Canal Ins Co Grp — Commercial Auto

Schedule P Part 3B — net commercial auto liability, 1988–1997 accident years. GRCODE 2623 (Canal 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)	64,523	49,466	58,136	74,222	81,017	93,522	102,327	95,842	95,732	82,991

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	9,352	18,101	22,309	25,361	26,942	27,707	27,965	27,377	27,411	27,445
1989	9,545	18,379	23,380	25,843	27,328	27,750	27,340	27,411	27,470	—
1990	10,928	21,003	26,380	29,084	30,421	29,677	29,949	30,004	—	—
1991	12,158	23,141	28,905	31,787	32,686	33,447	33,727	—	—	—
1992	15,268	27,550	33,918	36,671	38,734	39,237	—	—	—	—
1993	19,302	40,514	47,083	51,241	53,350	—	—	—	—	—
1994	22,591	47,111	56,139	60,726	—	—	—	—	—	—
1995	23,377	44,702	54,432	—	—	—	—	—	—	—
1996	22,506	42,563	—	—	—	—	—	—	—	—
1997	21,074	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	46,246	41,193	40,192	40,318	39,302	37,681	35,674	31,972	30,057	27,491
1989	40,877	40,677	39,745	39,335	37,406	35,638	31,998	30,467	27,548	—
1990	45,419	42,020	40,551	40,625	38,934	34,364	31,878	31,849	—	—
1991	52,316	50,674	50,020	48,611	43,222	40,609	39,510	—	—	—
1992	53,030	52,202	50,620	47,177	44,698	43,396	—	—	—	—
1993	64,094	60,205	57,803	56,699	56,883	—	—	—	—	—
1994	75,244	70,021	68,106	68,518	—	—	—	—	—	—
1995	82,886	77,775	74,040	—	—	—	—	—	—	—
1996	77,826	75,357	—	—	—	—	—	—	—	—
1997	67,622	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	9,352	18,101	22,309	25,361	26,942	27,707	27,965	27,377	27,411	27,445
1989	9,545	18,379	23,380	25,843	27,328	27,750	27,340	27,411	27,470	27,516
1990	10,928	21,003	26,380	29,084	30,421	29,677	29,949	30,004	29,998	30,073
1991	12,158	23,141	28,905	31,787	32,686	33,447	33,727	33,801	33,894	33,926
1992	15,268	27,550	33,918	36,671	38,734	39,237	39,716	40,058	40,076	40,109
1993	19,302	40,514	47,083	51,241	53,350	54,349	54,550	54,618	54,677	54,697
1994	22,591	47,111	56,139	60,726	63,184	64,443	65,065	64,842	64,890	64,934
1995	23,377	44,702	54,432	58,219	60,296	61,161	61,438	61,508	61,571	61,698
1996	22,506	42,563	53,267	60,724	65,085	67,143	67,878	68,992	69,148	69,338
1997	21,074	36,393	48,131	56,639	60,148	61,827	62,305	62,462	62,518	62,690

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	46,246	41,193	40,192	40,318	39,302	37,681	35,674	31,972	30,057	27,491
1989	40,877	40,677	39,745	39,335	37,406	35,638	31,998	30,467	27,548	27,698
1990	45,419	42,020	40,551	40,625	38,934	34,364	31,878	31,849	30,412	30,135
1991	52,316	50,674	50,020	48,611	43,222	40,609	39,510	34,797	34,041	34,033
1992	53,030	52,202	50,620	47,177	44,698	43,396	40,679	40,284	40,205	40,174
1993	64,094	60,205	57,803	56,699	56,883	56,674	55,101	54,883	54,763	54,728
1994	75,244	70,021	68,106	68,518	66,154	65,473	65,661	65,118	65,161	65,059
1995	82,886	77,775	74,040	69,050	62,226	61,930	61,829	61,746	61,685	61,734
1996	77,826	75,357	71,697	69,507	68,691	69,168	69,252	69,725	69,832	69,808
1997	67,622	67,725	65,011	63,929	63,652	63,225	62,857	62,735	62,765	62,774

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	27,445	27,445	0.0%
1989	9	27,504	27,516	-0.0%
1990	8	30,092	30,073	0.1%
1991	7	33,643	33,926	-0.8%
1992	6	39,271	40,109	-2.1%
1993	5	53,980	54,697	-1.3%
1994	4	64,354	64,934	-0.9%
1995	3	63,159	61,698	2.4%
1996	2	60,074	69,338	-13.4%
1997	1	58,055	62,690	-7.4%

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