Chain-Ladder Development
Project ultimate losses from a loss-development triangle using selectable age-to-age averaging methods, an optional fitted tail, and Mack (1993) standard errors.
Loaded: FL Farm Bureau Grp — Private Passenger Auto (paid, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| AY 1 | ||||||||||
| AY 2 | ||||||||||
| AY 3 | ||||||||||
| AY 4 | ||||||||||
| AY 5 | ||||||||||
| AY 6 | ||||||||||
| AY 7 | ||||||||||
| AY 8 | ||||||||||
| AY 9 | ||||||||||
| AY 10 |
Development factors
| Age | 1→2 | 2→3 | 3→4 | 4→5 | 5→6 | 6→7 | 7→8 | 8→9 | 9→10 |
|---|---|---|---|---|---|---|---|---|---|
| Method | |||||||||
| Factor | 1.664 | 1.120 | 1.042 | 1.017 | 1.007 | 1.003 | 1.001 | 1.000 | 1.000 |
| CDF to ult. | 1.997 | 1.200 | 1.071 | 1.028 | 1.011 | 1.004 | 1.002 | 1.000 | 1.000 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 205,921 | 1.000 | 205,921 | 0 | 0 | 0.0% |
| AY 2 | 227,553 | 1.000 | 227,564 | 11 | 45 | 404.3% |
| AY 3 | 260,062 | 1.000 | 260,166 | 104 | 127 | 121.2% |
| AY 4 | 266,822 | 1.002 | 267,241 | 419 | 333 | 79.5% |
| AY 5 | 288,748 | 1.004 | 289,971 | 1,223 | 420 | 34.3% |
| AY 6 | 307,179 | 1.011 | 310,575 | 3,396 | 771 | 22.7% |
| AY 7 | 334,928 | 1.028 | 344,294 | 9,366 | 1,474 | 15.7% |
| AY 8 | 337,595 | 1.071 | 361,649 | 24,054 | 2,100 | 8.7% |
| AY 9 | 306,832 | 1.200 | 368,275 | 61,443 | 4,519 | 7.4% |
| AY 10 | 196,865 | 1.997 | 393,129 | 196,264 | 11,264 | 5.7% |
| Total | 2,732,505 | 3,028,786 | 296,281 | 13,049 | 4.4% |
IBNR by origin year with Mack std. error
Assumptions & limitations
- Development patterns are stable across origin years and future development follows the same age-to-age factors as historical experience.
- Mack's model assumes the chain-ladder recursion is correctly specified (uncorrelated origin years, no calendar-year trend) and factors are the volume-weighted averages unless overridden per age.
- A fitted exponential-decay tail is an extrapolation; validate against industry benchmarks before relying on it.