Cape Cod method

The Bornhuetter-Ferguson method has a soft spot: where does the a-priori expected loss ratio come from? Often it is just an outside guess from pricing. The Cape Cod method closes that loophole by computing the expected loss ratio from the very same triangle — letting the company's own experience tell you what loss ratio to assume, instead of importing one. It keeps B-F's stabilising idea but makes the prior self-consistent with the data in hand.

Precisely, the Cape Cod (also called Stanard-Buhlmann) method estimates a single expected loss ratio across all accident years as: total reported losses, divided by total 'used-up' (or earned-and-reported) premium, where each year's premium is weighted by the fraction of its losses that have already emerged, i.e. premium x (1/LDF). Once that ELR is computed from the triangle, the method finishes exactly like Bornhuetter-Ferguson: ultimate equals reported losses plus expected-ELR-times-premium times the still-unreported fraction. For example, if total reported losses are 30 million and total used-up premium is 50 million, the Cape Cod ELR is 60 percent, and that 60 percent is then applied to each year's unreported portion. The 'used-up premium' weighting is the clever part: it stops green years, whose losses have barely emerged, from distorting the estimated loss ratio.

Cape Cod matters as the data-driven cousin of B-F, popular when you want the stabilising effect of an expected loss ratio but do not trust an externally supplied one — for example on lines where pricing assumptions are weak. Its honest limitation is that it assumes a single underlying loss ratio is appropriate across the years being blended; if true loss ratios drifted because of rate changes or shifting mix, a single Cape Cod ELR can be misleading, which is why practitioners often on-level the premiums first or use a 'decay' (generalized Cape Cod) variant that lets the ratio vary by year.