1. 1 Solving the Puzzle: The Hybrid Reinsurance Pricing Method John Buchanan CAS Ratemaking Seminar – REI 4 March 17, 2008 CAS RM 2008 – The Hybrid Reinsurance Pricing Method

2. 2 Agenda Traditional Methods Recap Hybrid Method: Experience / Exposure –Reserving analogy –Fundamental assumptions –Basic steps of the paper –Case studies Hybrid roll-ups –Testing default parameters Appendix –Other considerations in attempting to solve the puzzle –Underwriting cycle: soft market experience model bias

3. 3 Traditional Methods Recap Experience Relevant parameter defaults/overrides for: –LDFs (excess layers) –Trends (severity, frequency, exposure) –Rate changes –LOB/Hazard Grp indicators Adjust for historical changes in: –Policy limits –Exposure differences o Careful “as-if” Exposure Relevant parameters defaults/overrides for: –ILFs (or ELFs, PropSOLD) –Direct loss ratios (on-level) –ALAE loads –Policy profile (LOB, HzdGrp) o Limit/subLOB allocations Adjust for expected changes in: –Rating year policy limits –Rating year exposures expected to be written

4. 4 Hybrid Pricing Method Reserving Analogy From paper accepted by CAS Variance – John Buchanan / Mike Angelina THE HYBRID REINSURANCE PRICING METHOD: A PRACTITIONER’S GUIDE

5. 5 Fundamental Assumptions of the Hybrid Method In theory, with perfect modeling and sufficient data the results under the Experience and Exposure methods will be identical. (never attainable) In practice, –if the model and parameter selections for both Experience and Exposure methods are proper and relevant, –then the results from these methods will be similar, –except for credibility and random variations. Lower layer experience helps predict higher less credible layers. Frequency is a more stable indicator than total burn estimates.

6. 6 Basic Steps of The Hybrid Method 1.Estimate Experience burns & counts 2.Estimate Exposure burns & counts 3.Calculate Experience/Exposure frequency ratio by attachment point 4.Review Hybrid frequency ratio patterns - Adjust experience or exposure models if needed and re-estimate burns 5.Similarly review excess severities and/or excess burns 6.Combine Hybrid frequency/severity results 7.Determine overall weight to give Hybrid

7. 7 Step 4-Review Hybrid Frequency Ratios (Example #1 from Paper) Important Selection6.00 expos x 80.0%

8. 8 Steps 1-7: Bringing it All Together

9. 9 Exposure vs. Experience (Example #2 from REI-3 Case Study) In this case study, there is an inconsistent relationship as move up the attachment points While the low layer Experience is about half of Exposure, the upper layers are about equal to Exposure Need more investigation to reconcile and help solve the puzzle

10. 10 Adjusting Experience for historically higher policy limits (Example #2 from paper)

11. 11 Adjusting Exposure for clash potential (Example #3 from Paper)

12. 12 Benefits of Hybrid Method One of main benefits is questioning Experience and Exposure Selections –To the extent credible results don’t line up, this provides pressure to the various default parameters –For example, there would be downward pressure on default exposure ILF curves or loss ratios if Exposure consistently higher than experience, and Credible experience and experience rating factors A well constructed Hybrid method can sometimes be given 100% weight if credible Can roll-up Hybrid results across accounts to evaluate pressure on industry defaults

13. 13 Hybrid roll-ups: Test of Default Factors Well below 100%, pressure to reduce expos params or increase exper params…but credible??

14. 14 Other Considerations in Attempting to Solve the Puzzle Appendix

15. 15 Inspect Hybrid Ratios From forthcoming paper - THE HYBRID REINSURANCE PRICING METHOD: A PRACTITIONER’S GUIDE

16. 16 Pressure Indicators: Inspect Burn ratios by Year

17. 17 Assessing Credibility of Exposure Method Assess confidence due to: –Exposure curve selected –Exposure profile –Source of hazard or sub-line information –Prediction of next years primary loss ratio –Percentage of non-modeled exposure, clash, etc. –Company strategy and ability to realize strategy Possibly take questionnaire / scoring approach to mechanize (Patrik/Mashitz)

18. 18 Assessing Credibility of Experience Method Assess confidence due to: –Overall volume of claims –Volume of claims within layer (lucky or unlucky?) –Stability of year by year Experience results – “ layer to layer Hybrid ratios –Source of loss development, trend factors, historical rate changes and deviations –Changes in historical profile limits affecting claims –Appropriateness of any claims or divisions that may have been removed (or “as-if’d”) –Including additional large claim(s) if feel account “lucky” Underwriter “as-if” scorecard – soft market Experience score compared to exposure score to determine credibility weight

19. 19 Classical Credibility Weighting Techniques Select credibility weights using combination of: –Formulaic Approach Expected # of Claims / Variability Exposure ROL (or burn on line) –Questionnaire Approach Apriori Neutral vs. Experience vs. Exposure Patrik/Mashitz paper –Judgment Need to check that burn patterns make sense –i.e. higher layer ROL < lower ROL –similar to Miccolis ILF consistency test

20. 20 Classical Credibility Weighting o Credibility weights can be judgmentally or formula selected o Soft market pressure to give more weight to experience indication when lower (perhaps implicitly by underwriter or management override)

21. 21 Underwriting Cycle Hard market vs. Soft market Calendar year vs. accident year –Accident year – posted vs. “true” after adjusting for reserves Loss ratios, combined ratios, operating ratios Forensic analysis of cycle –Numerator impacts (loss trends, new plateaus, shock losses) –Denominator impacts (rate changes, terms and conditions) Relative magnitude of components –Losses –Rates –Reserve adequacy (no impact if able to review “true” AY results) –Which is larger impact, losses or rates? Perhaps vary by line Hypothesis –Soft market bias towards Experience model results –Could be implicit by underwriters or management override

22. 22 Underwriting Cycle - AY

23. 23 Underwriting Cycle – AY vs. CY Information Gap