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 — Private Passenger 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 | 6,815,646 | 6,815,646 | 6,815,646 | 6,815,646 |
| AY 2 | 7,719,821 | 7,712,077 | 7,719,813 | 7,712,077 |
| AY 3 | 8,396,601 | 8,364,955 | 8,396,482 | 8,364,955 |
| AY 4 | 8,288,545 | 8,215,810 | 8,287,906 | 8,215,810 |
| AY 5 | 9,043,728 | 8,876,813 | 9,040,647 | 8,876,813 |
| AY 6 | 9,702,726 | 9,337,099 | 9,688,948 | 9,337,099 |
| AY 7 | 10,422,621 | 9,640,098 | 10,363,870 | 9,640,098 |
| AY 8 | 10,571,471 | 9,006,113 | 10,339,682 | 9,006,113 |
| AY 9 | 10,490,872 | 7,486,113 | 9,630,259 | 7,486,113 |
| AY 10 | 10,933,658 | 4,344,144 | 6,962,280 | 4,344,144 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 7,744 | 0 | 7,736 | 0 |
| AY 3 | 31,646 | 0 | 31,527 | 0 |
| AY 4 | 72,735 | 0 | 72,096 | 0 |
| AY 5 | 166,915 | 0 | 163,834 | 0 |
| AY 6 | 365,627 | 0 | 351,849 | 0 |
| AY 7 | 782,523 | 0 | 723,772 | 0 |
| AY 8 | 1,565,358 | 0 | 1,333,569 | 0 |
| AY 9 | 3,004,759 | 0 | 2,144,146 | 0 |
| AY 10 | 6,589,514 | 0 | 2,618,136 | 0 |
| Total | 12,586,821 | 0 | 7,446,666 | 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.