n CATASTROPHE MODELING PORTFOLIO BUILDING AND OPTIMIZATION Why

n. CATASTROPHE MODELING, PORTFOLIO BUILDING AND OPTIMIZATION

Why Use Multiple Models ? n Natural Bias § Any model encompasses inherent biases § § § Input data and methodology Technical biases of the developer Simple errors and inconsistencies § Single model users nearly always “optimise into the model” § Single model users are very susceptible to model change n Assessing/Normalising Model Bias § Independent hazard/vulnerability tests § § No-one knows the “right” answer – some reasonability should apply Complexities of wind speed vs loss makes comparison difficult § Internal consistency § § 2 Many simple tests for this e. g. compare expected loss costs by Country and sub region Information easily obtainable within the model

European Windstorm Number of Countries with losses in Recent Events n Taking major events of last 30 years how many countries had meaningful losses in each event (>$50 m)? 3

European Windstorm Model Diversity 4

European wind % Events hitting each country 5

European windstorm Internal Consistency n Looking at expected loss cost and at the 99 th percentile - the spread is large n Check Denmark for internal consistency comparing Res/Com for models A and C – Which relationship makes most sense ? 6

mmercially available Property Cat models a comprehensive view o n Additional perils captured in REMS© increase loss estimates relative to vendor models (e. g. winter freeze, eastern European flood, Australian Hail and others) n Secondary factors like post-event inflation (demand surge) and fire following earthquake need to examined specifically to determine if they are adequately increasing loss estimates n Secondary factors are important differentiators of risk. 7

Modeling Malpractice n Poor model or incomplete model n Pilot error – model is used incorrectly or with incorrect ‘dial settings’ n Good model used for the wrong purpose n Too much or too little trust in the models; results = estimates not “facts” n Unstable model where small changes in assumptions drive large changes in results n Black box model where users are unable to link which assumptions are driving results n Too much output – leaves users lost in piles of data n Cumbersome model – takes too much time to run or does not provide the info needed to make decisions in a timely way n Separation of modeling from underwriting – All our modellers are 8

All lines of business should be incorporated into the same risk management framework to effectively manage entity risk n Cat Model needs to integrate with other Risk Models: § Flexible framework to add other lines § A tool for underwriters to make risk decisions § An exposure management system to track and control risk aggregations. n Do not rely on commercially available models; each book of business must be captured stochastically n Not every line of business can be modeled with the same level of sophistication and refinement as Property Cat § At Renaissance, we built proprietary models for terrorism and workers comp cat that are built off of the analytics and ‘engineering’ of the REMS© Property Cat models; capture correlation with Cat § Other lines of business modeled using stand-alone stochastic distributions; more judgment involved but approach needs to be compatible n Facilitates a complete aggregation of risk no gaps in the model or risk analysis 9

Calculation of marginal ROE by contract Beginning Portfolio Capital Rules: 10 New Deal Probability Distribution Portfolio & Contract “A” Probability Distribution Expected Profit § Expected Profit Required Capital § Required Capital

Portfolio Construction Matters n Portfolios: § Opt Universe: Reinsurance CAT Market - equal share § Opt Port x OLW: Optimal Portfolio no retro § Opt Port: Optimal Portfolio with retro n Optimization: § Maximize Expected Profit for a given level of capital § No more than 50% of any placement § Deals taken from Reinsurance CAT Market n Results: Opt Universe Exp Profit Opt Port 35% 59% 45% -355% -233% -82% Zero Profit Prob 20% 11% 9% Return Period 5. 0 8. 7 11. 4 7. 77% 3. 21% 0. 24% 13 31 417 99. 60% Default Prob Return Period 11 Opt Port x OLW

Portfolio Construction Matters 12

Be Very Afraid: n Allison n Sydney Hail n Tiawan Earthquake n World Trade Center n Four Storms in Florida n Anatol n Tsunami n Turkey Earthquake n Bushfires (California & Australia) n Canadian Freeze n 1999 Storms n The List goes on…. . 13