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DD&R/Extended Reserve Panel

DD&R/Extended Reserve Panel. Laura A. Johnson, FCAS, MAAA. Actual Practice - Using the Model proposed in the Walker & Skrodenis article Changes to the Model Additional Considerations. Changes to the Model Expected number of free tail executions Lapses Average load across all ages

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DD&R/Extended Reserve Panel

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  1. DD&R/Extended Reserve Panel Laura A. Johnson, FCAS, MAAA

  2. Actual Practice - Using the Model proposed in the Walker & Skrodenis article • Changes to the Model • Additional Considerations

  3. Changes to the Model • Expected number of free tail executions • Lapses • Average load across all ages • Applying the load • Reserve calculation if other than start up year

  4. Changes to the Model - Expected Number of Free Tail Executions • Apply Death, Disability & retirements rates all to the beginning of the year population rather than cumulative • More Conservative - assumes no “overlap” exists in the rates • Impact is small -> 12.166% changes to 12.322% • Specific calculation -> pg. 338, (7)=(3)x[(4)+(5)+(6)]

  5. Changes to the Model - Lapses • Apply Lapse (non renewal) rates to the beginning of the year population rather than to the end of year population • Correct method depends on how the lapse rate itself is calculated • Impact is moderate ->12.322% changes to 12.081% • Specific calculation ->pg. 338, (9) = (3) x (8)

  6. Changes to the Model - Average Load across all ages • Short term approach - weight together based on current insureds • Long term approach - give more weight to younger insureds since they will be around funding longer - i.e., weight by insured and time Advantages - average load does not change every year - consistent with calculation by age Danger - if in practice, the load is recalculated each year any way, you’ll end up short if you use the long term average • Impact -> 12.081% under short term approach 10.780% under long term approach • Specific calculation -> pg. 344, (4) (avg) = sum of (16) from Model 2 times number of insureds at each age over all ages divided by the sum of (14) from Model 2 times number of insureds at each age over all ages in other words, weight the numerator and the denominator and sum across those first, then divide

  7. Changes to the Model - Applying the Load • Note load is stated as a percentage of pure premium (loss) • Can use that pure premium load as a rate load only if there • are no Fixed Expenses • Otherwise, need to convert to a rate load

  8. Changes to the Model - Reserve Calculation • Reserve = Future DD&R Losses - Future DD&R Premium • Thus, same age insureds need the same reserve regardless of what • their entry age (the age they began funding) was • Need to restate Future DD&R Losses and Premiums so that the current • age is “time 0” • Impact -> none if current age = entry age (i.e., start up year) • -> potentially huge impact otherwise: 50-75% lower in our • experience • Specific calculation -> pg. 339, column (18) and (19): divide current • formula by column (10)

  9. Additional Considerations • No age bands - matrix of insureds by entry age and current age • Retirement requirements for free tail: i.e., 55&10 or 65&5 • Experience modification factor (note: don’t include expense • considerations) • Actual utilization rate • Expected future funding of the reserve • Expected redundancy/inadequacy of future rates

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