Free CAS Exam 5 (Basic Ratemaking and Reserving) Unpaid Claim Estimation Techniques Practice Questions

Unpaid claim estimation techniques are the core of the Estimating Claim Liabilities section of CAS Exam 5 (45-55% of the exam, CAS). Questions test the development (chain ladder), case outstanding development, expected claims, Bornhuetter-Ferguson, Cape Cod, frequency-severity, Berquist-Sherman, and Benktander methods, when each fits, and how to adjust an analysis when case reserve adequacy, settlement rates, business mix, or inflation move underneath it.

101 questions 15 easy 32 medium 54 hard 2026 syllabus

Sample Questions

Question 1 Easy
The reported development (chain ladder) technique relies most directly on which key assumption?
Solution
C is correct. The development technique projects ultimate losses by multiplying losses reported (or paid) to date by an age-to-ultimate factor derived from historical emergence patterns. This works only if the amounts reported to date are predictive of future development and that emergence pattern is stable across accident years.
Question 2 Medium
Cumulative paid losses (in thousands) are shown below.

| Accident Year | 12 months | 24 months |
|---|---|---|
| 2022 | 1,600 | 2,000 |
| 2023 | 2,400 | 3,120 |

Using the volume-weighted (all-year) average, what is the selected 12-to-24 month age-to-age factor?
Solution
C is correct. The volume-weighted factor divides the sum of the later cumulative values by the sum of the earlier cumulative values across all years: (2,000+3,120)/(1,600+2,400)=5,120/4,000=1.280(2{,}000 + 3{,}120)/(1{,}600 + 2{,}400) = 5{,}120/4{,}000 = 1.280. This weights each accident year by its loss volume rather than treating the two individual factors (1.25 and 1.30) equally.
Question 3 Hard
An actuary estimates ultimate losses for a long-tailed line using the Benktander (Gunnar-Benktander) method. Earned premium is $16,000,000 with an expected loss ratio of 62.5%. Age-to-age factors are 12-to-24 = 1.25 and 24-to-36 = 1.60 with a tail of 1.00, and reported losses at 12 months are $6,000,000. What is the Benktander ultimate loss estimate?
Solution
D is correct. Expected losses are 0.625×16,000,000=10,000,0000.625 \times 16{,}000{,}000 = 10{,}000{,}000. The CDF to ultimate at 12 months is 1.25×1.60=2.001.25 \times 1.60 = 2.00, so the reported percentage is 1/2.00=0.501/2.00 = 0.50 and the unreported percentage is 0.50. The BF ultimate is 6,000,000+10,000,000×0.50=11,000,0006{,}000{,}000 + 10{,}000{,}000 \times 0.50 = 11{,}000{,}000. Benktander uses the BF ultimate as the revised a priori: 6,000,000+11,000,000×0.50=11,500,0006{,}000{,}000 + 11{,}000{,}000 \times 0.50 = 11{,}500{,}000.
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CAS Exam 5 Study Guide (Basic Techniques for Ratemaking and Estimating Claim Liabilities, 2026)

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