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 — 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 | 125,049 | 125,049 | 125,049 | 125,049 |
| AY 2 | 149,216 | 147,358 | 149,193 | 147,358 |
| AY 3 | 192,674 | 187,760 | 192,549 | 187,760 |
| AY 4 | 224,115 | 213,396 | 223,602 | 213,396 |
| AY 5 | 230,811 | 213,904 | 229,572 | 213,904 |
| AY 6 | 219,624 | 193,676 | 216,558 | 193,676 |
| AY 7 | 185,415 | 151,081 | 179,057 | 151,081 |
| AY 8 | 157,873 | 111,268 | 144,115 | 111,268 |
| AY 9 | 125,746 | 66,033 | 97,390 | 66,033 |
| AY 10 | 129,150 | 25,265 | 45,588 | 25,265 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 1,858 | 0 | 1,835 | 0 |
| AY 3 | 4,914 | 0 | 4,789 | 0 |
| AY 4 | 10,719 | 0 | 10,206 | 0 |
| AY 5 | 16,907 | 0 | 15,668 | 0 |
| AY 6 | 25,948 | 0 | 22,882 | 0 |
| AY 7 | 34,334 | 0 | 27,976 | 0 |
| AY 8 | 46,605 | 0 | 32,847 | 0 |
| AY 9 | 59,713 | 0 | 31,357 | 0 |
| AY 10 | 103,885 | 0 | 20,323 | 0 |
| Total | 304,882 | 0 | 167,883 | 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.