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

Applying the load

Reserve calculation if other than start up year

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)]

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)

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

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

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)

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