Lumbermens Underwriting Alliance — Workers' Compensation

Schedule P Part 3B/4B/D — net workers' compensation, 1988–1997 accident years. GRCODE 23108 (Lumbermens Underwriting Alliance). 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 WC pricing model 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)	94,389	92,238	68,123	59,587	62,295	70,875	62,394	67,685	50,118	49,456

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	19,016	44,632	59,804	66,052	70,115	72,219	73,565	74,273	75,112	75,655
1989	17,346	42,058	59,686	64,821	67,313	69,036	69,942	70,428	70,846	—
1990	12,212	28,087	42,719	46,564	48,016	49,030	49,700	49,994	—	—
1991	9,490	19,697	32,062	38,698	40,369	41,220	41,970	—	—	—
1992	7,605	14,874	21,105	29,016	35,208	36,884	—	—	—	—
1993	5,596	11,527	14,677	17,073	20,813	—	—	—	—	—
1994	4,885	10,118	13,103	14,570	—	—	—	—	—	—
1995	4,056	8,435	10,439	—	—	—	—	—	—	—
1996	4,213	8,768	—	—	—	—	—	—	—	—
1997	5,258	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	72,857	72,189	74,370	74,938	77,038	77,441	76,279	76,974	77,729	78,078
1989	79,064	71,252	71,523	74,289	73,271	72,252	72,924	73,182	73,194	—
1990	60,774	63,008	53,522	52,774	50,896	51,882	52,214	52,068	—	—
1991	47,716	47,758	43,455	42,067	43,734	44,323	45,141	—	—	—
1992	46,880	45,986	43,665	38,331	41,840	42,090	—	—	—	—
1993	51,203	49,440	44,796	37,713	38,629	—	—	—	—	—
1994	41,436	37,140	35,371	33,838	—	—	—	—	—	—
1995	40,401	37,844	37,861	—	—	—	—	—	—	—
1996	26,715	25,572	—	—	—	—	—	—	—	—
1997	25,728	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	19,016	44,632	59,804	66,052	70,115	72,219	73,565	74,273	75,112	75,655
1989	17,346	42,058	59,686	64,821	67,313	69,036	69,942	70,428	70,846	71,001
1990	12,212	28,087	42,719	46,564	48,016	49,030	49,700	49,994	50,144	50,385
1991	9,490	19,697	32,062	38,698	40,369	41,220	41,970	42,359	42,720	42,887
1992	7,605	14,874	21,105	29,016	35,208	36,884	37,456	37,767	37,536	37,684
1993	5,596	11,527	14,677	17,073	20,813	24,037	26,021	27,557	27,593	27,752
1994	4,885	10,118	13,103	14,570	15,193	15,680	16,474	18,136	19,774	21,102
1995	4,056	8,435	10,439	11,424	13,000	13,611	13,847	14,252	14,526	14,678
1996	4,213	8,768	10,280	11,093	11,848	12,180	12,657	13,232	13,318	13,544
1997	5,258	10,661	13,346	15,717	17,620	18,884	19,382	19,914	20,523	20,734

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	72,857	72,189	74,370	74,938	77,038	77,441	76,279	76,974	77,729	78,078
1989	79,064	71,252	71,523	74,289	73,271	72,252	72,924	73,182	73,194	72,873
1990	60,774	63,008	53,522	52,774	50,896	51,882	52,214	52,068	51,807	51,756
1991	47,716	47,758	43,455	42,067	43,734	44,323	45,141	44,981	44,771	44,614
1992	46,880	45,986	43,665	38,331	41,840	42,090	42,262	42,018	41,074	39,584
1993	51,203	49,440	44,796	37,713	38,629	38,316	37,014	35,202	30,101	30,572
1994	41,436	37,140	35,371	33,838	34,406	33,644	31,671	25,932	26,095	26,703
1995	40,401	37,844	37,861	29,774	29,764	28,092	21,991	22,069	23,007	22,580
1996	26,715	25,572	25,395	24,612	22,995	17,750	17,905	19,162	18,416	18,608
1997	25,728	27,761	28,010	27,185	23,502	24,015	25,470	25,408	24,691	25,785

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	75,655	75,655	0.0%
1989	9	71,358	71,001	0.5%
1990	8	50,793	50,385	0.8%
1991	7	42,969	42,887	0.2%
1992	6	38,361	37,684	1.8%
1993	5	22,257	27,752	-19.8%
1994	4	16,746	21,102	-20.6%
1995	3	13,658	14,678	-6.9%
1996	2	16,214	13,544	19.7%
1997	1	21,676	20,734	4.5%

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