The Bornhuetter-Ferguson Method

Lucy Zhang and Enoch Starnes, ACI

Actuaries will use multiple actuarial methods to determine the estimated ultimate losses when completing an actuarial analysis of unpaid claim liabilities. The Bornhuetter-Ferguson (B-F) method and the development methods (also known as chain ladder methods) are two of the most popular claims reserving methods. In this blog post, we will take a look at the B-F method, the cases where B-F method are most useful, and the advantages and disadvantages of this method.

The Bornhuetter-Ferguson method is named after two U.S. actuaries – Ronald L. Bornhuetter and Ronald E. Ferguson. This method was first published in 1972 in the paper titled “The Actuary and IBNR.” The B-F method estimates the ultimate losses based on projected losses and actual loss experience – it is essentially a blend of the development methods and the loss projection. In the development methods, we multiply actual losses by a loss development factor to obtain an ultimate loss estimate. Loss development factors are usually based on a company’s unique data or industry data. Because loss development factors tend to be large for “green” years, development methods can lead to unreliable results. Loss projections are based on pure loss rates. Although the results can be more stable than when using the development methods, it ignores the actual results as reported. The B-F method combines the two methods by splitting ultimate losses into two components: actual losses and expected unreported (or unpaid) losses. As the years mature, more weight is given to actual losses and expected losses (the loss projection) gradually become less important. This method provides a more reasonable approach to estimating ultimate losses, especially for current or recently completely years, by smoothing the variance caused by the absence or presence of large claims.

The Bornhuetter-Ferguson method is most useful for situations where actual losses are not a good indicator of IBNR. This is often the case for low frequency but high severity lines of insurance. Another advantage of the B-F method is that it can be used even if there isn’t a credible volume of historical data. This method can be particularly useful when entering a new line of business. Additionally, the B-F method smooths the variance when there are random fluctuations or large claims at early maturities. This is useful for long-tailed lines of insurance such as medical malpractice or workers compensation, particularly for the most immature years.

Because the loss development factors used in the B-F method are the same as those selected and used in the development methods, the B-F method may not work when there is downward development (when loss development factors are less than 1.000). Automobile physical damage and property are lines in which actuaries can observe this type of downward development. The B-F method is also not effective for short-tailed lines of insurance as it will approximate the development methods. The B-F method results may also be distorted if claim reporting patterns change.

In general, the Bornhuetter-Ferguson method is very commonly used by actuaries as it provides more stable estimates than the development methods and more responsive estimates than the loss projection. In an actuarial report, the B-F method estimates can be most commonly found for current years or recently completed years. If you would like to take a closer look at the B-F method calculations, you can view the “Bornhuetter-Ferguson Method” video from our own RISK66 library.

You can access our video on this topic through's Education Portal. If you are already a RISK66 subscriber, click here. If you are not, but would like access to this video and other complimentary educational resources, click here to sign up.

We welcome your feedback by posting a comment or contacting Lucy Zhang at
© SIGMA Actuarial Consulting Group, Inc.

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