State Farm Mut Grp — Commercial Auto
Schedule P Part 3B — net commercial auto liability, 1988–1997 accident years. GRCODE 1767 (State Farm Mut Grp). Values in $000s, net earned premium and net losses.
Actual outcome known
Source: CAS Loss Reserve Database (Meyers & Shi), NAIC Schedule P. Meyers, G.G. and Shi, P. (2011). The Retrospective Testing of Stochastic Loss Reserve Models. CAS E-Forum, using data pulled from NAIC Schedule P Parts 1-4, 1988-1997.
Run quarterly rate & reserve reviewOpen in Chain-Ladder (paid)Open in Chain-Ladder (incurred)Open in Bornhuetter–FergusonOpen in Bootstrap
| Accident year | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 |
|---|---|---|---|---|---|---|---|---|---|---|
| Net earned premium ($000) | 286,378 | 308,908 | 326,503 | 332,616 | 341,890 | 355,840 | 379,781 | 398,755 | 406,609 | 406,516 |
Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 54,699 | 108,337 | 143,899 | 164,818 | 179,538 | 185,391 | 188,023 | 189,759 | 190,520 | 193,499 |
| 1989 | 60,091 | 119,366 | 151,151 | 174,665 | 185,469 | 192,213 | 196,152 | 198,013 | 199,997 | — |
| 1990 | 65,860 | 130,803 | 172,390 | 197,977 | 210,230 | 219,267 | 222,428 | 224,078 | — | — |
| 1991 | 61,946 | 121,108 | 158,880 | 182,689 | 195,247 | 201,854 | 204,911 | — | — | — |
| 1992 | 65,043 | 128,550 | 164,433 | 187,508 | 199,823 | 208,008 | — | — | — | — |
| 1993 | 72,295 | 144,579 | 185,446 | 208,388 | 219,345 | — | — | — | — | — |
| 1994 | 81,988 | 151,197 | 189,630 | 212,446 | — | — | — | — | — | — |
| 1995 | 83,207 | 152,470 | 190,974 | — | — | — | — | — | — | — |
| 1996 | 79,699 | 143,590 | — | — | — | — | — | — | — | — |
| 1997 | 75,827 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 172,262 | 180,112 | 187,158 | 188,775 | 190,569 | 190,701 | 190,344 | 191,752 | 192,087 | 194,099 |
| 1989 | 192,154 | 198,550 | 196,977 | 197,877 | 198,265 | 198,957 | 200,108 | 200,044 | 201,101 | — |
| 1990 | 215,766 | 218,769 | 222,694 | 225,682 | 226,110 | 226,247 | 226,698 | 226,739 | — | — |
| 1991 | 208,425 | 207,219 | 207,811 | 211,186 | 210,054 | 208,456 | 207,581 | — | — | — |
| 1992 | 216,172 | 217,665 | 216,400 | 214,510 | 212,937 | 214,979 | — | — | — | — |
| 1993 | 237,378 | 237,679 | 237,253 | 233,699 | 231,958 | — | — | — | — | — |
| 1994 | 249,592 | 248,849 | 242,493 | 243,140 | — | — | — | — | — | — |
| 1995 | 256,434 | 249,225 | 238,468 | — | — | — | — | — | — | — |
| 1996 | 237,860 | 227,353 | — | — | — | — | — | — | — | — |
| 1997 | 220,029 | — | — | — | — | — | — | — | — | — |
Realized paid-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 54,699 | 108,337 | 143,899 | 164,818 | 179,538 | 185,391 | 188,023 | 189,759 | 190,520 | 193,499 |
| 1989 | 60,091 | 119,366 | 151,151 | 174,665 | 185,469 | 192,213 | 196,152 | 198,013 | 199,997 | 200,480 |
| 1990 | 65,860 | 130,803 | 172,390 | 197,977 | 210,230 | 219,267 | 222,428 | 224,078 | 224,855 | 225,430 |
| 1991 | 61,946 | 121,108 | 158,880 | 182,689 | 195,247 | 201,854 | 204,911 | 205,535 | 206,051 | 206,719 |
| 1992 | 65,043 | 128,550 | 164,433 | 187,508 | 199,823 | 208,008 | 210,925 | 213,006 | 214,097 | 214,524 |
| 1993 | 72,295 | 144,579 | 185,446 | 208,388 | 219,345 | 225,981 | 230,040 | 231,594 | 232,739 | 233,365 |
| 1994 | 81,988 | 151,197 | 189,630 | 212,446 | 229,511 | 237,406 | 240,779 | 242,463 | 242,860 | 244,280 |
| 1995 | 83,207 | 152,470 | 190,974 | 212,923 | 226,193 | 233,723 | 237,024 | 237,748 | 239,596 | 240,184 |
| 1996 | 79,699 | 143,590 | 184,346 | 206,780 | 224,327 | 233,298 | 237,216 | 236,725 | 236,825 | 237,368 |
| 1997 | 75,827 | 143,120 | 184,965 | 206,565 | 220,052 | 225,837 | 229,414 | 230,996 | 230,301 | 230,775 |
Realized incurred-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 172,262 | 180,112 | 187,158 | 188,775 | 190,569 | 190,701 | 190,344 | 191,752 | 192,087 | 194,099 |
| 1989 | 192,154 | 198,550 | 196,977 | 197,877 | 198,265 | 198,957 | 200,108 | 200,044 | 201,101 | 201,380 |
| 1990 | 215,766 | 218,769 | 222,694 | 225,682 | 226,110 | 226,247 | 226,698 | 226,739 | 226,744 | 226,263 |
| 1991 | 208,425 | 207,219 | 207,811 | 211,186 | 210,054 | 208,456 | 207,581 | 207,273 | 206,990 | 207,092 |
| 1992 | 216,172 | 217,665 | 216,400 | 214,510 | 212,937 | 214,979 | 214,145 | 214,513 | 214,899 | 215,141 |
| 1993 | 237,378 | 237,679 | 237,253 | 233,699 | 231,958 | 232,944 | 233,677 | 233,264 | 233,786 | 233,698 |
| 1994 | 249,592 | 248,849 | 242,493 | 243,140 | 242,907 | 244,737 | 244,854 | 243,805 | 243,678 | 244,692 |
| 1995 | 256,434 | 249,225 | 238,468 | 236,970 | 239,422 | 241,843 | 241,497 | 240,784 | 241,707 | 241,793 |
| 1996 | 237,860 | 227,353 | 231,394 | 232,722 | 238,184 | 240,732 | 240,776 | 238,824 | 238,056 | 237,781 |
| 1997 | 220,029 | 226,968 | 228,101 | 230,540 | 232,679 | 234,313 | 233,572 | 232,942 | 231,590 | 232,101 |
Hindsight test: chain-ladder vs. realized outcome
A volume-weighted chain-ladder projection from the 1997 upper triangle, compared against the actual realized ultimate now that the full square is known.
| Accident year | Age at 1997 | Projected ultimate | Realized ultimate | Error % |
|---|---|---|---|---|
| 1988 | 10 | 193,499 | 193,499 | 0.0% |
| 1989 | 9 | 203,124 | 200,480 | 1.3% |
| 1990 | 8 | 229,193 | 225,430 | 1.7% |
| 1991 | 7 | 211,401 | 206,719 | 2.3% |
| 1992 | 6 | 218,032 | 214,524 | 1.6% |
| 1993 | 5 | 238,547 | 233,365 | 2.2% |
| 1994 | 4 | 246,282 | 244,280 | 0.8% |
| 1995 | 3 | 252,280 | 240,184 | 5.0% |
| 1996 | 2 | 243,622 | 237,368 | 2.6% |
| 1997 | 1 | 247,080 | 230,775 | 7.1% |