1. 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

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

3. 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

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

5. 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

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

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

8. 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

9. 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

10. 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.

11. 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)?

12. Optimal Risk Selection
A Sample Portfolio

13. Optimal Risk Selection
RORC

14. Optimal Risk Selection
A Sample Portfolio

15. Optimal Risk Selection
RORC

16. 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)?

17. 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

18. 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

19. 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

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

21. 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

22. 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