Tail-factor selection

3 days ago

2 min read

The Decision Question

How much judgement sits beyond the observed development period, and how much reserve depends on it?

Default Practice

A familiar actuarial curve-fitting view places observed age-to-age paid development factors beside fitted curves. It shows whether the curve follows the late development pattern and how quickly it approaches one. Here, exponential and inverse-power curves are fitted to the same six annual intervals ending at 60–120 months, then extended beyond the observed period..

Where the Default Can Improve

The chart helps assess each annual factor, but the factors flatten near one while their combined effect remains material. The reader must mentally compound the tail and then translate it into money.

Suggested Alternative

Replace the annual factors with cumulative development factors from each age to the projected ultimate. A factor of 1.0342 means multiplying cumulative paid at that age by 1.0342. Keep the age-to-age chart for assessing the fits, and pair the cumulative view with a monetary comparison.

· The black baseline compounds observed factors only as far as 120 months, where it reaches 1.0000 and stops.

· The coloured curves include the fitted or selected tail.

· The gap above 1.0000 now shows the full tail allowance.

What This Reveals and the Risks to Consider

The last black point is at 108 months, with a factor of 1.0120 representing the observed development from 108 to 120 months.

The candidate curves show how different assumptions translate into money. Their spread is a sensitivity comparison, not a probability range. A larger tail is not automatically better supported; the selection needs a reason tied to claims experience, settlement practice or relevant external evidence.

The main risks of presenting the chart this way are:

· Cumulative values can look like direct observations. The black points are products of historical factor estimates, rather than individual observed development factors.

· Earlier curve separation can be misread. The coloured curves include their assumed tails at earlier ages. Their separation before 120 does not represent different observed experience.

· The full scale hides the decision. Large early factors compress the tail differences near 1.000.

Decision Boundary

Use this when…	Don’t use this when…
You need to challenge a tail selection and its reserve effect.	You want to explain the selection of age-to-age development factors from the observed factors.
The selected run-off assumption need to be explained and documented.