Report of the Tail Factor Working Party

1. Report of the Tail Factor Working Party Steven C. Herman, FCAS, MAAA San Diego, California September 10-11, 2007

2. Tail Factor Working Party Co-Chairs Steven C. Herman Mark R. Shapland Members

3. Tail Factor Working Party Disclaimer: While this paper is the product of a CAS working party, its findings do not represent the official view of the Casualty Actuarial Society. Moreover, while we believe the approaches we describe are very good examples of how to address the issue of estimating development of loss and loss adjustment expense payments from a given evaluation to ultimate disposition, we do not claim they are the only acceptable ones, nor do they represent all possible applications of the specific methods presented.

4. The Motivation • Tail factors used to estimate additional development occurring • after the eldest maturity in a given loss development triangle, or • after the eldest credible link ratio. • Over the years, many valuable contributions have been made to the CAS literature describing methods for calculating tail factors. • However no overall paper compiling these contributions existed.

5. The Paper • The CAS Tail Factor Working Party prepared this paper on the methods currently used by actuaries in estimating loss development tail factors. • Standard terminology for discussing aspects of link ratios and tail development is communicated within the paper.

6. The Paper • Included are • Descriptions of advantages and disadvantages of each method and • Identification of what entities (companies, rating bureaus, or consulting firms) typically use each method.

7. Paper Description • Organized by “Type” of Method • Sections Describe: • Mechanics of each method, • Examples for most methods, • Results of our Testing, and • Results of our Surveys

8. Paper Description • Standard Notation: • Consistency, • Started with Notation from Reserve Variability Working Party • Added new notation where lacking • Summarize Areas for Future Research

9. Section Description • Bondy-Type Methods • Algebraic Methods • Benchmark Methods • Open Claim Methods • Curve Fitting Methods • Lifespan Methods • Miscellaneous Methods

10. Bondy-Type Methods Description • Bondy Method • Use last link ratio: • Modified Bondy Method • Double or square: • Generalized Bondy Method (Weller) • For 0<B<1: • Fully Generalized Bondy Method (Gile) • Let Vary by Accident Year

11. Bondy-Type Methods Description • Advantages • Simple to Implement • Pattern Described with One Factor • Only Requires Cumulative Paid Data • Disadvantages • Not Always Useful for Incurred Data • Will Fail with Increasing Development • May Fail with “More Complicated” Patterns

12. Algebraic Methods Description • Equalizing Paid & Incurred Loss Estimates • Use Cumulative Incurred / Cumulative Paid • Boor’s Method • Adjust Case Reserves • Mueller’s Method • Adjust Incremental Factors • NCCI Method

13. Algebraic Methods Description • Advantages • Simple to Implement • Only Requires Cumulative Data • Statistically Unbiased • Disadvantages • May Not be Sophisticated Enough • Subject to Case Reserve Distortions • Some Methods Not Generally Well Known

14. Benchmark Methods Description • Benchmark Development / Link Ratios • Adjusted Benchmark Development / Link Ratios • Use Link Ratios to Adjust Tail Factor • Benchmark Average Severity • Benchmark Adjusted by Claims Audit

15. Benchmark Methods Description • Advantages: • Supplement when Little Data • Adds Credibility • Various Degrees of Sophistication • Disadvantages: • Need Similar Data • Claim Handling Procedures • Relative Case Reserve Strength

16. Open Claim Methods Description • Maximum Possible Loss • Judgment of Open Claim Costs / Audit

17. Open Claim Methods Description • Advantages: • Incorporates Particulars of Open Claims • Uses Knowledge of Claim Staff • Can Provide Bounds • Disadvantages: • Requires Access to Individual Claims • Subject to Judgment/Availability of Auditors • May Underestimate Severe or IBNR/Reopened Claims

18. Curve Fitting Methods Description • Exponential Decay • Constant Rate of Factor Decay • McClenahan’s Method • Constant Monthly Incremental Paid Decay • Skurnick’s Method • Simplify Using Annual Decay • Sherman’s Method • Use “Inverse Power” Curves • England-Verrall Method • Smooth & Extrapolate Incremental Data

19. Curve Fitting Methods Description • Advantages: • Straightforward & Intuitive • Extrapolate Beyond End of Data • Various Levels of Sophistication • Disadvantages: • May Underestimate Tail for Long-Tail Lines • Sub-Optimal If Pattern Not Consistent • Sometimes No Closed Form Solution

20. Lifespan Methods Description • Static Mortality Method • Frequency / Severity Using Mortality Rates • Trended Mortality Method • Greatest Impact on “Distant” Years • Sherman-Diss Method • Separate Impact of Inflation & Mortality • Corro’s Method • Modeling of “Pension” Claims

21. Lifespan Methods Description • Advantages: • Extrapolate “Very-Long” Tail • Can Include “Increasing” Factors • Detailed Assumptions/Some Non-Subjective • Disadvantages: • More Complex • Need “Very Old” Data to Parameterize • Need Specific Mortality Rates

22. Miscellaneous Methods Description • Restating Historical Experience via a Claims Audit • Adjust for Changes

23. Miscellaneous Methods Description • Advantages: • Improves “Other” Methods • Adjustments Readily Understood • Add Claim Professional Judgment • Disadvantages: • Difficult to Reconstruct Old Claim Files • Auditor Must Ignore Prior Development • Auditor Must Evaluate at Multiple Points