Free CAS Exam 6-U.S. (Regulation and Financial Reporting) Solvency Metrics: RBC & IRIS Practice Questions

Risk-based capital and the IRIS ratios are the solvency metrics of the Financial Reporting section of CAS Exam 6-U.S. (60-75% of the exam, CAS). Questions test calculating RBC and reading the action levels it triggers, computing the IRIS ratios, and interpreting what unusual values signal about an insurer's solvency position.

120 questions 8 easy 24 medium 88 hard 2026 syllabus

Sample Questions

Question 1 Easy
The IRIS ratio that divides net written premium by policyholders' surplus is primarily a test of which condition?
Solution
C is correct. The net-premium-to-surplus ratio is an underwriting leverage test. It measures how much premium the insurer is writing relative to the surplus cushion available to absorb adverse deviation. A high value signals that a thin surplus base is supporting a large volume of business, so pricing or reserving errors could quickly erode solvency.
Question 2 Medium
An insurer's net premiums written were $360M in the prior year and $520M in the current year. Compute the IRIS change-in-net-writings ratio for the current year.
Solution
C is correct. The change-in-net-writings ratio divides the year-over-year change in net premiums written by the prior year's net premiums written:

520−360360=160360≈44.44%\frac{520 - 360}{360} = \frac{160}{360} \approx 44.44\%

Because the usual range for this ratio is roughly −33%-33\% to +33%+33\%, a value of 44.44%44.44\% falls outside the usual range and would be flagged as an unusual result signaling rapid growth that can strain surplus.
Question 3 Hard
An insurer's pre-covariance RBC charges (in millions) are R0=5R_0 = 5, R1=30R_1 = 30, R2=40R_2 = 40, R3=20R_3 = 20, R4=60R_4 = 60, and R5=50R_5 = 50. Using the property-casualty covariance formula, compute the Authorized Control Level RBC.
Solution
A is correct. The property-casualty covariance formula keeps R0R_0 outside the square root and combines the remaining charges: RBC=R0+R12+R22+R32+R42+R52.\text{RBC} = R_0 + \sqrt{R_1^2 + R_2^2 + R_3^2 + R_4^2 + R_5^2}. The sum of squares is 900+1600+400+3600+2500=9000900 + 1600 + 400 + 3600 + 2500 = 9000, and 9000=94.87\sqrt{9000} = 94.87. Adding R0R_0 gives 5+94.87=99.875 + 94.87 = 99.87 million, which is the Company Action Level RBC. The Authorized Control Level RBC is half of that: 0.5×99.87=49.90.5 \times 99.87 = 49.9 million.
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