Exam ASTAM Practice Question 2
Study guide: Exam ASTAM
A pricing actuary has measured a severity trend of 10% a year on an insurer's ground-up losses: every loss, whatever its size, is expected to be 10% larger next year. To see what that trend does to the losses the insurer actually prices, the actuary takes six ground-up losses from the current year as a representative sample:
| Loss | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Ground-up amount | 480 | 1,000 | 2,500 | 6,000 | 9,600 | 20,000 |
Next year each of these losses is 10% larger.
Part a (1 point)
The insurer sells a policy with a straight deductible of 500 per loss and no limit. Calculate the annual trend in the insurer's total payments on the six losses. Enter it as a percentage to one decimal place, without the % sign (for example, 3.5).
Part b (1 point)
The insurer's rates are based on basic-limits losses: each loss capped at 10,000. Calculate the annual trend in the six losses' total basic-limits amount. Enter it as a percentage to one decimal place, without the % sign.
Part c (1 point)
The actuary proposes to project both the deductible policy's payments and the basic-limits losses by applying the 10% ground-up severity trend directly. Which statement describes the effect?
- A) Both projections are correct, because a trend in every loss is a trend of the same size in every layer
- B) The deductible projection is understated and the basic-limits projection is overstated
- C) The deductible projection is overstated and the basic-limits projection is understated
- D) Both projections are understated, because a deductible and a limit each leverage the trend upward
- E) Both projections are overstated, because a deductible and a limit each dampen the trend
Part d (2 points)
Explain why the trend in the deductible policy's payments differs from the ground-up trend, why the trend in basic-limits losses differs from it in the other direction, and how the actuary should measure the trend to apply to each.
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