Federal Ins Co Grp — Workers' Compensation

Schedule P Part 3B/4B/D — net workers' compensation, 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 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)	181,359	185,362	186,566	216,514	222,594	237,322	250,129	266,950	289,700	336,415

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	21,898	56,339	78,457	92,820	101,261	103,929	107,855	111,901	112,388	111,727
1989	22,549	59,459	82,918	98,768	105,504	110,649	113,833	116,691	116,055	—
1990	23,881	60,315	85,828	98,656	106,590	110,107	113,159	113,243	—	—
1991	25,897	71,409	95,443	111,051	120,780	124,499	124,352	—	—	—
1992	23,486	59,165	81,511	96,077	107,063	109,505	—	—	—	—
1993	27,029	60,778	80,161	89,707	92,374	—	—	—	—	—
1994	25,845	60,543	76,743	82,470	—	—	—	—	—	—
1995	25,415	54,791	64,854	—	—	—	—	—	—	—
1996	32,804	59,141	—	—	—	—	—	—	—	—
1997	40,409	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	110,308	123,010	125,339	127,382	128,246	128,699	130,897	130,559	131,882	122,959
1989	121,104	128,545	132,244	133,841	135,043	136,807	137,598	138,111	138,113	—
1990	119,767	127,169	134,288	139,702	141,489	140,489	143,717	141,400	—	—
1991	142,657	149,282	157,683	159,055	159,992	164,199	158,833	—	—	—
1992	144,773	150,292	147,693	147,402	149,559	145,693	—	—	—	—
1993	154,516	156,009	153,949	138,152	135,266	—	—	—	—	—
1994	158,063	158,779	146,818	137,863	—	—	—	—	—	—
1995	154,023	155,796	148,799	—	—	—	—	—	—	—
1996	164,351	172,063	—	—	—	—	—	—	—	—
1997	196,269	—	—	—	—	—	—	—	—	—

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	21,898	56,339	78,457	92,820	101,261	103,929	107,855	111,901	112,388	111,727
1989	22,549	59,459	82,918	98,768	105,504	110,649	113,833	116,691	116,055	117,658
1990	23,881	60,315	85,828	98,656	106,590	110,107	113,159	113,243	115,410	116,719
1991	25,897	71,409	95,443	111,051	120,780	124,499	124,352	127,156	129,361	130,900
1992	23,486	59,165	81,511	96,077	107,063	109,505	116,756	120,222	122,914	125,026
1993	27,029	60,778	80,161	89,707	92,374	98,647	102,141	105,053	108,284	110,233
1994	25,845	60,543	76,743	82,470	90,914	96,312	100,470	103,893	106,207	107,465
1995	25,415	54,791	64,854	81,324	90,757	96,325	100,588	104,233	106,322	108,100
1996	32,804	59,141	83,846	101,438	111,371	117,702	123,209	126,577	130,417	132,144
1997	40,409	90,592	118,415	137,898	151,472	159,562	164,486	168,064	171,209	173,581

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

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	110,308	123,010	125,339	127,382	128,246	128,699	130,897	130,559	131,882	122,959
1989	121,104	128,545	132,244	133,841	135,043	136,807	137,598	138,111	138,113	130,154
1990	119,767	127,169	134,288	139,702	141,489	140,489	143,717	141,400	138,958	130,607
1991	142,657	149,282	157,683	159,055	159,992	164,199	158,833	154,906	153,027	146,315
1992	144,773	150,292	147,693	147,402	149,559	145,693	145,580	143,399	142,933	135,776
1993	154,516	156,009	153,949	138,152	135,266	133,629	130,088	126,100	126,064	121,077
1994	158,063	158,779	146,818	137,863	130,543	126,842	124,267	121,250	122,778	116,309
1995	154,023	155,796	148,799	134,691	128,415	123,101	122,254	122,885	121,436	117,944
1996	164,351	172,063	167,185	157,751	149,855	148,093	147,623	146,303	149,188	152,289
1997	196,269	207,335	199,833	195,183	192,812	197,076	192,639	195,363	202,372	200,203

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	111,727	111,727	0.0%
1989	9	115,372	117,658	-1.9%
1990	8	112,504	116,719	-3.6%
1991	7	126,118	130,900	-3.7%
1992	6	113,537	125,026	-9.2%
1993	5	98,870	110,233	-10.3%
1994	4	95,260	107,465	-11.4%
1995	3	86,320	108,100	-20.1%
1996	2	105,311	132,144	-20.3%
1997	1	170,432	173,581	-1.8%

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