Technical methods · Intermediate · ⏱ 20 min
Chain ladder from scratch: your first loss triangle
The reserving method every analyst meets in month one. Built with actual numbers, from raw triangle to IBNR, including the judgment calls the textbook skips.
Reserving is counting the cost of promises already made, and chain ladder is how the counting usually starts. Here it is with real numbers, no hand-waving.
The triangle
Cumulative paid claims ($000s) by accident year (rows) and months of development (columns):
| AY | 12m | 24m | 36m |
|---|---|---|---|
| 2023 | 1,000 | 1,800 | 2,070 |
| 2024 | 1,200 | 2,100 | ? |
| 2025 | 1,500 | ? | ? |
The shape is the problem: older years are nearly complete; recent years have barely developed. The question marks are the reserve.
Step 1: development factors
How much do claims grow between ages? Divide, then average across years:
- 12→24: 2023: 1,800/1,000 = 1.80 · 2024: 2,100/1,200 = 1.75 → average 1.775
- 24→36: 2023: 2,070/1,800 = 1.15
(Real triangles have more years, and you’ll choose between simple averages, volume-weighted averages, or excluding a freak year. That choice is the first place actuarial judgment enters the math.)
Step 2: complete the triangle
Multiply the last known value through the remaining factors:
- 2024 at 36m: 2,100 × 1.15 = 2,415
- 2025 at 24m: 1,500 × 1.775 = 2,662.5 → at 36m: 2,662.5 × 1.15 = 3,062
Step 3: the reserve
IBNR + development reserve = ultimate minus paid-to-date:
- 2024: 2,415 − 2,100 = 315
- 2025: 3,062 − 1,500 = 1,562
- Total indicated reserve ≈ $1,877k
That’s the whole method: history’s growth pattern, applied to the years still growing.
Where it breaks (the part interviews probe)
Chain ladder trusts the past completely. It fails when the book changed: new claims system, different case-reserving philosophy, a mix shift toward slower lines. And it’s wildly unstable for immature years, where one early claim swings the whole projection (2025’s estimate above hangs entirely on one observed cell). The standard rescue for that instability is Bornhuetter-Ferguson, the next lesson.
Go deeper: build this triangle again from a blank sheet, then four bigger ones, and annotate every factor you select with the reason you selected it. The annotation is the part that teaches.