Your triangle stops at 120 months, but a workers compensation claim can pay for thirty years. The tail factor is the single number that carries development past the last observed diagonal to ultimate.
Development factors measure how losses grow from one age to the next. A triangle only observes ages up to its oldest accident year. If that year is at 120 months but claims still pay past 120 months, the age-to-age factors miss everything beyond the edge. The tail factor fills that gap.
The tail is a cumulative factor from the last observed maturity to ultimate. Think of it as the product of all the age-to-age factors you would see if the triangle extended forever, but cannot observe.
KEY: The tail multiplies onto the cumulative development factor, extending it to ultimate. It does not replace any observed factor.
Suppose observed age-to-age factors take a year from 12 months to 120 months. Their product is the cumulative development factor (CDF) to 120 months. The tail carries 120 months to ultimate.
Common mistakes
- Adding the tail instead of multiplying. The tail is a factor, not a dollar amount. Writing CDF 3.018 + 1.06 instead of 3.018 × 1.06 destroys the estimate.
- Applying the tail to only the newest year. The tail extends every year to ultimate. The oldest year at 120 months still needs the 1.045 tail; it is not already at ultimate.
- Reflexively flooring every reported tail at 1.00. A sub-1.00 reported tail is legitimate when case outstanding runs off with savings or when recoveries are included in the claims data. Investigate the cause before overriding a factor like 0.99 up to 1.00.
Bottom line
- A tail factor extends development beyond the oldest observed age to ultimate, capturing payments or emergence the triangle cannot show.
- The tail is a cumulative development factor from the last observed age to ultimate; it multiplies onto the age-to-age product, never replaces it.
- Long-tail lines (WC, general liability, med mal) need tails; short-tail lines (auto physical damage) often have a tail near 1.00.
- Common selection methods: curve fitting to reported factors, using an industry benchmark, the bondy method, and inference from a paid-versus-incurred comparison.
Exam shortcut
When a problem gives a tail, multiply it into the front of the cumulative factor product before touching any diagonal. The tail and the observed factors form one CDF. If the line is long-tail (WC, general liability, med mal), expect a tail above 1.05; if short-tail (auto physical damage), expect a tail near 1.00. Use the line to sanity-check any number you compute.
The full lesson (about 1,804 words, 12 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- B7
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