Federal Ins Co Grp — Commercial Auto

Schedule P Part 3B — net commercial auto liability, 1988–1997 accident years. GRCODE 388 (Federal 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 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)	91,701	91,905	94,492	103,361	105,558	91,202	106,537	117,950	132,895	150,549

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	13,457	34,825	47,886	54,133	58,087	58,570	59,505	60,207	60,312	60,516
1989	19,839	35,763	50,410	57,288	59,881	61,554	63,265	64,574	65,511	—
1990	12,539	39,729	50,719	55,531	58,555	59,949	62,243	62,626	—	—
1991	10,985	43,846	53,507	56,949	61,031	63,387	64,518	—	—	—
1992	8,211	47,369	60,200	67,407	72,494	74,048	—	—	—	—
1993	13,549	28,099	36,806	49,346	53,599	—	—	—	—	—
1994	15,013	31,542	47,702	54,388	—	—	—	—	—	—
1995	18,861	36,113	49,835	—	—	—	—	—	—	—
1996	25,002	44,377	—	—	—	—	—	—	—	—
1997	27,309	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	75,802	67,043	66,213	63,829	62,156	61,295	60,544	60,346	60,502	60,516
1989	70,154	67,812	68,565	66,837	65,967	65,642	65,072	65,193	65,923	—
1990	66,582	66,119	64,969	64,568	63,758	64,074	63,957	63,904	—	—
1991	74,394	72,389	69,512	67,056	66,988	66,923	66,427	—	—	—
1992	78,699	80,785	80,657	80,478	78,609	78,850	—	—	—	—
1993	59,677	59,582	59,088	57,561	58,348	—	—	—	—	—
1994	66,720	64,170	66,375	64,884	—	—	—	—	—	—
1995	75,113	74,430	75,797	—	—	—	—	—	—	—
1996	82,313	92,033	—	—	—	—	—	—	—	—
1997	97,148	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	13,457	34,825	47,886	54,133	58,087	58,570	59,505	60,207	60,312	60,516
1989	19,839	35,763	50,410	57,288	59,881	61,554	63,265	64,574	65,511	65,212
1990	12,539	39,729	50,719	55,531	58,555	59,949	62,243	62,626	62,465	62,896
1991	10,985	43,846	53,507	56,949	61,031	63,387	64,518	65,491	65,683	65,849
1992	8,211	47,369	60,200	67,407	72,494	74,048	75,689	76,085	76,790	77,074
1993	13,549	28,099	36,806	49,346	53,599	55,392	56,513	57,159	57,465	57,649
1994	15,013	31,542	47,702	54,388	58,228	61,518	61,642	61,936	62,034	62,554
1995	18,861	36,113	49,835	65,202	70,809	73,982	76,522	76,371	76,731	77,372
1996	25,002	44,377	66,385	86,191	94,430	99,266	102,248	102,747	103,152	103,595
1997	27,309	61,134	84,679	100,369	106,290	109,345	111,492	112,759	113,212	113,280

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	75,802	67,043	66,213	63,829	62,156	61,295	60,544	60,346	60,502	60,516
1989	70,154	67,812	68,565	66,837	65,967	65,642	65,072	65,193	65,923	65,397
1990	66,582	66,119	64,969	64,568	63,758	64,074	63,957	63,904	63,787	63,233
1991	74,394	72,389	69,512	67,056	66,988	66,923	66,427	66,438	66,433	66,035
1992	78,699	80,785	80,657	80,478	78,609	78,850	78,572	78,528	78,622	78,654
1993	59,677	59,582	59,088	57,561	58,348	58,920	57,564	58,053	57,891	57,809
1994	66,720	64,170	66,375	64,884	64,890	63,580	63,296	62,926	62,836	63,129
1995	75,113	74,430	75,797	76,590	76,562	79,270	79,693	78,350	77,613	77,431
1996	82,313	92,033	96,709	103,027	105,868	106,878	105,155	104,081	105,162	104,651
1997	97,148	114,343	115,099	115,974	116,034	114,114	113,934	113,425	114,007	113,620

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	60,516	60,516	0.0%
1989	9	65,733	65,212	0.8%
1990	8	63,363	62,896	0.7%
1991	7	66,121	65,849	0.4%
1992	6	77,781	77,074	0.9%
1993	5	57,656	57,649	0.0%
1994	4	62,453	62,554	-0.2%
1995	3	65,105	77,372	-15.9%
1996	2	77,432	103,595	-25.3%
1997	1	118,442	113,280	4.6%

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