# Bornhuetter Ferguson Method

*Bornhuetter-Ferguson (aka BF Method) combines features of the chain ladder and expected loss ratio methods and assigns weights for the percentage of losses paid and losses incurred*

### What is Bornhuetter Ferguson Technique

The Bornhuetter Ferguson technique (BF Method) is a method for calculating an estimate of an insurance company’s losses. The Bornhuetter Ferguson technique, also called the Bornhuetter Ferguson method (BF Method), estimates incurred but not yet reported (IBNR) losses for a policy year. This technique was created by two actuaries, Bornhuetter and Ferguson, and was first presented in 1975.

### BREAKING DOWN Bornhuetter Ferguson Technique

Bornhuetter-Ferguson is one of the most-widely used loss reserve valuation methods, second only to the chain ladder method. It combines features of the chain ladder and expected loss ratio methods and assigns weights for the percentage of losses paid and losses incurred. Unlike the chain ladder method, which builds a model based on past experience, the Bornhuetter-Ferguson technique builds a model based on the insurer’s exposure to loss.

The chain ladder method examines the point over a period in time in which a claim is reported or paid. Insurers use this to “budget” for future losses, with the sum of all of the future losses equaling the IBNR. Claim estimates from past time periods are made concrete, based on loss experience. This means that the actuary swaps past estimates with actual claims.

The Bornhuetter-Ferguson technique estimates IBNR during a period of time by estimating the ultimate loss for a particular risk exposure, and then estimating the percent of this ultimate loss that was not reported at the time. Bornhuetter-Ferguson calculates the estimated loss as the sum of reported loss plus IBNR, with IBNR calculated as the estimated ultimate loss multiplied by the percentage of loss that is unreported. Loss estimates use priori loss estimates.

Bornhuetter Ferguson (BF Method) may be the most useful in cases where actual reported losses do not provide a good indicator of IBNR. This is more likely to be an issue when losses are low frequency but high severity. Severity refers to the amount you have received Insurance claim for. Average Severity would be the loss associated with an average Insurance claim., a combination that makes it more difficult to provide accurate estimates. It is easier for an insurer to predict what will happen with high frequency, low severity. Severity refers to the amount you have received Insurance claim for. Average Severity would be the loss associated with an average Insurance claim. claims.

### The Bornhuetter Ferguson Calculation

There are two algebraically equivalent methods for calculating loss, according to the Bornhuetter-Ferguson technique. In the first approach, undeveloped reported (or paid) losses are added directly to expected losses (based on an a priori loss ratio), multiplied by an estimated percent unreported.

**BF=L+ELR∗Exposure∗(1−w)**

In the second calculation method, reported (or paid) losses are first developed to ultimate using a chain ladder approach and applying a loss development factor (LDF). Next, the chain ladder ultimate is multiplied by an estimated percent reported. Finally, expected losses multiplied by an estimated percent unreported are added (as in the first approach).

**BF=L∗LDF∗w+ELR∗Exposure∗(1−w)**

The estimated percent reported is the reciprocal of the loss development factor. IBNR claims are then figured by subtracting reported losses from the Bornhuetter-Ferguson ultimate loss estimate.