Bornhuetter-Ferguson: Initial Expected Losses Working Party

1. Bornhuetter-Ferguson: Initial Expected Losses Working Party • Co-Chair: Jeff Carlson FCAS, MAAA Towers Perrin (Tillinghast) • Co-Chair: Chris Olson FCAS, MAAA St. Paul Travelers 2005 CLRS Boston, MA Session 5: Report of the Bornhuetter-Ferguson Initial Expected Losses Working Party

2. Rationale • Bornhuetter-Ferguson is one of the most heavily relied upon reserving methods • Can be thought of as a credibility weighted estimate of chain-ladder indication and initial expected losses • Much written about chain-ladder method, relatively little about initial expected losses

3. Rationale (continued) • Seminal paper for the method simply says that if the “expected loss ratio cannot be selected with much accuracy, a high ratio should be used.” • It can be argued that over-reliance on (possibly flawed) initial expected loss estimates contributed to the underestimation of reserves in recent years

4. Rationale (continued) • Goal of this working party is to publish a paper to provide guidance for practitioners and education for students • Initial expected losses can be applicable to methods beyond Born-Ferg

5. Working Party Scope • Have not engaged in primary research • Want to leverage initial expected loss approaches already in use, whether documented or not • Many smart people using Bornhuetter-Ferguson method, probably many very good IEL approaches already exist

6. Tasks Completed To-Date • Have completed surveying the workplaces of working party members. Received 14 responses from a variety of actuaries, representing many companies/individuals • Have identified and summarized relevant published literature. Identified 24 items to summarize of which 7 were deemed to be of high importance. • Have laid the groundwork for evaluating various options for IEL development

7. Workplace Surveys Identified methods grouped into: -BFIEL obtained from information in the triangle -BFIEL obtained from outside source -Other

8. BFIEL Obtained from Triangle Method # Observations Price (or exposure)/Trend Rollforward 13 Stanard-Buhlmann /Cape Cod 6 Average of LDF methods 6 Historical average of ultimates/loss costs 6 Frequency/Severity 5 Least Squares Regression/Simulation 4

9. BFIEL Obtained from Outside Source Method # Observations Pricing Indication 8 Industry loss ratio/loss costs 8 Corporate Plan 3 Underwriter loss ratio 2 Competitor loss ratio 2

10. BFIEL Other Method # Observations Benktander 3 method adjusts BFIEL arrived at via other means by giving more weight to LDF indication. Prior Selected Ultimate 6 Experience Rating Results 3

11. Summary of Published Literature – High Importance Articles • “The Actuary and IBNR”, Bornhuetter and Ferguson • Discussions of “The Actuary and IBNR” by Cooper and White • “Estimating Salvage and Subrogation Reserves-Adapting the Bornhuetter-Ferguson Approach”, Grace

12. Summary of Published Literature – High Importance Articles (cont’d) • “Using Best Practices to Determine a Best Reserve Estimate”, Struzzieri and Hussian • “Balancing Development and Trend in Loss Reserve Analysis”, Gluck • “Credible Claims Reserves: Benktander Method”, Mack

13. Examples of Methods to be Shown • Price Trend Rollforward – Several versions varying the point at which losses are rolled forward from • Stanard-Buhlmann/Cape Cod – Original and Gluck’s version • Benktander • Frequency/Severity • Least Squares Regression • Excess Ratio of 1st dollar expected losses • Grace’s Method for Salvage and Subrogation

14. Bases for Initial Expected Losses • Basis: source information from which the initial expected losses are measured • Comparable to an exposure basis for pricing an insurance risk

15. Commonly Used Bases • Ultimate loss estimate from another source • From prior analyses • From other projection methods • From more mature exposure years • Premiums • Exposures (e.g. payroll, car years) • Ultimate claim counts • A related group of losses • Estimate of industry losses • Estimate of primary layer losses • Estimate of losses of a related coverage

16. The Basis is “Converted” to the IEL

17. A particular approach can be evaluated based on the “quality” of the basis and the conversion statistic • Both the basis and the conversion statistic can be judged on several criteria • Availability • Accuracy • Uncertainty/ Variability • Expected correlation to losses

18. IEL approaches can be categorized by Basis and Source

19. Proposed BFIEL Principles • The purpose of estimating initial expected losses is to provide a (better?) predictor of future loss development that is not based directly on the current paid and outstanding losses. • If the estimate of initial expected losses is developed from past loss history and pricing and loss trend assumptions, then the estimate should be revised as the loss history develops and changes and/or the pricing and loss trend assumptions change.

20. Proposed BFIEL Principles (cont’d) • The reliance to be placed on a loss projection based on an estimate of initial expected losses, relative to the reliance on loss projections based on other approaches, depends on the level of confidence in the estimate. For example, an estimate based upon past loss experience, modified by robust pricing and trend information, should be relied upon more so than an estimate obtained from a business plan with no rigorous supporting rationale.

21. ISSUES • Many methods seem to use the link-ratio method to “improve” the BFIEL. Is this a good thing to do? • There seems to be a lot of actuaries that use their prior selected ultimates as their BFIEL for periods more than a year or two old. Is this really your “expected” loss ratio?

22. BF IEL Working Party • Questions?