Sample Questions
Question 1
Easy
In estimating unpaid claims with the development (chain-ladder) technique, what does a tail factor represent?
Solution
C is correct. A tail factor extends development beyond the oldest maturity observed in the triangle out to ultimate, capturing the loss emergence that occurs after the latest available data point. Triangles are finite, so the tail factor accounts for development the observed link ratios cannot measure.
Question 2
Medium
During calendar year 2024, an insurer paid $400,000 in claims. Case reserves on its open claims were $500,000 at January 1, 2024 and $650,000 at December 31, 2024. Ignoring IBNR, what is the calendar-year 2024 reported (incurred) loss?
Solution
D is correct. Calendar-year reported (incurred) loss equals payments made during the year plus the change in case reserves over the year: The reserve change of $150,000 captures the movement in the estimated liability on still-open claims, and adding it to the $400,000 paid gives the total incurred activity recognized in calendar year 2024.
Question 3
Hard
A commercial property insurer raised its standard per-occurrence deductible for all policies written on or after January 1, 2025; policies written before that date kept the old deductible through their full terms. All policies are annual and are written approximately uniformly through each year. Management wants a triangle built on the basis that first produces a cohort composed entirely of the new deductible, and the reserve study is being performed as of December 31, 2025. Which basis should the actuary select for this study, and what is the principal consequence of that choice?
Solution
B is correct. The change is defined by the date a policy was written, so the only basis that sorts claims the same way the change does is policy year: policy year 2025 contains every policy written on or after January 1, 2025 and nothing else, making it a clean cohort as soon as it exists. Accident year sorts by date of loss instead, and annual policies written throughout 2024 remain in force well into 2025, so losses occurring in 2025 arise under both the old and the new deductible. Accident year 2025 is therefore a blend, and the first fully clean accident year is 2026, which does not exist at the December 31, 2025 valuation. The cost of choosing policy year is maturity: with annual policies written uniformly, a policy year takes twenty-four months to become fully earned, so policy year 2025 at twelve months of development is only about half earned and carries roughly a year more development, and a correspondingly larger cumulative factor, than an accident year at the same nominal age. That is the trade the actuary accepts in exchange for a homogeneous deductible cohort a full year earlier.
