United Services Automobile Asn Grp — Private Passenger Auto
Schedule P Part 3B — net private passenger auto liability/physical damage, 1988–1997 accident years. GRCODE 2003 (United Services Automobile Asn 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) | 1,106,097 | 1,195,676 | 1,331,317 | 1,517,404 | 1,749,378 | 1,964,229 | 2,104,556 | 2,156,649 | 2,170,004 | 2,187,056 |
Paid loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 271,778 | 530,060 | 700,671 | 783,609 | 844,980 | 870,606 | 879,943 | 883,870 | 885,627 | 886,334 |
| 1989 | 296,828 | 601,823 | 780,171 | 888,761 | 944,970 | 968,118 | 976,165 | 979,221 | 982,148 | — |
| 1990 | 334,331 | 676,028 | 878,584 | 990,678 | 1,039,004 | 1,061,058 | 1,070,862 | 1,075,537 | — | — |
| 1991 | 354,530 | 741,578 | 950,130 | 1,063,478 | 1,112,208 | 1,131,215 | 1,138,375 | — | — | — |
| 1992 | 423,048 | 855,543 | 1,061,020 | 1,157,675 | 1,204,510 | 1,226,650 | — | — | — | — |
| 1993 | 484,849 | 955,067 | 1,171,931 | 1,270,740 | 1,324,732 | — | — | — | — | — |
| 1994 | 541,361 | 1,016,328 | 1,214,955 | 1,320,130 | — | — | — | — | — | — |
| 1995 | 547,102 | 986,025 | 1,185,300 | — | — | — | — | — | — | — |
| 1996 | 561,687 | 966,162 | — | — | — | — | — | — | — | — |
| 1997 | 542,021 | — | — | — | — | — | — | — | — | — |
Incurred loss triangle, cumulative ($000), as-of 1997
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 1,004,718 | 943,338 | 904,527 | 903,953 | 907,103 | 908,622 | 906,790 | 900,625 | 897,725 | 893,764 |
| 1989 | 1,087,641 | 1,038,985 | 1,030,782 | 1,019,298 | 1,015,535 | 1,009,769 | 998,765 | 994,009 | 989,663 | — |
| 1990 | 1,241,178 | 1,189,747 | 1,166,289 | 1,140,782 | 1,124,084 | 1,104,031 | 1,092,985 | 1,086,891 | — | — |
| 1991 | 1,333,590 | 1,290,793 | 1,274,984 | 1,235,943 | 1,189,132 | 1,157,715 | 1,151,469 | — | — | — |
| 1992 | 1,532,336 | 1,480,702 | 1,408,227 | 1,303,835 | 1,262,138 | 1,253,181 | — | — | — | — |
| 1993 | 1,777,164 | 1,634,241 | 1,566,779 | 1,391,535 | 1,378,086 | — | — | — | — | — |
| 1994 | 1,892,532 | 1,674,298 | 1,462,731 | 1,438,025 | — | — | — | — | — | — |
| 1995 | 1,577,620 | 1,548,129 | 1,417,382 | — | — | — | — | — | — | — |
| 1996 | 1,669,006 | 1,418,105 | — | — | — | — | — | — | — | — |
| 1997 | 1,326,522 | — | — | — | — | — | — | — | — | — |
Realized paid-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 271,778 | 530,060 | 700,671 | 783,609 | 844,980 | 870,606 | 879,943 | 883,870 | 885,627 | 886,334 |
| 1989 | 296,828 | 601,823 | 780,171 | 888,761 | 944,970 | 968,118 | 976,165 | 979,221 | 982,148 | 982,763 |
| 1990 | 334,331 | 676,028 | 878,584 | 990,678 | 1,039,004 | 1,061,058 | 1,070,862 | 1,075,537 | 1,077,444 | 1,079,195 |
| 1991 | 354,530 | 741,578 | 950,130 | 1,063,478 | 1,112,208 | 1,131,215 | 1,138,375 | 1,142,954 | 1,144,658 | 1,146,042 |
| 1992 | 423,048 | 855,543 | 1,061,020 | 1,157,675 | 1,204,510 | 1,226,650 | 1,237,658 | 1,242,377 | 1,244,268 | 1,244,693 |
| 1993 | 484,849 | 955,067 | 1,171,931 | 1,270,740 | 1,324,732 | 1,350,902 | 1,365,208 | 1,373,813 | 1,376,732 | 1,377,723 |
| 1994 | 541,361 | 1,016,328 | 1,214,955 | 1,320,130 | 1,383,536 | 1,411,569 | 1,424,231 | 1,429,402 | 1,432,062 | 1,433,285 |
| 1995 | 547,102 | 986,025 | 1,185,300 | 1,303,824 | 1,378,296 | 1,410,263 | 1,423,618 | 1,431,633 | 1,434,171 | 1,435,077 |
| 1996 | 561,687 | 966,162 | 1,161,589 | 1,282,220 | 1,352,624 | 1,385,713 | 1,402,002 | 1,408,909 | 1,412,920 | 1,413,844 |
| 1997 | 542,021 | 938,503 | 1,151,496 | 1,274,648 | 1,341,678 | 1,372,219 | 1,384,169 | 1,391,004 | 1,393,302 | 1,394,268 |
Realized incurred-loss square, all 10 development lags ($000)
| AY \ Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1988 | 1,004,718 | 943,338 | 904,527 | 903,953 | 907,103 | 908,622 | 906,790 | 900,625 | 897,725 | 893,764 |
| 1989 | 1,087,641 | 1,038,985 | 1,030,782 | 1,019,298 | 1,015,535 | 1,009,769 | 998,765 | 994,009 | 989,663 | 990,425 |
| 1990 | 1,241,178 | 1,189,747 | 1,166,289 | 1,140,782 | 1,124,084 | 1,104,031 | 1,092,985 | 1,086,891 | 1,086,859 | 1,087,971 |
| 1991 | 1,333,590 | 1,290,793 | 1,274,984 | 1,235,943 | 1,189,132 | 1,157,715 | 1,151,469 | 1,152,041 | 1,150,030 | 1,148,829 |
| 1992 | 1,532,336 | 1,480,702 | 1,408,227 | 1,303,835 | 1,262,138 | 1,253,181 | 1,253,067 | 1,251,098 | 1,249,993 | 1,249,668 |
| 1993 | 1,777,164 | 1,634,241 | 1,566,779 | 1,391,535 | 1,378,086 | 1,382,978 | 1,391,719 | 1,393,639 | 1,392,549 | 1,393,273 |
| 1994 | 1,892,532 | 1,674,298 | 1,462,731 | 1,438,025 | 1,440,568 | 1,445,231 | 1,438,262 | 1,437,594 | 1,439,459 | 1,439,464 |
| 1995 | 1,577,620 | 1,548,129 | 1,417,382 | 1,419,347 | 1,445,693 | 1,442,934 | 1,441,466 | 1,442,847 | 1,441,607 | 1,441,046 |
| 1996 | 1,669,006 | 1,418,105 | 1,359,629 | 1,388,744 | 1,410,276 | 1,414,508 | 1,418,790 | 1,418,285 | 1,419,452 | 1,417,426 |
| 1997 | 1,326,522 | 1,343,923 | 1,349,673 | 1,390,307 | 1,399,745 | 1,400,350 | 1,400,126 | 1,402,100 | 1,399,878 | 1,401,626 |
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 | 886,334 | 886,334 | 0.0% |
| 1989 | 9 | 982,932 | 982,763 | 0.0% |
| 1990 | 8 | 1,079,102 | 1,079,195 | -0.0% |
| 1991 | 7 | 1,146,697 | 1,146,042 | 0.1% |
| 1992 | 6 | 1,246,146 | 1,244,693 | 0.1% |
| 1993 | 5 | 1,375,073 | 1,377,723 | -0.2% |
| 1994 | 4 | 1,440,528 | 1,433,285 | 0.5% |
| 1995 | 3 | 1,430,755 | 1,435,077 | -0.3% |
| 1996 | 2 | 1,455,908 | 1,413,844 | 3.0% |
| 1997 | 1 | 1,568,804 | 1,394,268 | 12.5% |