A Hybrid Experience / Exposure Method Presented by John Buchanan - Platinum Reinsurance Seminar on Reinsurance – Advanc

1. A Hybrid Experience / Exposure MethodPresented byJohn Buchanan - Platinum ReinsuranceSeminar on Reinsurance – Advanced Experience RatingJune 7 & 8, 2004 CARe 2004 – A Hybrid Experience / Exposure Method

2. Agenda • Overriding Assumptions • Traditional Methods • Experience Rating • Exposure Rating • Credibility Weighting • Hybrid: Experience / Exposure Method • Highlight differences between traditional methods • Testing Default Parameters CARe 2004 – A Hybrid Experience / Exposure Method

3. Overriding Assumptionsof Hybrid Experience / Exposure Method • With perfect modeling and data the results under the experience and exposure methods will be identical. • 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. CARe 2004 – A Hybrid Experience / Exposure Method

4. Traditional Methods • Experience • Relevant parameter defaults/overrides for: • LDFs (excess layers) • Trends (severity, frequency, exposure) • Rate changes • LOB/HzdGrp indicators • Adjust for historical changes in: • Policy limits • Exposure differences • Careful “as-if” • Exposure • Relevant parameters defaults/overrides for: • ILFs (or ELFs, PropSOLD) • Direct loss ratios (on-level) • ALAE loads • Policy profile (LOB, HzdGrp) • Limit/subLOB allocations • Adjust for expected changes in: • Rating year policy limits • Rating year exposures expected to be written CARe 2004 – A Hybrid Experience / Exposure Method

5. Classical Credibility Weighting • Estimate separate Experience and Exposure burns • Select credibility weights using combination of: • Judgment • Formulaic Approach • Expected # of Claims / Variability • Exposure ROL (or burn on line) • Questionnaire Approach • Apriori Neutral vs. Experience vs. Exposure • Need to be careful of unintended weighted burn patterns CARe 2004 – A Hybrid Experience / Exposure Method

6. Classical Credibility Weighting Credibility weights judgmentally selected CARe 2004 – A Hybrid Experience / Exposure Method

7. Basic Steps of The Hybrid Method Step 1: Estimate Experience burns & counts • Select base attachment points above data threshold • Estimate total burns using projection factors • Estimate counts using frequency trends, claim count LDFs • Calculate implied severities Step 2: Estimate Exposure burns & counts • Use same attachment points/layers as Experience • Bifurcate burns between counts, average severity Step 3: Calculate experience/exposure frequency ratio by attachment point CARe 2004 – A Hybrid Experience / Exposure Method

8. Basic Steps of The Hybrid Method (cont.) Step 4: Estimate base layer weights • Possibly use number of claims/variability by attachment Step 5: Review frequency ratio patterns • Adjust underlying experience or exposure models if needed and re-estimate burns (!!) • Select indicated exper/expos frequency ratio Step 6: Similarly review excess severities Step 7: Combine frequency/severity results • Using experience adjusted exposure frequencies and severities CARe 2004 – A Hybrid Experience / Exposure Method

9. Estimation of Experience CountsExample - Step 1 A: Select base attachment points above data threshold • Example: threshold=150k; reins layers=500x500k, 1x1mm • Select 200k, 250k, 350k, 500k, 750k, 1mm attachment points B: Review year by year patterns • At lower attachment points, should be variable about some mean • For example, if upward trend, then perhaps: • Overdeveloping or trending later years C: Review attachment point patterns • Should be relatively stable until credibility runs out CARe 2004 – A Hybrid Experience / Exposure Method

10. Step 1B: Estimation of Experience CountsYear Variability:>350,000 Attachment Apparently random pattern around selection of #=12.05 CARe 2004 – A Hybrid Experience / Exposure Method

11. Step 1B: Estimation of Experience CountsYear Variability: >1,000,000 Attachment Credibility runs out; indication is #=.36 CARe 2004 – A Hybrid Experience / Exposure Method

12. Step 1-Recap: Estimation of Experience Burns, Counts and Implied Severities To be compared to exposure counts CARe 2004 – A Hybrid Experience / Exposure Method

13. Step 2-Recap: Estimation of Exposure Burns Bifurcated Between Counts and Severities 12.05 exper / 15.34 expos = 78.6% CARe 2004 – A Hybrid Experience / Exposure Method

14. Step 3: Review Exper/Expos FrequenciesAttachment Point Variability: 200k…1mm Expos and Exper counts relatively consistent - IF experience very credible through 350k, then perhaps pressure to reduce exposure L/R; check out spikes CARe 2004 – A Hybrid Experience / Exposure Method

15. Steps 3-5: Calculate Exper/Expos Frequency Ratio, Base Layer Weights, & Selected Exper/Expos Ratio 6.00 expos x 80.0% Important Selection CARe 2004 – A Hybrid Experience / Exposure Method

16. Step 6: Selected Severity Unrealistic experience severity CARe 2004 – A Hybrid Experience / Exposure Method

17. Step 7: Selected Overall Burn Hybrid: Experience adjusted Exposure count & severity… 100% credibility to burn?? CARe 2004 – A Hybrid Experience / Exposure Method

18. 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 • Well constructed frequency / severity method can sometimes be given 100% weight if credible • Can review account by account, and aggregate across accounts to evaluate pressure on industry defaults CARe 2004 – A Hybrid Experience / Exposure Method

19. Test of Default Parameters • Aggregate across “similar” accounts to evaluate pressure on industry defaults • May want to re-rate accounts using e.g. default rate changes, ILFs, premium allocations, LDFs, trends, etc. • Each individual observation represents a cedant/attachment point exper/expos ratio • Review dispersion of results and overall trend • E.g. if weighted and/or fitted exper/expos ratios are well below 100% (or e.g. 90% if give some underwriter credit) then perhaps default L/Rs overall are too high (or conversely LDFs or trends too light) • If trend is up when going from e.g. 100k to 10mm att pt, then perhaps expos curve is predicting well at lower points but is underestimating upper points CARe 2004 – A Hybrid Experience / Exposure Method

20. Test of Default Parameters (cont.) • Before making overall judgments, must consider • UW contract selectivity (contracts seen vs. written), • Sample size (# of cedants/years), • Impact “as-if” data (either current or historical) • “Lucky” CARe 2004 – A Hybrid Experience / Exposure Method

21. Test of Default Rating Factors – Example 1 Well below 100%, pressure to reduce expos params or increase exper params…but credible?? CARe 2004 – A Hybrid Experience / Exposure Method

22. Test of Default Rating Factors – Example 2 Exposure curve too light with higher attachment points? CARe 2004 – A Hybrid Experience / Exposure Method