Tail development factor
Factor applied beyond the last observed column of the triangle to cover development the observation window does not show, and the single biggest source of divergence between two reserve reviews of the same book.
A twelve-column triangle stops at one hundred forty-four months, but a bodily injury claim or a legacy pollution claim settles well beyond that. The tail development factor is what you apply to the last column's cumulative to reach ultimate, and it is never observed: it is extrapolated. Three families of technique coexist. You fit a parametric curve to the last observed factors, such as inverse exponential or inverse power; you benchmark against market data; or you rely on expert judgment. The tail factor concentrates most of the reserve uncertainty on long-tail lines because it applies to the whole book, not just the most recent year. A two-point move in the tail factor shifts more reserve than a full revision of the observed factors. That is why it must be documented and justified line by line, never carried forward silently from the previous closing.
Medical malpractice book as of December 31, 2025, twelve-column triangle, last-column cumulative 340M EUR. The selected tail factor moves from 1.04 to 1.07 after fitting an inverse power curve to the last four factors. The reserve rises by 10.2M EUR on that parameter alone, against 3.1M EUR for all the observed-factor revisions in the same closing.
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