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: Federal Ins Co 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 | 111,727 | 111,727 | 111,727 | 111,727 |
| AY 2 | 115,372 | 116,055 | 115,368 | 116,055 |
| AY 3 | 112,504 | 113,243 | 112,499 | 113,243 |
| AY 4 | 126,118 | 124,352 | 126,094 | 124,352 |
| AY 5 | 113,537 | 109,505 | 113,393 | 109,505 |
| AY 6 | 98,870 | 92,374 | 98,443 | 92,374 |
| AY 7 | 95,260 | 82,470 | 93,543 | 82,470 |
| AY 8 | 86,320 | 64,854 | 80,982 | 64,854 |
| AY 9 | 105,311 | 59,141 | 85,069 | 59,141 |
| AY 10 | 170,432 | 40,409 | 71,237 | 40,409 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | -683 | -0 | -687 | -0 |
| AY 3 | -739 | -0 | -744 | -0 |
| AY 4 | 1,766 | 0 | 1,742 | 0 |
| AY 5 | 4,032 | 0 | 3,888 | 0 |
| AY 6 | 6,496 | 0 | 6,069 | 0 |
| AY 7 | 12,790 | 0 | 11,073 | 0 |
| AY 8 | 21,466 | 0 | 16,128 | 0 |
| AY 9 | 46,170 | 0 | 25,928 | 0 |
| AY 10 | 130,023 | 0 | 30,828 | 0 |
| Total | 221,321 | 0 | 94,226 | 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.