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 — Commercial Auto (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 | 60,516 | 60,516 | 60,516 | 60,516 |
| AY 2 | 65,733 | 65,511 | 65,732 | 65,511 |
| AY 3 | 63,363 | 62,626 | 63,354 | 62,626 |
| AY 4 | 66,121 | 64,518 | 66,083 | 64,518 |
| AY 5 | 77,781 | 74,048 | 77,602 | 74,048 |
| AY 6 | 57,656 | 53,599 | 57,370 | 53,599 |
| AY 7 | 62,453 | 54,388 | 61,412 | 54,388 |
| AY 8 | 65,105 | 49,835 | 61,523 | 49,835 |
| AY 9 | 77,432 | 44,377 | 63,321 | 44,377 |
| AY 10 | 118,442 | 27,309 | 48,321 | 27,309 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 222 | 0 | 221 | 0 |
| AY 3 | 737 | 0 | 728 | 0 |
| AY 4 | 1,603 | 0 | 1,565 | 0 |
| AY 5 | 3,733 | 0 | 3,554 | 0 |
| AY 6 | 4,057 | 0 | 3,771 | 0 |
| AY 7 | 8,065 | 0 | 7,024 | 0 |
| AY 8 | 15,270 | 0 | 11,688 | 0 |
| AY 9 | 33,055 | 0 | 18,944 | 0 |
| AY 10 | 91,133 | 0 | 21,012 | 0 |
| Total | 157,873 | 0 | 68,507 | 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.