California Cas Grp — Workers' Compensation
Schedule P Part 3B/4B/D — net workers' compensation, 1988–1997 accident years. GRCODE 337 (California Cas 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) | 99,779 | 85,110 | 82,187 | 94,997 | 100,508 | 114,352 | 106,540 | 74,652 | 60,244 | 45,933 |
Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 9,558 | 22,778 | 33,298 | 40,348 | 45,146 | 48,048 | 49,782 | 50,623 | 51,812 | 51,939 |
| 1989 | 7,913 | 19,472 | 29,622 | 36,816 | 40,975 | 43,302 | 44,707 | 45,871 | 46,229 | — |
| 1990 | 8,744 | 24,302 | 35,406 | 43,412 | 48,057 | 50,897 | 52,879 | 53,956 | — | — |
| 1991 | 13,301 | 32,950 | 47,201 | 56,394 | 61,650 | 65,039 | 66,566 | — | — | — |
| 1992 | 11,424 | 29,086 | 42,034 | 50,910 | 56,406 | 59,437 | — | — | — | — |
| 1993 | 11,792 | 27,161 | 38,229 | 46,722 | 50,742 | — | — | — | — | — |
| 1994 | 11,194 | 26,893 | 38,488 | 45,580 | — | — | — | — | — | — |
| 1995 | 12,550 | 31,604 | 44,045 | — | — | — | — | — | — | — |
| 1996 | 13,194 | 31,474 | — | — | — | — | — | — | — | — |
| 1997 | 9,372 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 62,679 | 64,000 | 65,607 | 65,292 | 62,250 | 61,185 | 59,387 | 57,138 | 53,473 | 53,261 |
| 1989 | 62,058 | 56,660 | 56,598 | 56,831 | 55,294 | 53,481 | 51,379 | 48,446 | 48,300 | — |
| 1990 | 63,955 | 61,523 | 63,166 | 61,402 | 59,474 | 57,613 | 57,161 | 56,971 | — | — |
| 1991 | 73,918 | 75,094 | 73,188 | 71,199 | 71,056 | 70,831 | 70,532 | — | — | — |
| 1992 | 77,143 | 75,133 | 73,284 | 73,155 | 68,284 | 67,845 | — | — | — | — |
| 1993 | 79,925 | 78,263 | 78,163 | 68,546 | 67,697 | — | — | — | — | — |
| 1994 | 73,628 | 73,554 | 70,736 | 69,720 | — | — | — | — | — | — |
| 1995 | 69,521 | 80,281 | 79,381 | — | — | — | — | — | — | — |
| 1996 | 69,720 | 73,181 | — | — | — | — | — | — | — | — |
| 1997 | 50,171 | — | — | — | — | — | — | — | — | — |
Realized paid-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 9,558 | 22,778 | 33,298 | 40,348 | 45,146 | 48,048 | 49,782 | 50,623 | 51,812 | 51,939 |
| 1989 | 7,913 | 19,472 | 29,622 | 36,816 | 40,975 | 43,302 | 44,707 | 45,871 | 46,229 | 46,483 |
| 1990 | 8,744 | 24,302 | 35,406 | 43,412 | 48,057 | 50,897 | 52,879 | 53,956 | 54,440 | 54,857 |
| 1991 | 13,301 | 32,950 | 47,201 | 56,394 | 61,650 | 65,039 | 66,566 | 67,783 | 68,323 | 68,965 |
| 1992 | 11,424 | 29,086 | 42,034 | 50,910 | 56,406 | 59,437 | 61,029 | 62,354 | 63,037 | 63,406 |
| 1993 | 11,792 | 27,161 | 38,229 | 46,722 | 50,742 | 53,480 | 55,960 | 56,826 | 57,810 | 57,917 |
| 1994 | 11,194 | 26,893 | 38,488 | 45,580 | 48,836 | 50,559 | 52,119 | 53,426 | 54,666 | 55,255 |
| 1995 | 12,550 | 31,604 | 44,045 | 52,539 | 57,122 | 60,526 | 62,882 | 64,470 | 65,799 | 67,011 |
| 1996 | 13,194 | 31,474 | 44,070 | 51,693 | 57,120 | 60,453 | 63,499 | 66,205 | 67,423 | 68,225 |
| 1997 | 9,372 | 23,735 | 34,191 | 39,726 | 44,685 | 48,438 | 50,775 | 52,694 | 54,217 | 55,377 |
Realized incurred-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 62,679 | 64,000 | 65,607 | 65,292 | 62,250 | 61,185 | 59,387 | 57,138 | 53,473 | 53,261 |
| 1989 | 62,058 | 56,660 | 56,598 | 56,831 | 55,294 | 53,481 | 51,379 | 48,446 | 48,300 | 48,162 |
| 1990 | 63,955 | 61,523 | 63,166 | 61,402 | 59,474 | 57,613 | 57,161 | 56,971 | 56,634 | 56,368 |
| 1991 | 73,918 | 75,094 | 73,188 | 71,199 | 71,056 | 70,831 | 70,532 | 70,260 | 70,104 | 71,274 |
| 1992 | 77,143 | 75,133 | 73,284 | 73,155 | 68,284 | 67,845 | 67,620 | 66,445 | 67,382 | 67,515 |
| 1993 | 79,925 | 78,263 | 78,163 | 68,546 | 67,697 | 65,321 | 64,226 | 62,411 | 62,578 | 62,122 |
| 1994 | 73,628 | 73,554 | 70,736 | 69,720 | 67,578 | 66,760 | 60,916 | 59,795 | 59,806 | 59,974 |
| 1995 | 69,521 | 80,281 | 79,381 | 78,694 | 77,901 | 73,164 | 71,733 | 71,656 | 71,910 | 71,829 |
| 1996 | 69,720 | 73,181 | 72,878 | 72,188 | 72,063 | 72,348 | 72,404 | 72,498 | 72,402 | 72,573 |
| 1997 | 50,171 | 49,770 | 50,240 | 56,703 | 57,924 | 59,809 | 59,230 | 59,232 | 59,300 | 59,939 |
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 | 51,939 | 51,939 | 0.0% |
| 1989 | 9 | 46,342 | 46,483 | -0.3% |
| 1990 | 8 | 54,955 | 54,857 | 0.2% |
| 1991 | 7 | 69,217 | 68,965 | 0.4% |
| 1992 | 6 | 63,786 | 63,406 | 0.6% |
| 1993 | 5 | 57,583 | 57,917 | -0.6% |
| 1994 | 4 | 57,070 | 55,255 | 3.3% |
| 1995 | 3 | 66,813 | 67,011 | -0.3% |
| 1996 | 2 | 68,709 | 68,225 | 0.7% |
| 1997 | 1 | 50,439 | 55,377 | -8.9% |