Bornhuetter–Ferguson / Benktander / Cape Cod

Blend a-priori expected losses with emerged experience via BF, its iterated Benktander form, and the data-driven Cape Cod method, side by side with chain-ladder.

Open with agent

Loaded: Canal Ins Co Grp — Commercial Auto (paid, CAS Loss Reserve DB)

Triangle size

Paste rows (CSV / TSV / whitespace)

Origin \ Dev	1	2	3	4	5	6	7	8	9	10
AY 1
AY 2
AY 3
AY 4
AY 5
AY 6
AY 7
AY 8
AY 9
AY 10

Premium by origin year & expected loss ratio

Expected loss ratio (a priori)

AY 1 premium

AY 2 premium

AY 3 premium

AY 4 premium

AY 5 premium

AY 6 premium

AY 7 premium

AY 8 premium

AY 9 premium

AY 10 premium

Ultimate comparison

Origin year	CL ultimate	BF ultimate	Benktander ultimate	Cape Cod ultimate
AY 1	27,445	27,445	27,445	27,445
AY 2	27,504	27,470	27,504	27,470
AY 3	30,092	30,004	30,092	30,004
AY 4	33,643	33,727	33,643	33,727
AY 5	39,271	39,237	39,271	39,237
AY 6	53,980	53,350	53,973	53,350
AY 7	64,354	60,726	64,150	60,726
AY 8	63,159	54,432	61,953	54,432
AY 9	60,074	42,563	54,970	42,563
AY 10	58,055	21,074	34,498	21,074

IBNR comparison

Origin year	CL IBNR	BF IBNR	Benktander IBNR	Cape Cod IBNR
AY 1	0	0	0	0
AY 2	34	0	34	0
AY 3	88	0	88	0
AY 4	-84	-0	-84	-0
AY 5	34	0	34	0
AY 6	630	0	623	0
AY 7	3,628	0	3,424	0
AY 8	8,727	0	7,521	0
AY 9	17,511	0	12,407	0
AY 10	36,981	0	13,424	0
Total	67,550	0	37,470	0

IBNR by method

Assumptions & limitations

Premium is on-level (rate and mix adjusted) so that a single expected loss ratio is meaningful across origin years.
The a-priori expected loss ratio is a credible, independent estimate (e.g., pricing plan or industry benchmark) — not derived from the same data being reserved.
Cape Cod pools all origin years to estimate a single ELR from the data; it will differ from a manually chosen BF a-priori.