CAS Exam 5Basic Techniques for Ratemaking & Estimating Claim Liabilities

The trended, developed experience loss ratio is 68%. Variable expenses are 28% of premium and the target underwriting profit is 3% of premium. There are no fixed expenses. Calculate the indicated rate change.

All policies are annual and written uniformly. A +10% rate change took effect on July 1 of calendar year X. Using the parallelogram method, calculate the on-level factor to bring CY X earned premium to the current rate level.

Cumulative paid losses for accident year 2023 are 1,200 at 12 months. Selected age-to-age factors are 1.50 (12–24), 1.20 (24–36) and a tail of 1.05 from 36 to ultimate. Calculate the estimated unpaid claims for AY 2023.

Earned premium for an accident year is 5,000, the expected loss ratio is 65%, reported losses to date are 1,900, and the reported CDF to ultimate is 1.60. Calculate the Bornhuetter–Ferguson ultimate loss estimate.

Projected frequency is 0.08 claims per exposure and projected severity is 12,000. Fixed expenses are 50 per exposure, variable expenses are 25% of premium and the profit provision is 5% of premium. Calculate the indicated rate per exposure.

Reported losses and earned premium by accident year, with reported CDFs to ultimate:

(a) Calculate the Cape Cod expected loss ratio. (b) Estimate AY 2023 IBNR under Cape Cod and under Bornhuetter–Ferguson with an a priori ELR of 70%. (c) Briefly explain when Cape Cod is preferable to BF.

Historical losses occurred, on average, 2.5 years before the average date the new rates will be in effect. Annual severity trend is 5%. Calculate the trend factor to be applied to historical losses.

A rating plan currently gives Class X a relativity of 1.20 relative to base. The indicated loss ratio for the base class is 0.70 and for Class X is 0.84 (both relative to the same premium base). Calculate the indicated relativity for Class X (before any off-balance correction).

Reported losses for accident year 2022 are 900 at the current evaluation with a reported age-to-ultimate CDF of 1.35. Paid losses at the same evaluation are 500 with a paid CDF of 2.10. Calculate the difference between the paid-method and reported-method ultimate loss estimates (paid minus reported).

An insurer notices that the reported loss development factors have been declining sharply in recent diagonals even though the case-reserving philosophy has not changed. This pattern is most consistent with a:

An insurer's book is written on annual policies, uniformly throughout the year. A rate change of +8% took effect on April 1 of calendar year 2023 (the only rate change in the two years shown). Calculate the on-level factor needed to bring calendar year 2022 earned premium to the current (post 4/1/2023) rate level, and briefly explain why the parallelogram method is needed instead of simply using the stated rate change.