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
Managing a Global Catastrophe Portfolio
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
Managing a Global Catastrophe Portfolio
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.
Managing a Global Catastrophe Portfolio
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
Managing a Global Catastrophe Portfolio
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
Managing a Global Catastrophe Portfolio
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
Managing a Global Catastrophe Portfolio
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
Managing a Global Catastrophe Portfolio
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.
Managing a Global Catastrophe Portfolio
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.
Managing a Global Catastrophe Portfolio
11May 19, 2005
Model overview: sensitivity analysis
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Return periods (years)
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Model 1 Model 2 Gaussian model
Managing a Global Catastrophe Portfolio
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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
Managing a Global Catastrophe Portfolio
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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
Managing a Global Catastrophe Portfolio
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.
Managing a Global Catastrophe Portfolio
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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
Managing a Global Catastrophe Portfolio
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Applications: calibration of Capital Charge for pricing
Expected Loss / Limit
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