May 19, 2005 Managing a Global Catastrophe Portfolio CARe

Managing a Global Catastrophe Portfolio 2May 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

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

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 CatFocus TM 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

Managing a Global Catastrophe Portfolio 12May 19, 2005 Model overview: architecture Graphical User Interface Process new Report / Visualization / Drives Core Engine System Report EL, Cover, etc, for in-force portfolio at particular date Core Engine Generates loss distributions using mixed methodology PM Database Process Report and generated loss curves GIS Loss files for in-force portfolio Loss file DB Loss files and event information Loss files for treaties not in force

Managing a Global Catastrophe Portfolio 13May 19, 2005 Model overview: architecture

Managing a Global Catastrophe Portfolio 14May 19, 2005 Applications: most damaging event

Managing a Global Catastrophe Portfolio 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

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 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

Managing a Global Catastrophe Portfolio 18May 19, 2005 Applications: efficient frontier

Managing a Global Catastrophe Portfolio 19May 19, 2005 Applications: calibration of Capital Charge for pricing

Managing a Global Catastrophe Portfolio 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