Managing a Global Catastrophe Portfolio

1. Managing a Global Catastrophe Portfolio CARe

2. Agenda • Motivation • Model overview: • Input data • Dependencies • Measure of profitability • Sensitivity Analysis • Architecture • Applications: • Reporting • Portfolio optimization: • Scenario analysis • Efficient frontier • Capital Charge

3. Motivation to build a portfolio model • Dynamic monitoring of Portfolio ROE and Capital deployed • Rapid and reliable risk profiles for reporting to internal/external parties • Efficient planning, scenario evaluation and portfolio optimisation • Evaluation of the capital implications of non-standard products

4. 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.

5. 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

6. 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

7. 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

8. 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

9. 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.

10. 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.

11. Model overview: sensitivity analysis

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

13. Model overview: architecture

14. Applications: most damaging event

15. 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

16. 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.

17. 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

18. Applications: efficient frontier

19. Applications: calibration of Capital Charge for pricing

20. 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