Premium

Question 1

Goal of ratemaking

Answer 1

Balance the fundamental insurance equation:

Premium = Losses + LAE + UW expenses + UW Profit

Question 2

Adjustment to historical premium

Answer 2

1. Bring the historical premium to the rate level currently in effect
2. Develop premium to ultimate levels if the premium is still changing
3. Project the historical premium to the premium level expected in the future

Question 3

2 premium aggregation methods

Answer 3

Calendar year

Policy Year

Question 4

“15th of the month” rule

Answer 4

Treat all policies as if they were written at the mid-point of the period.

Question 5

Is “15th of the month” rule reasonable?

Answer 5

Good approximation if policies are written uniformly during each time period.

Question 6

adjusting the premium “to current rate level”

Answer 6

aka. putting the premium “on-level”, adjustment made to historical premium for rate changes that occurred during or after the historical experience period or the projected premium will be understated or overstated

Question 7

premium trend

Answer 7

actual or expected distributional changes

Question 8

Extension of exposures method

Answer 8

Rerating every policy to restate the historical premium to the amount that would be charged under the current rates

Question 9

Parallelogram method

Answer 9

aka. geometric method, undertaken on a group of policies and less accurate than extension of exposures

Question 10

assumption of parallelogram method

Answer 10

Premium is written evenly throughout the time period

Question 11

Steps for the parallelogram method: 1

Answer 11

Determine the timing and amount of the rate changes during and after the experience period and group the policies into rate level groups according to the timing of each rate change

Question 12

Steps for the parallelogram method: 2

Answer 12

Calculate the portion of the year’s earned premium corresponding to each rate level group

Question 13

Steps for the parallelogram method: 3

Answer 13

Calculate the cumulative rate level index for each rate level group

Question 14

Steps for the parallelogram method: 4

Answer 14

Calculate the weighted average cumulative rate level index for each year

Question 15

Steps for the parallelogram method: 5

Answer 15

Calculate the on-level factor as the ratio of the current cumulative rate level index for each year

Question 16

Steps for the parallelogram method: 6

Answer 16

Apply the on-level factor to the earned premium for the appropriate year

Question 17

Two problems with the parallelogram method

Answer 17

1. Method assumes policies are written evenly throughout the year
2. Applied at the aggregate level