Cape Cod — Qualified

The Cape Cod (or Stanard-Bühlmann) reserving method is a variation of the Bornhuetter-Ferguson method where the Expected Loss Ratio (ELR) is calculated directly from the historical experience rather than selected judgmentally.

Key Assumptions

Credibility of Development: Like B-F, actual losses to date are accepted, and future unpaid losses are expected to develop based on an expected loss ratio.
Experience-Driven ELR: The expected loss ratio is estimated using the collective historical experience of all accident years combined, including the subject accident year.

Mathematical Formulation

Instead of selecting an a priori ELR, the Cape Cod method calculates a single, exposure-weighted Expected Loss Ratio ( $\text{ELR}_{\text{CC}}$ ):

\text{ELR}_{\text{CC}} = \frac{\sum_i \text{Cumulative Reported Losses}_i}{\sum_i \left( \text{OLEP}_i \times \% \text{Reported}_i \right)}

Where:

$\text{OLEP}_i$ : On-level earned premium for accident year $i$ .
$\% \text{Reported}_i$ : The expected percentage of losses reported at the current maturity of accident year $i$ (defined as $\frac{1}{\text{CDF}_i}$ ).
$\text{OLEP}_i \times \% \text{Reported}_i$ : Represents the used-up premium (or developed premium) to date.

Cape Cod Reserving and IBNR

Once $\text{ELR}_{\text{CC}}$ is calculated, the ultimate losses and IBNR for each accident year are determined using the standard B-F framework:

\text{IBNR}_i = \text{OLEP}_i \times \text{ELR}_{\text{CC}} \times \left(1 - \% \text{Reported}_i \right)

\text{Ultimate Losses}_i = \text{Cumulative Reported Losses}_i + \text{IBNR}_i

Differences Between B-F and Cape Cod Methods

Feature	B-F Method	Cape Cod (CC)
A Priori ECR	Selected judgmentally (often from pricing or external data).	Calculated directly from the development triangle data.
Premium Basis	Typically utilizes nominal (actual) earned premium.	Must utilize On-Level Earned Premium (OLEP) to ensure rate consistency.
Premium Exposure	Does not adjust for development of premium.	Uses “used-up” premiums (adjusted by $\% \text{Reported}$ ) as the exposure weight.
Experience Period	Experience period being reserved is typically excluded from ECR selection.	The subject experience period is explicitly included in the ECR calculation.

Technical Nitty-Gritties

[!IMPORTANT] OLEP for IBNR vs. Actual EP for Accident Year Loss Ratios

When calculating Ultimate Losses / IBNR: You must utilize On-Level Earned Premium (OLEP) because the ECR was derived using OLEP.

When calculating the final Loss Ratio for a specific Accident Year: You must utilize the Actual (Nominal) Earned Premium for that year. The definition of an accident year loss ratio is the ultimate losses divided by the actual premium earned during that period: $\text{Accident Year Loss Ratio}_i = \frac{\text{Ultimate Losses}_i}{\text{Actual Earned Premium}_i}$ Do not use OLEP in the denominator of the final loss ratio.