Understanding Actuarial Methods

Current actuarial standards of practice indicate that multiple actuarial methods should be used to determine the estimated ultimate losses when completing an actuarial analysis of unpaid claim liabilities. One source of guidance related to actuarial methods and models is Actuarial Standard of Practice 43 (ASOP 43), particularly in Section 3.6.1. For example ASOP 43 states in Section 3.6.1 that if only one method is used, the actuary should disclose why other methods are not considered.

Frequently used methods for property & casualty risks (primarily for companies with large deductible or self-insured polices) are standard development methods (also known as chain ladder methods), Bornhuetter-Ferguson methods, frequency/severity methods and loss projection methods. It is important to review the range of results, based on the various methods used, to determine, given the situation, which methods produce the most credible indications.

Development methods rely on the application of a development factor to the reported incurred losses, the paid losses, or the case reserves. Development factors can be based on a company’s unique data or industry data. Generally speaking the use of unique development factors produces more credible indications.

The incurred loss development method is one of the most frequently used actuarial methods. Incurred losses (case reserves plus paid losses) are multiplied by an incurred loss development factor to determine an estimate of ultimate losses. The assumptions related to the incurred loss development factor are important. If no unique history (loss development triangle) is available, industry loss development factors are often used. Using industry loss development factors assumes the development for the company will be similar to industry development patterns. Even if unique loss development factors are available, there is still the underlying assumption that future development patterns will be similar to historical patterns. The incurred method works well in a fairly stable environment. It can be sensitive to changes in claims administration (e.g., reserve strengthening), changes in demographics, changes in policy structure, and changes in other organizational structure.

Paid losses are multiplied by a paid loss development factor to determine estimated ultimate losses in the paid loss development method. A paid method may indicate more reasonable results when changes in claims administration affect case reserve adequacy. However, the paid loss development factors are larger than incurred factors and often produce more volatile results. Additionally, the paid method is very sensitive to changes in the claims payment rate, such as payment acceleration.

The case reserve method may be useful when there are only a very few open claims. The case reserve method applies a case reserve development factor to the case reserves to determine an estimate of ultimate losses. The case reserve factor is often derived from the incurred and paid loss development factors and so an underlying assumption is that future development will be similar to historical development, if unique factors are used. An example of where the case reserve method may not be appropriate is an immature policy period with few case reserves established as of the evaluation date.

The Bornhuetter-Ferguson (B-F) method uses projected losses and actual loss experience to estimate ultimate incurred losses. This technique often provides a more reasonable approach to estimating ultimate losses for current or recently completed policy periods by smoothing the variance caused by the absence or presence of large claims. The method can be employed based on incurred or paid losses.

There are different types of frequency/severity methods which focus on a review of the number of anticipated claims and the anticipated claims severity. These methods can be used for most risks but are often used to provide insight in the analysis of long-tailed risks.

A projection method, which is based on longer term historical averages, is often appropriate for years that are very immature with little emerged experience as of the evaluation date. A projection method can also be useful for long-tailed coverages. Projection methods often have the implicit assumption that projected losses will be similar to historical losses. Changes in the underlying exposure base should therefore, be monitored.

Occasionally it is appropriate for an organization to change the methods used or to change the weightings given to various methods. The following provide some examples:

  • As policies naturally mature over time, one method often becomes more appropriate than another.
  • Changes in claims administration philosophy, such as reserve strengthening or payment acceleration, often require additional methods or review.
  • It is not uncommon for an actuary to change the weightings from year to year based on the number of open claims and the range (variance) of indications by method.

However, significant changes in methodology should be disclosed and documented. It is not reasonable to change methodology simply to lower or raise the indicated unpaid liability estimate. The methodology should remain relatively consistent unless there are specific factors over time that lead to some methods becoming more or less credible.

When an organization reviews an actuarial report, the methods used should be clear and documented. Auditors often specifically inquire regarding any changes in actuarial methods. Statements of Actuarial Opinion letters normally contain verbiage indicating if there has been a significant change in methodology. If it appears that significant changes have occurred in the methods used, or in the weightings given to various methods, further questions should be asked.

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© 2012 SIGMA Actuarial Consulting Group, Inc.

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Michelle Bradley, ACAS, MAAA, ARM, CERA

About Michelle Bradley, ACAS, MAAA, ARM, CERA

Michelle graduated summa cum laude as valedictorian from Lipscomb University in 1988, receiving a B.S. Degree in Mathematics. She then attended Vanderbilt University and received a M.S. degree in Mathematics. Michelle is an Associate in the Casualty Actuarial Society and is a Member of the American Academy of Actuaries. She also obtained the Associate in Risk Management designation in 1996 and received the award for academic excellence in that program. She served as president for the Casualty Actuaries of the Southeast for the 1999-2000 year. From 1990 to September 2003, she was Vice President and Consulting Actuary for Willis Risk Solutions of Willis North America. During this time she consulted extensively in the areas of actuarial, risk management and enterprise risk management. Michelle received the CERA (Chartered Enterprise Risk Analyst) designation in 2013. She has also served on the board of directors for the Society of Risk Management Consultants. She currently serves on the Advisory Council for Middle Tennessee State University’s Master of Science in Professional Science Program (MSPS). In the area of enterprise risk management, she has focused on modeling issues as regards integrated programs that often include non-traditional risks. She has significant expertise in risk mapping and alternative risk transfer mechanisms. She has been a member of numerous project teams that provided enterprise risk consultancy services and was part of the project team that completed the integrated program that was hailed the “Deal of the Decade” by CFO Magazine (June 2000).

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