Managing a Global Catastrophe Portfolio
CARe
May 19, 2005
Managing a Global Catastrophe Portfolio
May 19, 2005
Agenda
Motivation
Model overview:
 Input data
 Dependencies
 Measure of profitability
 Sensitivity Analysis
 Architecture
Applications:
 Reporting
 Portfolio optimization:
 Scenario analysis
 Efficient frontier
Capital Charge
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Managing a Global Catastrophe Portfolio
May 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 nonstandard products
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Managing a Global Catastrophe Portfolio
May 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.
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Managing a Global Catastrophe Portfolio
May 19, 2005
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Model overview: input data
Combination of risk-rate
data and cat model output
(loss files) allows a very
complete description of
catastrophe exposure.
Percentage of expected loss
Modeled perils
US quake
Japan quake
US wind
Europe wind
Japan wind
Total
6%
5%
17%
20%
7%
56%
Non / poorly modeled perils
Unusual in the industry
Other quake
Flood
Hail
Others
Total
18%
9%
3%
14%
44%
Managing a Global Catastrophe Portfolio
May 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
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Managing a Global Catastrophe Portfolio
May 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
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Managing a Global Catastrophe Portfolio
May 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
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Managing a Global Catastrophe Portfolio
May 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.
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Managing a Global Catastrophe Portfolio
May 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 riskrates
 Correlation inherent in cat model outputs for several models
Ultimately we have several views of our portfolio based on
different models.
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Managing a Global Catastrophe Portfolio
May 19, 2005
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Model overview: sensitivity analysis
Annual aggregate losses (arbitrary unit)
30
25
20
15
10
5
0
10
100
1000
Return periods (years)
Model 1
Model 2
Gaussian model
Managing a Global Catastrophe Portfolio
May 19, 2005
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Model overview: architecture
Graphical User Interface
Process new Report / Visualization / Drives Core Engine
Core Engine
Generates loss
distributions using
mixed methodology
System Report
EL, Cover, etc, for
in-force portfolio at
particular date
Loss files for
treaties not in
force
PM Database
Process Report and
generated loss curves
Loss file DB
Loss files and event
information
GIS
Loss files for
in-force
portfolio
Managing a Global Catastrophe Portfolio
May 19, 2005
Model overview: architecture
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Managing a Global Catastrophe Portfolio
May 19, 2005
Applications: most damaging event
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Managing a Global Catastrophe Portfolio
May 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
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Managing a Global Catastrophe Portfolio
May 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.
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Managing a Global Catastrophe Portfolio
May 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
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Managing a Global Catastrophe Portfolio
May 19, 2005
Applications: efficient frontier
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Managing a Global Catastrophe Portfolio
May 19, 2005
Capital cost / Limit
Applications: calibration of Capital Charge
for pricing
Expected Loss / Limit
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Managing a Global Catastrophe Portfolio
May 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
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