FL Farm Bureau Grp — Private Passenger Auto
Schedule P Part 3B — net private passenger auto liability/physical damage, 1988–1997 accident years. GRCODE 4839 (FL Farm Bureau 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) | 258,278 | 277,280 | 316,221 | 359,146 | 407,777 | 440,132 | 468,723 | 499,637 | 517,336 | 533,638 |
Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 102,260 | 168,086 | 190,196 | 199,058 | 203,783 | 204,531 | 205,280 | 205,779 | 205,911 | 205,921 |
| 1989 | 113,438 | 188,826 | 211,976 | 221,104 | 225,131 | 226,632 | 227,314 | 227,532 | 227,553 | — |
| 1990 | 128,209 | 213,190 | 241,623 | 253,582 | 257,674 | 259,489 | 259,970 | 260,062 | — | — |
| 1991 | 129,181 | 218,195 | 248,903 | 259,789 | 264,556 | 266,188 | 266,822 | — | — | — |
| 1992 | 139,085 | 242,303 | 271,847 | 282,231 | 286,041 | 288,748 | — | — | — | — |
| 1993 | 154,914 | 262,070 | 291,947 | 303,199 | 307,179 | — | — | — | — | — |
| 1994 | 172,025 | 291,837 | 322,487 | 334,928 | — | — | — | — | — | — |
| 1995 | 188,892 | 304,583 | 337,595 | — | — | — | — | — | — | — |
| 1996 | 191,839 | 306,832 | — | — | — | — | — | — | — | — |
| 1997 | 196,865 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 225,414 | 208,497 | 207,803 | 208,583 | 208,035 | 206,341 | 206,188 | 206,039 | 205,881 | 205,997 |
| 1989 | 247,731 | 232,846 | 233,104 | 232,197 | 229,821 | 228,243 | 227,930 | 227,703 | 227,651 | — |
| 1990 | 290,505 | 269,680 | 268,524 | 265,149 | 263,004 | 261,447 | 261,109 | 260,842 | — | — |
| 1991 | 303,790 | 282,919 | 274,778 | 271,232 | 269,510 | 267,925 | 267,632 | — | — | — |
| 1992 | 343,457 | 306,462 | 299,060 | 294,903 | 292,479 | 291,705 | — | — | — | — |
| 1993 | 376,913 | 330,855 | 320,521 | 315,124 | 313,454 | — | — | — | — | — |
| 1994 | 402,824 | 365,186 | 354,292 | 350,261 | — | — | — | — | — | — |
| 1995 | 417,102 | 385,604 | 376,371 | — | — | — | — | — | — | — |
| 1996 | 438,743 | 390,974 | — | — | — | — | — | — | — | — |
| 1997 | 444,654 | — | — | — | — | — | — | — | — | — |
Realized paid-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 102,260 | 168,086 | 190,196 | 199,058 | 203,783 | 204,531 | 205,280 | 205,779 | 205,911 | 205,921 |
| 1989 | 113,438 | 188,826 | 211,976 | 221,104 | 225,131 | 226,632 | 227,314 | 227,532 | 227,553 | 227,567 |
| 1990 | 128,209 | 213,190 | 241,623 | 253,582 | 257,674 | 259,489 | 259,970 | 260,062 | 260,440 | 260,647 |
| 1991 | 129,181 | 218,195 | 248,903 | 259,789 | 264,556 | 266,188 | 266,822 | 267,036 | 267,110 | 267,228 |
| 1992 | 139,085 | 242,303 | 271,847 | 282,231 | 286,041 | 288,748 | 289,701 | 291,113 | 290,978 | 291,031 |
| 1993 | 154,914 | 262,070 | 291,947 | 303,199 | 307,179 | 309,058 | 310,106 | 310,530 | 311,168 | 311,353 |
| 1994 | 172,025 | 291,837 | 322,487 | 334,928 | 340,905 | 343,633 | 344,415 | 345,678 | 345,767 | 345,797 |
| 1995 | 188,892 | 304,583 | 337,595 | 353,235 | 361,719 | 364,926 | 367,210 | 367,680 | 367,780 | 367,921 |
| 1996 | 191,839 | 306,832 | 343,871 | 361,767 | 369,513 | 372,768 | 373,847 | 374,628 | 375,497 | 375,078 |
| 1997 | 196,865 | 306,138 | 345,204 | 361,646 | 369,787 | 372,702 | 373,760 | 374,292 | 374,515 | 374,519 |
Realized incurred-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 225,414 | 208,497 | 207,803 | 208,583 | 208,035 | 206,341 | 206,188 | 206,039 | 205,881 | 205,997 |
| 1989 | 247,731 | 232,846 | 233,104 | 232,197 | 229,821 | 228,243 | 227,930 | 227,703 | 227,651 | 227,589 |
| 1990 | 290,505 | 269,680 | 268,524 | 265,149 | 263,004 | 261,447 | 261,109 | 260,842 | 260,670 | 260,749 |
| 1991 | 303,790 | 282,919 | 274,778 | 271,232 | 269,510 | 267,925 | 267,632 | 267,421 | 267,224 | 267,259 |
| 1992 | 343,457 | 306,462 | 299,060 | 294,903 | 292,479 | 291,705 | 291,295 | 291,427 | 291,277 | 291,188 |
| 1993 | 376,913 | 330,855 | 320,521 | 315,124 | 313,454 | 312,365 | 311,884 | 311,369 | 311,577 | 311,675 |
| 1994 | 402,824 | 365,186 | 354,292 | 350,261 | 347,757 | 346,084 | 345,574 | 346,227 | 346,014 | 346,070 |
| 1995 | 417,102 | 385,604 | 376,371 | 372,472 | 371,674 | 369,024 | 369,220 | 368,908 | 368,797 | 368,233 |
| 1996 | 438,743 | 390,974 | 380,356 | 377,508 | 375,924 | 375,620 | 375,493 | 375,806 | 375,892 | 375,324 |
| 1997 | 444,654 | 398,635 | 381,525 | 378,026 | 377,518 | 376,654 | 375,895 | 375,442 | 375,065 | 375,038 |
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 | 205,921 | 205,921 | 0.0% |
| 1989 | 9 | 227,564 | 227,567 | -0.0% |
| 1990 | 8 | 260,166 | 260,647 | -0.2% |
| 1991 | 7 | 267,241 | 267,228 | 0.0% |
| 1992 | 6 | 289,971 | 291,031 | -0.4% |
| 1993 | 5 | 310,575 | 311,353 | -0.2% |
| 1994 | 4 | 344,294 | 345,797 | -0.4% |
| 1995 | 3 | 361,649 | 367,921 | -1.7% |
| 1996 | 2 | 368,275 | 375,078 | -1.8% |
| 1997 | 1 | 393,129 | 374,519 | 5.0% |