State Farm Mut Grp — Workers' Compensation
Schedule P Part 3B/4B/D — net workers' compensation, 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 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) | 177,104 | 201,118 | 246,010 | 286,019 | 340,183 | 418,755 | 366,031 | 338,186 | 286,631 | 245,378 |
Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 22,190 | 60,834 | 85,104 | 100,151 | 108,812 | 114,967 | 118,790 | 121,558 | 123,492 | 125,049 |
| 1989 | 26,542 | 77,798 | 106,407 | 122,422 | 133,359 | 138,599 | 143,029 | 145,712 | 147,358 | — |
| 1990 | 32,977 | 100,494 | 134,886 | 157,758 | 168,991 | 178,065 | 182,787 | 187,760 | — | — |
| 1991 | 38,604 | 114,428 | 157,103 | 181,322 | 197,411 | 208,804 | 213,396 | — | — | — |
| 1992 | 42,466 | 125,820 | 164,776 | 189,045 | 204,377 | 213,904 | — | — | — | — |
| 1993 | 46,447 | 116,764 | 154,897 | 179,419 | 193,676 | — | — | — | — | — |
| 1994 | 41,368 | 100,344 | 132,021 | 151,081 | — | — | — | — | — | — |
| 1995 | 35,719 | 83,216 | 111,268 | — | — | — | — | — | — | — |
| 1996 | 28,746 | 66,033 | — | — | — | — | — | — | — | — |
| 1997 | 25,265 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 91,892 | 120,466 | 129,785 | 134,401 | 134,051 | 134,264 | 134,169 | 133,158 | 133,800 | 133,513 |
| 1989 | 117,540 | 160,490 | 163,802 | 162,824 | 164,650 | 163,326 | 161,246 | 161,836 | 161,673 | — |
| 1990 | 155,671 | 210,607 | 208,274 | 211,660 | 209,823 | 208,629 | 208,662 | 210,204 | — | — |
| 1991 | 189,021 | 251,182 | 253,292 | 247,771 | 244,882 | 245,666 | 244,669 | — | — | — |
| 1992 | 229,435 | 289,785 | 268,235 | 255,528 | 252,878 | 253,878 | — | — | — | — |
| 1993 | 251,804 | 259,975 | 245,594 | 251,196 | 251,129 | — | — | — | — | — |
| 1994 | 212,555 | 212,160 | 206,811 | 202,911 | — | — | — | — | — | — |
| 1995 | 178,437 | 181,175 | 174,496 | — | — | — | — | — | — | — |
| 1996 | 151,415 | 143,042 | — | — | — | — | — | — | — | — |
| 1997 | 125,429 | — | — | — | — | — | — | — | — | — |
Realized paid-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 22,190 | 60,834 | 85,104 | 100,151 | 108,812 | 114,967 | 118,790 | 121,558 | 123,492 | 125,049 |
| 1989 | 26,542 | 77,798 | 106,407 | 122,422 | 133,359 | 138,599 | 143,029 | 145,712 | 147,358 | 149,252 |
| 1990 | 32,977 | 100,494 | 134,886 | 157,758 | 168,991 | 178,065 | 182,787 | 187,760 | 192,576 | 196,092 |
| 1991 | 38,604 | 114,428 | 157,103 | 181,322 | 197,411 | 208,804 | 213,396 | 221,596 | 226,756 | 229,642 |
| 1992 | 42,466 | 125,820 | 164,776 | 189,045 | 204,377 | 213,904 | 221,659 | 228,415 | 231,760 | 235,831 |
| 1993 | 46,447 | 116,764 | 154,897 | 179,419 | 193,676 | 206,073 | 212,193 | 216,710 | 220,900 | 224,868 |
| 1994 | 41,368 | 100,344 | 132,021 | 151,081 | 165,667 | 173,167 | 177,960 | 181,932 | 185,039 | 190,572 |
| 1995 | 35,719 | 83,216 | 111,268 | 127,221 | 136,597 | 142,371 | 146,359 | 148,538 | 151,476 | 153,299 |
| 1996 | 28,746 | 66,033 | 87,748 | 100,432 | 108,442 | 116,297 | 119,566 | 121,885 | 124,377 | 126,403 |
| 1997 | 25,265 | 61,872 | 81,038 | 92,519 | 99,006 | 103,738 | 106,810 | 108,329 | 110,509 | 111,592 |
Realized incurred-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 91,892 | 120,466 | 129,785 | 134,401 | 134,051 | 134,264 | 134,169 | 133,158 | 133,800 | 133,513 |
| 1989 | 117,540 | 160,490 | 163,802 | 162,824 | 164,650 | 163,326 | 161,246 | 161,836 | 161,673 | 159,995 |
| 1990 | 155,671 | 210,607 | 208,274 | 211,660 | 209,823 | 208,629 | 208,662 | 210,204 | 208,913 | 211,620 |
| 1991 | 189,021 | 251,182 | 253,292 | 247,771 | 244,882 | 245,666 | 244,669 | 248,935 | 250,619 | 249,836 |
| 1992 | 229,435 | 289,785 | 268,235 | 255,528 | 252,878 | 253,878 | 253,301 | 256,898 | 257,831 | 257,872 |
| 1993 | 251,804 | 259,975 | 245,594 | 251,196 | 251,129 | 252,888 | 250,921 | 248,491 | 247,936 | 247,046 |
| 1994 | 212,555 | 212,160 | 206,811 | 202,911 | 200,624 | 205,076 | 207,871 | 207,980 | 207,197 | 209,982 |
| 1995 | 178,437 | 181,175 | 174,496 | 170,389 | 171,587 | 169,742 | 169,247 | 169,122 | 172,579 | 177,199 |
| 1996 | 151,415 | 143,042 | 139,484 | 141,236 | 139,567 | 138,183 | 137,267 | 138,623 | 143,859 | 141,744 |
| 1997 | 125,429 | 131,373 | 133,706 | 126,973 | 126,965 | 126,137 | 128,079 | 134,218 | 134,059 | 133,934 |
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 | 125,049 | 125,049 | 0.0% |
| 1989 | 9 | 149,216 | 149,252 | -0.0% |
| 1990 | 8 | 192,674 | 196,092 | -1.7% |
| 1991 | 7 | 224,115 | 229,642 | -2.4% |
| 1992 | 6 | 230,811 | 235,831 | -2.1% |
| 1993 | 5 | 219,624 | 224,868 | -2.3% |
| 1994 | 4 | 185,415 | 190,572 | -2.7% |
| 1995 | 3 | 157,873 | 153,299 | 3.0% |
| 1996 | 2 | 125,746 | 126,403 | -0.5% |
| 1997 | 1 | 129,150 | 111,592 | 15.7% |