 | - | $32 | $86 |
| 3 | $950 | $748 | - | $59 | - | $33 | $110 |
| 4 | $1,036 | $799 | - | $64 | - | $34 | $139 |
| 5 | $1,129 | $853 | - | $70 | - | $36 | $170 |
| Policy Year | Persistency | Cumulative Persistency | Profit | Discount Factor | Present Value of Profits | Present Value of Premiums |
|---|---|---|---|---|---|---|
| 1 | 100% | 100% | $(240) | 1.00 | $(240) | $800 |
| 2 | 85% | 85% | $73 | 1.12 | $65 | $662 |
| 3 | 86% | 73% | $81 | 1.25 | $64 | $554 |
| 4 | 87% | 64% | $88 | 1.40 | $63 | $469 |
| 5 | 88% | 56% | $95 | 1.57 | $61 | $402 |
| Total | $13 | $2,886 |
- Premium-to-surplus ratio is 2 to 1.
- Surplus equals GAAP equity.
- The company seeks growth in this market.
- Management requires the present value of profit of policy years 1 to 5 to be positive in total.
Part a (0.5 points)
Briefly describe two differences between asset share pricing and pure premium ratemaking when they are used to price property and casualty products.
Part b (1 point)
After preparing the asset share model shown above, the actuary evaluates an alternative set of persistency assumptions in which persistency in the third and fourth policy years are changed to 81% and 82%, respectively. Calculate the revised present value of premiums.
Part c (1 point)
Briefly discuss the results of the asset share model under each set of persistency assumptions with regard to Management's profitability requirement. Provide a recommendation to management on whether to make a change to the current rating structure.
Answer this question and see the worked solution