Optimal Risk Selection Using Cat Models Lixin Zeng, Ph.D. CAS Seminar on Funding of Catastrophe Risks Providence RI October 17, 2000 beyond The Box Thinking

Optimal Risk Selection Outline Use and Misuse of Cat Model Optimal Risk Selection Example

Optimal Risk Selection What a Cat Model Tells Us Loss Probability Distribution Expected Loss Probable Maximum Loss (a.k.a. Value at Risk) Relative Value Deal A is riskier than Deal B Correlation: Constructing a Portfolio with High Return on Risk Capital

Optimal Risk Selection Great! Cat Problem Solved? Underwriting Decisions Rate Making Reinsurance Purchasing Securitization

Optimal Risk Selection What’s Inside a Cat Model State-of-the-Art Science in Meteorology and Seismology Engineering Experts’ Opinions for Structure Damage Modern Simulation Technology Lack of Consensus in Scientific Community on Key Issues Best Guesses Given Limited Data and Modeling Computation Hurdles vs. Convergence

Optimal Risk Selection User’s Responsibilities Understand Key Assumptions Appreciate Sources of Uncertainty Independent Model Evaluation Integrate Multiple Models

Optimal Risk Selection What’s a Cat Model Good For? Relative (Not Absolute) Indicators Differentiate Good and Bad Risks/Areas Risk Selection Portfolio Optimization

Maximum Return on Risk Capital Optimal Risk Selection Goal of Risk Selection “Bad” Risks “Good” Risks Existing Portfolio Final Portfolio Maximum Return on Risk Capital

Optimal Risk Selection Return on Risk Capital (RORC) Return Cat premium minus expected cat loss Risk Capital Probable maximum loss (or value at risk) Expected policy holder deficit Loss standard deviation Applicable to Both Individual Risks and Portfolios

Cat Premium - Expected Cat Loss Optimal Risk Selection RORC: Definition A Simple Definition Cat Premium - Expected Cat Loss Cat X-Year PML Different Definitions Financial strength Risk tolerance etc.

Optimal Risk Selection Identify “Bad” Individual Risks An Individual Risk Is the Worst in a Portfolio if (1) It has the lowest RORC among all risks (2) Removing it will increase the portfolio’s RORC the most vs. removing any other individual risk The right answer: (1) or (2)?

Optimal Risk Selection A Sample Portfolio

Optimal Risk Selection RORC

Optimal Risk Selection A Sample Portfolio

Optimal Risk Selection RORC

Optimal Risk Selection Identify “Good” Prospective Risks: Same Idea An Individual Risk Is the Best Prospect for a Portfolio if (1) It has the highest RORC among all prospects (2) Including it in the portfolio will increase the portfolio’s RORC the most vs. including any other prospect The right answer: (1) or (2)?

Optimal Risk Selection Real World: Computational Issues Finding the X Worst (or Best) from N Risks Requires CNX calculations E.g. requires ~ 17,000,000,000,000 calculations to pick 10 worst (or best) out of 100 risks Need a Faster, More Practical Approach

Portfolio w/o worst risk Portfolio w/o X worst risks Optimal Risk Selection A Real Solution: Discrete Steepest Descent Existing Portfolio Portfolio w/o worst risk Portfolio w/o X worst risks Remove #1 only Remove #2 only ………. ……... Remove #N-1 only Remove #N only Remove #1 only Remove #2 only ……... Remove #N-1 only Remove #1 only ……….. Remove #N-X only

Optimal Risk Selection Finding the X Worst (or Best) from N Risks Requires O(N2) Calculations E.g. requires 1,000 calculations to pick 10 worst (or best) out of 100 risks Innovative algorithm to handle large portfolios Stochastic Perturbation to Avoid Local Minimum

Optimal Risk Selection Real-World Example: Portfolio of 1500 Risks Optimal Risk Selection Benchmark

Optimal Risk Selection Cautions Cat Model Relative Bias Geographical and structural Usually less than absolute bias But cannot be ignored Use of a Single Point on the PML Curve Potentially misleading

Optimal Risk Selection Conclusions Cat Model Relative indications more credible than absolute values Portfolio Optimization One of the best uses of cat models Cat model relative bias must be evaluated and understood