may 19, 2005 managing a global catastrophe portfolio care

May 19, 2005

Managing a Global Catastrophe PortfolioCARe

Managing a Global Catastrophe Portfolio

2May 19, 2005

AgendaMotivation

Model overview: Input data Dependencies Measure of profitability Sensitivity Analysis Architecture

Applications: Reporting Portfolio optimization:

Scenario analysis Efficient frontier

Capital Charge


3May 19, 2005

Motivation to build a portfolio model

1. Dynamic monitoring of Portfolio ROE and Capital deployed

2. Rapid and reliable risk profiles for reporting to internal/external parties

3. Efficient planning, scenario evaluation and portfolio optimisation

4. Evaluation of the capital implications of non-standard products


4May 19, 2005

Model Overview: input data

Data Source on exposure to natural catastrophe Risk Rates and exposure entered by underwriters in

operating systems: Give frequency and severity for particular peril/region hitting a

layer Very complete inventory of natural perils (300 separate

combinations of region and peril modeled)

Outputs from Cat models stored in PRECED: Simulated loss for particular natural peril event and for

particular cedant

Actual model uses a mix of both types of data.


5May 19, 2005

Model overview: input data

Combination of risk-rate data and cat model output (loss files) allows a very complete description of catastrophe exposure.

Unusual in the industry

Modeled perils

US quake 6%Japan quake 5%US wind 17%Europe wind 20%Japan wind 7%Total 56%

Non / poorly modeled perils

Other quake 18%Flood 9%Hail 3%Others 14%Total 44%

Percentage of expected loss


6May 19, 2005

Model overview: input data

Cat model outputs: List of losses to a particular cedant for all events in

catalogue of Cat model Loss file

The portfolio model handles both our internal CatFocusTM suite of models and commercial models: AIR, RMS, EQECat

Primary advantage of using loss files is the ability to aggregate losses across different portfolios


7May 19, 2005

Model Overview: Dependencies

Dependencies Achilles heel of any portfolio model

Overall capital and its allocation are very sensitive to dependency structure.

Methodology for Risk rates: Same peril-Same region: fully correlated Correlation matrices: Atlantic Hurricane, EU Wind, EU Flood

based on simulated events/meteorological study. Otherwise Independent

Methodology for cat model outputs: Natural correlation via aggregation at the event level Same event may affect different cedants/regions Portfolios within the same region are only partially correlated


8May 19, 2005

Model overview: measure of profitability

Overall capital for Cat portfolio Statistical measure on distribution of financial results Use of Tail Value at Risk:

Mean of losses exceeding the corresponding VaR


9May 19, 2005

Model overview: measure of profitability

Allocation of capital It serves two purposes:

Portfolio optimization by over-/under-weighting segments with profitability higher/lower than overall portfolio

Calibration of capital charge for different key markets We use contribution to portfolio TailVar Credit for diversification to each segment according to how it

correlates with the main risks in the overall portfolio Marginal allocation ensures that profitability at segment level is

a good indicator of where to grow/reduce business.


10May 19, 2005

Model overview: sensitivity analysis

Sensitivity analysis is essential in order to build confidence in model and to assess its limitations

We reviewed the impact of different correlation models on aggregate loss distributions as well as profitability: Dependency structures (copulas) for methodology based on risk-

rates Correlation inherent in cat model outputs for several models

Ultimately we have several views of our portfolio based on different models.


11May 19, 2005

Model overview: sensitivity analysis

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10 100 1000

Return periods (years)

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Model 1 Model 2 Gaussian model


12May 19, 2005

Model overview: architecture

Graphical User Interface

Process new Report / Visualization / Drives Core Engine

System ReportEL, Cover, etc, for

in-force portfolio atparticular date

Core EngineGenerates loss

distributions usingmixed methodology

PM DatabaseProcess Report and

generated loss curvesGIS

Loss files for in-force portfolio

Loss file DBLoss files and event

information

Loss files for treaties not in

force


13May 19, 2005

Model overview: architecture


14May 19, 2005

Applications: most damaging event


15May 19, 2005

Applications: scenario analysis for planning

Scenario analysis rather than full-blown automatic optimization: Scenario based on underwriters projections rather than

theoretical model of rate changes

Criteria to define scenario: Total EPI/exposure is fixed. Scenario should increase overall profitability Portfolio should be achievable in practice


16May 19, 2005

Applications: scenario analysis for planning

Underwriters’ projections Base portfolio to create other scenarios Realized by applying changes to portfolio in-force as

of July 1: Change our share Change ROL

Apply changes selectively to key markets and to treaties with similar risk rates.


17May 19, 2005

Applications: efficient frontier Efficient frontier: line on risk-return graph showing optimal portfolios that:

maximize profit for a given level of capital or minimize capital for a given profit

Assumptions for optimizations: Price elasticity:

an increase/decrease in market share will result in an decrease/increase in rates

Portfolio profile is similar to the reference portfolio, only shares of different markets vary


18May 19, 2005

Applications: efficient frontier


19May 19, 2005

Applications: calibration of Capital Charge for pricing

Expected Loss / Limit

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20May 19, 2005

Conclusion

Cat portfolio model: Aggregates the exposure to all natural catastrophe

risks that affect our in-force portfolio Calculates our risk profile and capital needs on a

frequent basis Is applied in: reporting, optimization, and planning

may 19, 2005 managing a global catastrophe portfolio care

Documents

portfolio model handles

portfolio optimisation

input data cat model

portfolio tailvar credit

catalogue of cat model

cat model output loss

particular cedant actual

natural catastrophe