June 2006

Predictable Unpredictability:Thoughts on Reconciling Model Results With Actual Experience

M. Mark CravensWellington Underwriting Inc.

CAS Limited Attendance SeminarNew York, September 18, 2006

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June 2006

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?

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June 2006

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

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June 2006

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

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June 2006

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

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June 2006

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?

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June 2006

Example: Data Variance

Data provided at zip level, modelled at centroid

Actual exposures were concentrated on barrier island

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June 2006

“Misbehavior” is Not Uniform

Percent Overall Incurred-Modelled Difference

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

0 10 20 30 40 50 60 70 80 90 100

• Analysis of 134 claims cases

• Focus: Actual > modeled

• Top 10 cases drive over 50% total difference

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June 2006

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

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June 2006

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

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June 2006

Distributions And Financial Structures

DeductibleDeductible

11stst Layer Layer

22ndnd Layer Layer

33rdrd Layer LayerLoss DistributionLoss Distribution

MeanMean

• Distribution reflects uncertainty

• Derived from population-driven behavior

• Various methods of applying to structure– Allocate/distribute loss– Select a point: that’s the

loss

9090thth Percentile Percentile

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June 2006

Ideas For Integrating These Effects

DeductibleDeductible

11stst Layer Layer

22ndnd Layer Layer

33rdrd Layer Layer

MeanMean

• 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

9090thth Percentile Percentile

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June 2006

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

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June 2006

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

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June 2006

Building Ranges: Integration & Reporting

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8

Low

Mean

High

Footprint/Stochastic ResultsFootprint/Stochastic Results

Additional Peril LoadAdditional Peril Load

Layer CompressionLayer Compression

Claim Vol & CTLClaim Vol & CTL

Exposure-Model VarianceExposure-Model Variance

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June 2006

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

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June 2006

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

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June 2006

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

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June 2006

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?

June 2006

Predictable Unpredictability:Thoughts on Reconciling Model Results With Actual Experience

M. Mark CravensWellington Underwriting Inc.

CAS Limited Attendance SeminarNew York, September 18, 2006