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: FL Farm Bureau Grp — Private Passenger 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	205,921	205,921	205,921	205,921
AY 2	227,564	227,553	227,564	227,553
AY 3	260,166	260,062	260,166	260,062
AY 4	267,241	266,822	267,240	266,822
AY 5	289,971	288,748	289,966	288,748
AY 6	310,575	307,179	310,538	307,179
AY 7	344,294	334,928	344,039	334,928
AY 8	361,649	337,595	360,049	337,595
AY 9	368,275	306,832	358,024	306,832
AY 10	393,129	196,865	295,147	196,865

IBNR comparison

Origin year	CL IBNR	Benktander IBNR
AY 1	0	0
AY 2	11	11
AY 3	104	104
AY 4	419	418
AY 5	1,223	1,218
AY 6	3,396	3,359
AY 7	9,366	9,111
AY 8	24,054	22,454
AY 9	61,443	51,192
AY 10	196,264	98,282
Total	296,281	186,150

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.