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: Lumbermens Underwriting Alliance — 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 | 75,655 | 75,655 | 75,655 | 75,655 |
| AY 2 | 71,358 | 70,846 | 71,354 | 70,846 |
| AY 3 | 50,793 | 49,994 | 50,780 | 49,994 |
| AY 4 | 42,969 | 41,970 | 42,946 | 41,970 |
| AY 5 | 38,361 | 36,884 | 38,304 | 36,884 |
| AY 6 | 22,257 | 20,813 | 22,164 | 20,813 |
| AY 7 | 16,746 | 14,570 | 16,464 | 14,570 |
| AY 8 | 13,658 | 10,439 | 12,899 | 10,439 |
| AY 9 | 16,214 | 8,768 | 12,794 | 8,768 |
| AY 10 | 21,676 | 5,258 | 9,241 | 5,258 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 512 | 0 | 508 | 0 |
| AY 3 | 799 | 0 | 786 | 0 |
| AY 4 | 999 | 0 | 976 | 0 |
| AY 5 | 1,477 | 0 | 1,420 | 0 |
| AY 6 | 1,444 | 0 | 1,351 | 0 |
| AY 7 | 2,176 | 0 | 1,894 | 0 |
| AY 8 | 3,219 | 0 | 2,460 | 0 |
| AY 9 | 7,446 | 0 | 4,026 | 0 |
| AY 10 | 16,418 | 0 | 3,983 | 0 |
| Total | 34,490 | 0 | 17,404 | 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.