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: State Farm Mut Grp — Private Passenger Auto (incurred, 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 | 0.968 | 0.977 | 0.987 | 0.991 | 0.995 | 0.995 | 1.000 | 1.000 | 1.000 |
| CDF to ult. | 0.915 | 0.945 | 0.968 | 0.980 | 0.989 | 0.995 | 0.999 | 1.000 | 1.000 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 6,826,501 | 1.000 | 6,826,501 | 0 | 0 | 0.0% |
| AY 2 | 7,733,559 | 1.000 | 7,730,688 | -2,871 | 1,620 | -56.4% |
| AY 3 | 8,405,128 | 1.000 | 8,402,250 | -2,878 | 3,100 | -107.7% |
| AY 4 | 8,291,065 | 0.999 | 8,285,251 | -5,814 | 5,211 | -89.6% |
| AY 5 | 9,060,858 | 0.995 | 9,013,604 | -47,254 | 7,551 | -16.0% |
| AY 6 | 9,714,779 | 0.989 | 9,611,411 | -103,368 | 32,774 | -31.7% |
| AY 7 | 10,462,749 | 0.980 | 10,254,451 | -208,298 | 62,581 | -30.0% |
| AY 8 | 10,612,837 | 0.968 | 10,268,035 | -344,802 | 95,939 | -27.8% |
| AY 9 | 10,479,410 | 0.945 | 9,903,561 | -575,849 | 170,719 | -29.6% |
| AY 10 | 10,648,978 | 0.915 | 9,739,379 | -909,599 | 272,004 | -29.9% |
| Total | 92,235,864 | 90,035,131 | -2,200,733 | 370,256 | -16.8% |
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.