Predictable Unpredictability: Thoughts on Reconciling Model Results With Actual Experience

1. Predictable Unpredictability:Thoughts on Reconciling Model Results With Actual Experience M. Mark Cravens Wellington Underwriting Inc. CAS Limited Attendance Seminar New York, September 18, 2006

2. Topics • Actual event experience vs. modeled estimates • What have we seen and what does it mean? • Implications for using model results • What drives the differences? • How can we account for them? • Downstream impacts on risk management • How does this affect how I use models in my business?

3. Wellington Business Profile • Lloyd’s Syndicate 2020 • £800 million in premium capacity for 2006 • 87% written in London, 13% written in US • Complex mix of portfolios and exposures • Large property books including commercial, industrial, energy exposures • Individual risk, binding authorities, and treaty reinsurance • Primary, pro rata and excess of loss

4. What Happened • Significant investment in cat modeling discipline • Time, money, people, process, culture • Significant hurricane activity • Seven major hurricanes plus one Katrina • Losses invariably higher than modeled estimates • Substantive review and adjustment of process (ongoing) • New exposure/risk management measures • Change in model usage • Reassessment of risk management focus

5. Why Were Estimates So Far Off? • Problem #1: Data • Garbage in, guess what... • Problem #2: Outliers drive performance • Risks do not respect the law of large numbers • Problem #3: Damage ≠ Loss • Social and economic variance from modeled performance envelopes • Katrina amplifies issues and correlations

6. Data Issues • Completeness • Amount of book captured • Level of descriptive data • Accuracy • Location, TIV, interpretable data... • Treatment of missing data? • Leave it to the model? • Adjust results? • Make conservative data assumptions?

7. Data provided at zip level, modelled at centroid Actual exposures were concentrated on barrier island Example: Data Variance

8. “Misbehavior” is Not Uniform • Analysis of 134 claims cases • Focus: Actual > modeled • Top 10 cases drive over 50% total difference

9. Outliers: Any Patterns Emerge? • Data issues • Non-modeled causes of loss • Excess of Loss • Attachment points and limit size • Compression in lower layers: 100% loss • Skewed values • Low property, high BI

10. Damage Does Not Equal Loss • Demand Surge predictability • Triggers and step functions • Partial damage creates near total loss • Swing factors on BI exposures • Subjective valuation • Event size/sequence exacerbates impacts

11. Distribution reflects uncertainty Derived from population-driven behavior Various methods of applying to structure Allocate/distribute loss Select a point: that’s the loss 90th Percentile Mean Distributions And Financial Structures 3rd Layer Loss Distribution 2nd Layer 1st Layer Deductible

12. Model multiple points on distribution, as well as mean/allocated losses Include Layer Compression and Constructive Total Loss triggers Identify claims development volatility Based on class of business, spread of effects Ideas For Integrating These Effects 3rd Layer 2nd Layer 90th Percentile Mean 1st Layer Deductible

13. Mechanics Of Making Adjustments • Generate granular deterministic output • Policy and/or location level results • Segment book for different treatment • Layer/attachment sensitive business • Potentially volatile occupancies/exposures • Locations with heavy potential damage • Some business may be in multiple segments • Qualify potential outliers

14. Loss Estimates: Issues, Expectations • Numbers create their own reality: controlled communication is critical • Expectations: are they clear? • Means are convenient but can be misleading • Probabilistic vs. Deterministic applications • Case-by-case behavior varies considerably • Goal is to develop realistic range of losses • Identify most volatile components and account for them

15. Exposure-Model Variance Claim Vol & CTL Layer Compression Additional Peril Load Footprint/Stochastic Results Building Ranges: Integration & Reporting

16. Chase The Wind Or Stay Grounded? • Replicating experience ≠ risk management • Footprints/Stochastic events leverage model behavior, may amplify limitations • Exposure-Model Variance: How wrong can we be? • Exposure profile critical • Data/nature of exposure and spread relative to direct/indirect hazards • Large limits, layered structures, terms • Requires understanding correlated exposures • Identify areas of volatility outside/on fringe of model • Integrate with model results to manage risk

17. How Does All This Change Using Models? • Reassert role of severity • Exposure management • Data conservatism • Differentiating predictability • Type of business and structure • Subdivide portfolio for treatment • Change application of volatility • Modeled volatility (uncertainty) • Correlations of possible amplifiers

18. Shifts in Risk Management Perspective • Models remain primary tools • Provides common framework for correlating exposures/risk • Still currency in trading • Changed perspectives on optimization • Diversification vs. adding more risk • Additional dimensions • Exposures vs. estimates vs. confidence • Managing volatility correlations

19. Downstream Effects On Business • Underwriting and risk selection • New emphases on correlation, selecting risk relative to existing commitments • Pricing • Size/nature of portfolio: pricing volatility? • Special issues for treaty reinsurance here • Capital allocation and RBC • Impacts of volatility on cost of capital • What happens if nothing happens?

20. Predictable Unpredictability:Thoughts on Reconciling Model Results With Actual Experience M. Mark Cravens Wellington Underwriting Inc. CAS Limited Attendance Seminar New York, September 18, 2006