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.
Loaded: California Cas Grp — Workers' Compensation (paid, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
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Premium by origin year & expected loss ratio
Ultimate comparison
| Origin year | CL ultimate | BF ultimate | Benktander ultimate | Cape Cod ultimate |
|---|---|---|---|---|
| AY 1 | 51,939 | 51,939 | 51,939 | 51,939 |
| AY 2 | 46,342 | 46,229 | 46,342 | 46,229 |
| AY 3 | 54,955 | 53,956 | 54,937 | 53,956 |
| AY 4 | 69,217 | 66,566 | 69,115 | 66,566 |
| AY 5 | 63,786 | 59,437 | 63,490 | 59,437 |
| AY 6 | 57,583 | 50,742 | 56,770 | 50,742 |
| AY 7 | 57,070 | 45,580 | 54,756 | 45,580 |
| AY 8 | 66,813 | 44,045 | 59,054 | 44,045 |
| AY 9 | 68,709 | 31,474 | 48,530 | 31,474 |
| AY 10 | 50,439 | 9,372 | 17,003 | 9,372 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 113 | 0 | 113 | 0 |
| AY 3 | 999 | 0 | 981 | 0 |
| AY 4 | 2,651 | 0 | 2,549 | 0 |
| AY 5 | 4,349 | 0 | 4,053 | 0 |
| AY 6 | 6,841 | 0 | 6,028 | 0 |
| AY 7 | 11,490 | 0 | 9,176 | 0 |
| AY 8 | 22,768 | 0 | 15,009 | 0 |
| AY 9 | 37,235 | 0 | 17,056 | 0 |
| AY 10 | 41,067 | 0 | 7,631 | 0 |
| Total | 127,514 | 0 | 62,597 | 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.