Sample Questions
Question 1
Easy
When restating historical premium for a rate indication, an actuary reflects premium audits. What is the primary purpose of doing so?
Solution
D is correct. Many policies (e.g., workers compensation, general liability) are written on estimated exposures such as payroll or sales and are audited after the term. Reflecting the audit trues the recorded premium up or down to the actual exposure, so the premium in the experience period matches the exposure that actually generated the losses.
Question 2
Medium
An insurer implemented a +8% rate change effective October 1, 2023, its most recent change. Annual policies are written uniformly throughout the year. Using the parallelogram method, what on-level factor restates calendar year 2024 earned premium to the current rate level?
Solution
E is correct. The change effective October 1, 2023 falls 0.75 of a year into 2023. For annual policies, the portion of CY2024 earned premium still at the old rate is the triangle ; the remaining 0.71875 is at the new level. Setting the old index to 1.00 and the new index to 1.08, the average CY2024 rate index is . The on-level factor brings this to the current level: .
Question 3
Hard
An actuary prepares the loss and LAE input for a rate indication. Reported losses are $3,600,000 with a loss development factor of 1.15 to ultimate. ALAE is estimated at 8% of ultimate loss, and ULAE is estimated at 6% of ultimate loss and ALAE combined. What is the ultimate loss and LAE amount for the indication?
Solution
C is correct. First develop reported losses to ultimate: . Add ALAE at 8% of ultimate loss: , giving loss and ALAE of . Then add ULAE at 6% of that combined figure: . Total ultimate loss and LAE is .
