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: State Farm Mut 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 | 193,499 | 193,499 | 193,499 | 193,499 |
| AY 2 | 203,124 | 199,997 | 203,076 | 199,997 |
| AY 3 | 229,193 | 224,078 | 229,079 | 224,078 |
| AY 4 | 211,401 | 204,911 | 211,202 | 204,911 |
| AY 5 | 218,032 | 208,008 | 217,571 | 208,008 |
| AY 6 | 238,547 | 219,345 | 237,001 | 219,345 |
| AY 7 | 246,282 | 212,446 | 241,633 | 212,446 |
| AY 8 | 252,280 | 190,974 | 237,382 | 190,974 |
| AY 9 | 243,622 | 143,590 | 202,549 | 143,590 |
| AY 10 | 247,080 | 75,827 | 128,383 | 75,827 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 3,127 | 0 | 3,079 | 0 |
| AY 3 | 5,115 | 0 | 5,001 | 0 |
| AY 4 | 6,490 | 0 | 6,291 | 0 |
| AY 5 | 10,024 | 0 | 9,563 | 0 |
| AY 6 | 19,202 | 0 | 17,656 | 0 |
| AY 7 | 33,836 | 0 | 29,187 | 0 |
| AY 8 | 61,306 | 0 | 46,408 | 0 |
| AY 9 | 100,032 | 0 | 58,959 | 0 |
| AY 10 | 171,253 | 0 | 52,556 | 0 |
| Total | 410,384 | 0 | 228,700 | 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.