Free CAS Exam 5 (Basic Ratemaking and Reserving) Premium, Loss & Trend Adjustments Practice Questions
Premium, loss, and trend adjustments sit in the Ratemaking section of CAS Exam 5 (45-55% of the exam, CAS). Questions test bringing historical premium on-level with the parallelogram and extension-of-exposures methods, reflecting premium audits, preparing loss and LAE inputs with the standard ratios and adjustments, fitting exponential and linear trends over the correct trend periods, keeping large losses and catastrophes from distorting the data, and the claims-made versus occurrence distinction.
34 questions3 easy14 medium17 hard2026 syllabus
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?
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Correct Answer: D
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?
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Correct Answer: A
Solution
A 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 21(0.75)2=0.28125; 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 0.28125(1.00)+0.71875(1.08)=1.0575. The on-level factor brings this to the current level: 1.08/1.0575=1.0213.
Question 3
Hard
Summit Casualty is preparing the loss input to a rate indication. Reported experience losses are $5,400,000, including a single shock claim of $900,000. The actuary caps individual claims at $400,000 and reloads the capped losses with an excess factor of 1.08. The result is then trended exponentially at 4.5% per year over a 2.0-year trend period. What are the trended, adjusted losses?
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Correct Answer: D
Solution
D is correct. The shock claim's excess over the $400,000 cap is $900,000 − $400,000 = $500,000, so capped losses are $5,400,000 − $500,000 = $4,900,000. Reload for the removed excess: 4,900,000×1.08=5,292,000. Trend exponentially: 5,292,000×(1.045)2=5,292,000×1.0920=5,779,000.
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