State Farm Mut Grp — Private Passenger Auto

Schedule P Part 3B — net private passenger auto liability/physical damage, 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 review Open in Chain-Ladder (paid)Open in Chain-Ladder (incurred)Open in Bornhuetter–Ferguson Open in Bootstrap

Accident year	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997
Net earned premium ($000)	7,809,394	8,764,863	9,796,463	10,594,952	11,457,922	12,240,633	13,277,675	14,125,898	14,664,665	14,923,375

Paid loss triangle, cumulative ($000), as-of 1997

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	2,439,272	4,722,902	5,705,646	6,238,289	6,519,491	6,677,426	6,750,431	6,787,444	6,808,809	6,815,646
1989	2,828,267	5,368,026	6,494,597	7,096,377	7,417,869	7,575,814	7,655,217	7,693,240	7,712,077	—
1990	3,186,948	5,913,490	7,140,613	7,774,615	8,096,374	8,251,086	8,325,184	8,364,955	—	—
1991	3,192,619	5,878,000	7,075,254	7,698,459	7,996,404	8,140,065	8,215,810	—	—	—
1992	3,561,950	6,474,291	7,763,969	8,404,713	8,716,926	8,876,813	—	—	—	—
1993	3,895,076	7,024,867	8,343,417	9,003,120	9,337,099	—	—	—	—	—
1994	4,323,103	7,590,944	8,924,062	9,640,098	—	—	—	—	—	—
1995	4,491,070	7,664,190	9,006,113	—	—	—	—	—	—	—
1996	4,444,088	7,486,113	—	—	—	—	—	—	—	—
1997	4,344,144	—	—	—	—	—	—	—	—	—

Incurred loss triangle, cumulative ($000), as-of 1997

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	6,906,902	6,943,321	6,919,414	6,903,460	6,877,558	6,870,358	6,836,352	6,830,186	6,829,036	6,826,501
1989	7,945,895	7,892,149	7,857,362	7,822,945	7,794,124	7,768,352	7,734,044	7,731,989	7,733,559	—
1990	8,966,387	8,737,600	8,621,906	8,549,596	8,496,837	8,446,880	8,405,156	8,405,128	—	—
1991	9,000,161	8,781,727	8,603,817	8,495,201	8,405,955	8,322,901	8,291,065	—	—	—
1992	9,918,853	9,635,080	9,423,831	9,260,641	9,116,785	9,060,858	—	—	—	—
1993	10,680,478	10,368,083	10,063,788	9,850,861	9,714,779	—	—	—	—	—
1994	11,453,285	11,036,246	10,653,018	10,462,749	—	—	—	—	—	—
1995	11,693,004	11,090,985	10,612,837	—	—	—	—	—	—	—
1996	11,229,928	10,479,410	—	—	—	—	—	—	—	—
1997	10,648,978	—	—	—	—	—	—	—	—	—

Realized paid-loss square, all 10 development lags ($000)

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	2,439,272	4,722,902	5,705,646	6,238,289	6,519,491	6,677,426	6,750,431	6,787,444	6,808,809	6,815,646
1989	2,828,267	5,368,026	6,494,597	7,096,377	7,417,869	7,575,814	7,655,217	7,693,240	7,712,077	7,721,911
1990	3,186,948	5,913,490	7,140,613	7,774,615	8,096,374	8,251,086	8,325,184	8,364,955	8,382,479	8,394,117
1991	3,192,619	5,878,000	7,075,254	7,698,459	7,996,404	8,140,065	8,215,810	8,256,338	8,279,401	8,288,143
1992	3,561,950	6,474,291	7,763,969	8,404,713	8,716,926	8,876,813	8,959,761	8,998,462	9,016,704	9,026,329
1993	3,895,076	7,024,867	8,343,417	9,003,120	9,337,099	9,509,203	9,599,735	9,642,522	9,660,532	9,673,610
1994	4,323,103	7,590,944	8,924,062	9,640,098	10,030,681	10,216,964	10,299,231	10,340,679	10,361,560	10,375,605
1995	4,491,070	7,664,190	9,006,113	9,736,570	10,120,120	10,312,088	10,412,421	10,461,753	10,497,027	10,512,108
1996	4,444,088	7,486,113	8,845,221	9,583,622	9,999,739	10,196,271	10,293,776	10,347,058	10,373,438	10,387,245
1997	4,344,144	7,305,064	8,614,474	9,379,418	9,792,901	9,988,209	10,076,219	10,123,792	10,148,983	10,165,481

Realized incurred-loss square, all 10 development lags ($000)

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	6,906,902	6,943,321	6,919,414	6,903,460	6,877,558	6,870,358	6,836,352	6,830,186	6,829,036	6,826,501
1989	7,945,895	7,892,149	7,857,362	7,822,945	7,794,124	7,768,352	7,734,044	7,731,989	7,733,559	7,739,353
1990	8,966,387	8,737,600	8,621,906	8,549,596	8,496,837	8,446,880	8,405,156	8,405,128	8,410,395	8,408,337
1991	9,000,161	8,781,727	8,603,817	8,495,201	8,405,955	8,322,901	8,291,065	8,307,875	8,307,570	8,307,051
1992	9,918,853	9,635,080	9,423,831	9,260,641	9,116,785	9,060,858	9,055,186	9,046,855	9,053,419	9,052,266
1993	10,680,478	10,368,083	10,063,788	9,850,861	9,714,779	9,712,959	9,708,995	9,695,452	9,694,057	9,694,442
1994	11,453,285	11,036,246	10,653,018	10,462,749	10,437,221	10,428,674	10,416,488	10,400,814	10,407,112	10,410,296
1995	11,693,004	11,090,985	10,612,837	10,558,636	10,540,680	10,539,357	10,531,731	10,530,414	10,549,951	10,549,648
1996	11,229,928	10,479,410	10,399,815	10,375,237	10,413,747	10,422,225	10,419,325	10,427,357	10,424,594	10,427,810
1997	10,648,978	10,348,604	10,168,446	10,200,207	10,235,345	10,235,821	10,218,514	10,203,855	10,204,664	10,209,496

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	6,815,646	6,815,646	0.0%
1989	9	7,719,821	7,721,911	-0.0%
1990	8	8,396,601	8,394,117	0.0%
1991	7	8,288,545	8,288,143	0.0%
1992	6	9,043,728	9,026,329	0.2%
1993	5	9,702,726	9,673,610	0.3%
1994	4	10,422,621	10,375,605	0.5%
1995	3	10,571,471	10,512,108	0.6%
1996	2	10,490,872	10,387,245	1.0%
1997	1	10,933,658	10,165,481	7.6%

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