W&M Ch 5

Question 1

Adjustments to historical premium

Answer 1

• Premium to current rate level
• -projections distorted if historical premium doesn’t reflect past rate changes
• Develop premium to ultimate levels when premium is still changing
• Project to expected future premium level
• -includes premium trend and changes in mix of business

Question 2

Calendar Year aggregation and Accident Year aggregation of premium

Answer 2

All premium transactions within calendar period

• regardless of policy effective date
• represented graphically by squares

Question 3

Policy Year aggregation of premium

Answer 3

All premium transactions on policies with effective dates during the year

• represented graphically by parallelograms
• need 24 calendar months to complete (assuming annual policies)
• -reason that calendar year more often used

Question 4

Describe Written Premium

Answer 4

1. Dollar amounts charged by an insurer for policies written during a specific time period
2. Calendar Year Written Premium includes:
   - premium for policies with effective dates during the calendar period
   - mid-term adjustments during calendar year regardless of policy effective date

Question 5

Describe Policy Year Written Premium

Answer 5

All premium and adjustments for policies with effective dates in policy period

Question 6

What is an Earned Premium?

Answer 6

Amount of the policy premiums that have been exposed to risk during a specified time period

• Premium for coverage that has to be provided
• Represents the portion of total premium that insurer can retain if policy is canceled

Question 7

Describe a Policy Year

Answer 7

• Earned premium assign to year policy is effective
• -when policy expires, PY Written = PY Earned
• -unlike CY, premium for one policy cannot be earned in two different policy years
• Policy year premium is not fixed at end of PY for audited LOBs
• -will continue to develop after end of PY period

Question 8

Describe an Unearned Premium

Answer 8

Portion of written premium for which coverage has not been provided

• Amount of premium company has not yet earned
• -insured is due back upon policy cancellation

Written Premium = Earned Premium + Unearned Premium

Question 9

Describe an Inforce Premium

Answer 9

• Full-term premium of all policies in effect at a specific point in time
• Best estimate of the company’s mix of business as of a given date

Question 10

Current Rate Level Adjustments to Premium

Answer 10

Adjustments made to historical premium to account for rate changes
-Failure to adjust will incorrectly project future premium

Question 11

Extension of Exposures Adjustments to Premium

Answer 11

Method to bring rates to current level by re-rating each policy using current rates

• Advantage
• -most accurate method to bring rates to current level
• Disadvantage
• -need detailed data

Question 12

Parallelogram Method (aka geometric method) Adjustment to Premium

Answer 12

Adjusts the aggregated historical premium by an average factor to get premium on-level
-Assumes exposure is uniformly distributed over time

Question 13

Parallelogram Method factors that affect application of method

Answer 13

• Policy term
• Calendar Year vs Policy Year
• Whether rate change affects policies midterm or only on effective date of policies

Question 14

What are the Standard Calculations for the Parallelogram Method?

Answer 14

• Group policies into rate level groups according to timing of each rate change
• Calculate the portion of earned premium corresponding to each rate level group
• Calculate the cumulative relative rate level for each group
• Calculate the average relative rate level for each year
• Calculate the on-level factor = current relative rate level / average relative rate level
• Apply on-level factor to earned premium for appropriate year

Question 15

What are some problems with the Parallelogram Method?

Answer 15

Problem 1 - Assumes policies are written uniformly throughout the year
-Reasonable for some lines but inappropriate for others
Problem 2 - Generally applied at aggregate level using overall average changes
-Adjusted premium will likely not be acceptable for classification analysis

Question 16

What is Premium Development needed for?

Answer 16

At time of analysis, ultimate premium for experience period may be unknown

• Incomplete year of data
• Premium audits

Question 17

Premium Trend

Answer 17

Distributional changes causing average premium level to change

• Rating Characteristic
• -ex. Homeowners Amount of Insurance
• Premium Level Changes
• -ex. Insurer chooses to move policyholders to a higher deductible
• Shifts in Mix of Business
• -ex. Company purchases another insurer’s book of business

Question 18

What are the steps to adjust for premium trend?

Answer 18

• Determine how to measure any changes that have occurred
• Determine if distributional shifts were one-time events or continuous
• Judgmentally include any expected future shifts

Question 19

Written vs. Earned Premium to select premium trend

Answer 19

Argument for Earned:
-Used in most other parts of ratemaking analysis
Arguments for Written:
-Allows for capture of more recent data because premium is not earned until well after it is written
-Using earned would postpone recognition of effects of most recent changes
-Trends in written will eventually emerge in earned

Question 20

Selection of trend

Answer 20

1. Often use quarterly average written premium
   - More responsive than annual average written
2. Adjust data for rate changes and other one-time effects
   - If not done, selected trend will account for change, which will then adjust for it twice
3. Compare quarterly average written to prior year quarterly average
4. May fit exponential or linear trend to data

Question 21

Describe One-Step Trending

Answer 21

• Applies a single annual trend factor across the entire experience period and into the future period
• Each year’s earned premium in the experience period is trended separately to same point in time

Question 22

One Step Trending Period

Answer 22

1. Trend period from the average experience period written date to the average effective period written date
2. Average written date is half the policy term earlier than the average earned date
3. Average written date for future policy period is effective date of new rates plus half of the period in which the rates are projected to be effective

Question 23

Items that can affect the length of the trending period

Answer 23

• Policy term
• Historical premium is policy year rather than calendar year
• Length of time rates are expected to be in effect

Question 24

Difficulties in applying one-step trending

Answer 24

• Changes in average premium vary significantly year-by-year

- Historical changes are significantly different than expected future changes

Question 25

What are the advantages of Two-Step Trending?

Answer 25

1. Single annual premium trend is not appropriate for each year in experience period
2. Trend in historical period is significantly different than what is expected in future

Question 26

What is Step 1 in Two-Step Trending?

Answer 26

Trend all experience period data to the latest trend data point

• Trend premium to the midpoint of the latest trend data point in the series
• -may use latest available quarter average written
• -may use latest annual average written

Question 27

What is Step 2 in Two-Step Trending?

Answer 27

Trend from the latest data trend point to the average effective period written date