A chain-ladder factor tells you how losses grow. It does not tell you why. When the number moves, you turn the triangle into a diagnostic and ask whether claims got bigger, more numerous, or slower to settle.
A standard triangle holds cumulative dollars by accident year and development age. A diagnostic set adds companion triangles: claim counts closed, claim counts reported, and ratios built from them. The point is to decompose a change in loss development into its drivers.
Every cell of a loss triangle is severity times frequency times exposures. When a development factor drifts, at least one of those pieces moved. The diagnostic triangles isolate which one.
Before you compute any count ratio or average value, settle the data questions, or your diagnosis rests on a moving definition.
CHECK FIRST: Pin down these before you read a single count or average. - Whether claims closed with no payment (CNP) sit in both the closed and the reported count triangles...
Common mistakes
- Calling a diagonal a trend. A spike shared by every open year in one calendar period is a calendar-year effect (inflation or a reserve change), not an accident-year severity trend. Reading it down a column mislabels the cause.
- Confusing paid and reported signals. Settlement speedup biases the paid chain ladder high; case strengthening biases the reported chain ladder high. They point in opposite triangles, so name which one moved.
- Miscomputing the ratios. Losses over exposures is pure premium, not severity. Frequency is counts over exposures. Severity is losses over counts. Swapping denominators inverts the diagnosis.
Bottom line
- Before any count ratio or average value, pin definitions and data: CNP in counts, reopened-claim coding, expense-only claims, large-claim distortion, deductibles and retentions, and the partial-payment mismatch in the average paid triangle.
- Build parallel triangles (paid loss, reported loss, closed counts, reported counts, average severity, paid-to-reported ratio) and read them together, not one alone.
- Read three directions: down a column is maturity, across a row is one accident year growing up, along a diagonal is a shared calendar-year effect.
- Severity = losses over counts; frequency = counts over exposures; loss ratio = losses over premium.
Exam shortcut
When a triangle "changes," immediately build the two companion triangles (counts and average severity). Flat counts with rising severity is a severity story; rising counts with flat severity is a frequency story. To separate operational from economic change, trace the pattern's geometry: a diagonal streak is calendar-year (inflation, reserve directive, system switch); a stair-step by accident year at the same age is rate adequacy or underwriting drift.
The full lesson (about 2,900 words, 19 min read) adds 3 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- B8
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