Allstate Ins Co Grp — Workers' Compensation
Schedule P Part 3B/4B/D — net workers' compensation, 1988–1997 accident years. GRCODE 86 (Allstate Ins Co 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 WC pricing modelOpen 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) | 394,742 | 374,252 | 280,320 | 313,982 | 252,698 | 201,055 | 174,381 | 146,366 | 93,294 | 7,651 |
Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 70,571 | 155,905 | 220,744 | 251,595 | 274,156 | 287,676 | 298,499 | 304,873 | 321,808 | 325,322 |
| 1989 | 66,547 | 136,447 | 179,142 | 211,343 | 231,430 | 244,750 | 254,557 | 270,059 | 273,873 | — |
| 1990 | 52,233 | 133,370 | 178,444 | 204,442 | 222,193 | 232,940 | 253,337 | 256,788 | — | — |
| 1991 | 59,315 | 128,051 | 169,793 | 196,685 | 213,165 | 234,676 | 239,195 | — | — | — |
| 1992 | 39,991 | 89,873 | 114,117 | 133,003 | 154,362 | 159,496 | — | — | — | — |
| 1993 | 19,744 | 47,229 | 61,909 | 85,099 | 87,215 | — | — | — | — | — |
| 1994 | 20,379 | 46,773 | 88,636 | 91,077 | — | — | — | — | — | — |
| 1995 | 18,756 | 84,712 | 87,311 | — | — | — | — | — | — | — |
| 1996 | 42,609 | 44,916 | — | — | — | — | — | — | — | — |
| 1997 | 691 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 367,404 | 362,988 | 347,288 | 330,648 | 354,690 | 350,092 | 346,808 | 349,124 | 348,157 | 347,762 |
| 1989 | 336,928 | 316,483 | 278,496 | 303,033 | 299,496 | 295,061 | 299,251 | 297,492 | 300,620 | — |
| 1990 | 289,198 | 311,381 | 277,980 | 277,732 | 276,563 | 278,067 | 276,704 | 281,101 | — | — |
| 1991 | 297,174 | 277,209 | 269,739 | 272,666 | 271,318 | 267,578 | 269,592 | — | — | — |
| 1992 | 181,796 | 205,079 | 199,106 | 187,833 | 185,663 | 184,940 | — | — | — | — |
| 1993 | 114,807 | 114,774 | 101,460 | 98,430 | 96,930 | — | — | — | — | — |
| 1994 | 107,934 | 107,569 | 97,730 | 96,185 | — | — | — | — | — | — |
| 1995 | 100,686 | 94,456 | 92,314 | — | — | — | — | — | — | — |
| 1996 | 53,381 | 51,205 | — | — | — | — | — | — | — | — |
| 1997 | 6,725 | — | — | — | — | — | — | — | — | — |
Realized paid-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 70,571 | 155,905 | 220,744 | 251,595 | 274,156 | 287,676 | 298,499 | 304,873 | 321,808 | 325,322 |
| 1989 | 66,547 | 136,447 | 179,142 | 211,343 | 231,430 | 244,750 | 254,557 | 270,059 | 273,873 | 277,574 |
| 1990 | 52,233 | 133,370 | 178,444 | 204,442 | 222,193 | 232,940 | 253,337 | 256,788 | 261,166 | 263,000 |
| 1991 | 59,315 | 128,051 | 169,793 | 196,685 | 213,165 | 234,676 | 239,195 | 245,499 | 247,131 | 248,319 |
| 1992 | 39,991 | 89,873 | 114,117 | 133,003 | 154,362 | 159,496 | 164,013 | 166,212 | 167,397 | 168,844 |
| 1993 | 19,744 | 47,229 | 61,909 | 85,099 | 87,215 | 88,602 | 89,444 | 89,899 | 90,446 | 90,686 |
| 1994 | 20,379 | 46,773 | 88,636 | 91,077 | 92,583 | 93,346 | 93,897 | 94,165 | 94,558 | 94,730 |
| 1995 | 18,756 | 84,712 | 87,311 | 89,200 | 90,001 | 90,247 | 90,687 | 91,068 | 91,001 | 91,161 |
| 1996 | 42,609 | 44,916 | 46,981 | 47,899 | 48,583 | 49,109 | 49,442 | 49,073 | 49,161 | 49,255 |
| 1997 | 691 | 2,085 | 2,795 | 2,866 | 2,905 | 2,909 | 2,908 | 2,909 | 2,909 | 2,909 |
Realized incurred-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 367,404 | 362,988 | 347,288 | 330,648 | 354,690 | 350,092 | 346,808 | 349,124 | 348,157 | 347,762 |
| 1989 | 336,928 | 316,483 | 278,496 | 303,033 | 299,496 | 295,061 | 299,251 | 297,492 | 300,620 | 296,626 |
| 1990 | 289,198 | 311,381 | 277,980 | 277,732 | 276,563 | 278,067 | 276,704 | 281,101 | 278,023 | 279,032 |
| 1991 | 297,174 | 277,209 | 269,739 | 272,666 | 271,318 | 267,578 | 269,592 | 267,745 | 266,677 | 264,467 |
| 1992 | 181,796 | 205,079 | 199,106 | 187,833 | 185,663 | 184,940 | 184,507 | 184,705 | 183,888 | 181,261 |
| 1993 | 114,807 | 114,774 | 101,460 | 98,430 | 96,930 | 96,121 | 98,085 | 93,795 | 93,753 | 95,363 |
| 1994 | 107,934 | 107,569 | 97,730 | 96,185 | 96,124 | 95,821 | 95,722 | 95,496 | 96,374 | 95,766 |
| 1995 | 100,686 | 94,456 | 92,314 | 92,241 | 92,929 | 92,214 | 92,107 | 92,362 | 91,470 | 93,060 |
| 1996 | 53,381 | 51,205 | 51,087 | 51,015 | 50,226 | 50,343 | 50,060 | 49,564 | 49,739 | 49,459 |
| 1997 | 6,725 | 6,663 | 6,473 | 2,917 | 2,933 | 3,103 | 3,002 | 2,909 | 2,907 | 2,909 |
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 | 325,322 | 325,322 | 0.0% |
| 1989 | 9 | 276,864 | 277,574 | -0.3% |
| 1990 | 8 | 268,961 | 263,000 | 2.3% |
| 1991 | 7 | 258,402 | 248,319 | 4.1% |
| 1992 | 6 | 180,151 | 168,844 | 6.7% |
| 1993 | 5 | 104,286 | 90,686 | 15.0% |
| 1994 | 4 | 119,003 | 94,730 | 25.6% |
| 1995 | 3 | 132,157 | 91,161 | 45.0% |
| 1996 | 2 | 90,948 | 49,255 | 84.6% |
| 1997 | 1 | 3,110 | 2,909 | 6.9% |