Werner ch 5

• 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

• All premium transactions within calendar period
• Regardless of policy effective date
• Represented graphically by squares

• 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

• 1. Dollar amounts charged by an insurer for policies written during a specific 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

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

• Amount of the policy premiums that have been exposed to risk during a specified time period
• Premium for coverage that has been provided
• Represents portion of total premium that insurer can retain if policy is canceled

• 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 dierent policy years
• Policy year premium is not fixed at end of PY for audited LOBs
• Will continue to develop after end of PY period

• 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

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

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

• 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

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

• Policy term
• Calendar year versus policy year
• Whether rate change affects policies midterm or only on effective date of policies

• 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

• Problem 1 - Assumes policies 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 classification analysis

• At time of analysis, ultimate premium for experience period may be unknown
• Incomplete year of data
• Premium audits

• Distributional changes causing average premium level to change
• Rating Characteristic: Example - Homeowners Amount of Insurance
• Premium Level Changes: Example - Insurer chooses to move policyholders to a higher deductible
• Shifts in Mix of Business: Example - Company purchases another insurer's book of business

• 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

• Argument for Earned
• Used in most other parts of ratemaking analysis
• Argument for Written
• Allows for capture of more recent data because premium 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

• 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 fit exponential or linear trend to data

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

• 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

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

• Changes in average premium vary signicantly year-by-year
• Historical changes are significantly different than expected future changes

• 1. Single annual premium trend is not appropriate for each year in experience period
• 2. Trend in historical period is significantly different that what is expected in future

• 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

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