1. Risk Measures CARE Meeting Hamilton, Bermuda June 6-7, 2005 Paul Kneuer, FCAS MAAA, Holborn Corporation Susan Patschak, FCAS MAAA, Endurance Specialty

2. Risk Measures Why do different reinsurers often make different decisions when it comes to pricing the same risk? Why do different reinsurers often make different decisions when it comes to pricing the same risk? Different reinsurers have different measures of profitability. Different reinsurers have different measures of profitability. 2

3. Risk Measures Possible measures Contract Profit/Contract Premium Contract Profit/Contract Standard Deviation Contract Profit/Contribution to Portfolio Std Dev Contract Profit/Contract TCE or TVar Contract Profit/Contract PML Contract Profit/Contribution to Portfolio PML 3

4. Risk Measures The following four contracts will be used to compare different risk measures: 1.Net Account Quota Share 2.Umbrella Cessions Facility 3.Catastrophe XOL 4.Catastrophe XOL in a Peak Zone 1.Net Account Quota Share 2.Umbrella Cessions Facility 3.Catastrophe XOL 4.Catastrophe XOL in a Peak Zone 4

5. Risk Measures Risk Measures used for the first two contracts 1)Risk Measure: Contract Profit/Contract Premium Used by companies constrained by premium-to-surplus ratios Used by companies constrained by premium-to-surplus ratios Analogous measures: Combined ratio, Operating ratio Analogous measures: Combined ratio, Operating ratio 2)Risk Measure: Contract Profit/Contract Standard Deviation Used by companies that are constrained by operating volatility, and that cannot give contracts credit for diversification due to correlation or large contract size. Used by companies that are constrained by operating volatility, and that cannot give contracts credit for diversification due to correlation or large contract size. Analogous Measures: Rate on-line, Value at Risk Analogous Measures: Rate on-line, Value at Risk 5

6. Risk Measures Net Account Quota Share Terms Terms $50Mn expected ceded premium $50Mn expected ceded premium $1Mn occurrence cap $1Mn occurrence cap Expected profit of $2Mn, after sliding scale commission. (Remember them?) Expected profit of $2Mn, after sliding scale commission. (Remember them?) Standard Deviation of returns is $4Mn Standard Deviation of returns is $4Mn 6

7. Risk Measures Net Account Quota Share Risk Measure: Contract Profit/Contract Premium Risk Measure: Contract Profit/Contract Premium $2Mn/$50Mn = 4% Conclusion: Well below average. Should decline. Risk Measure: Contract Profit/Contract Std Dev Risk Measure: Contract Profit/Contract Std Dev $2Mn/$4Mn = 50% Conclusion: Well above average. Should write. 7

8. Risk Measures Umbrella Cessions Facility Terms Terms $5Mn expected ceded premium $5Mn expected ceded premium $10Mn per policy limit $10Mn per policy limit Expected profit of $2Mn, after PC Expected profit of $2Mn, after PC Standard Deviation of returns is $20Mn Standard Deviation of returns is $20Mn 8

9. Risk Measures Umbrella Cessions Facility Risk Measure: Contract Profit/Contract Premium Risk Measure: Contract Profit/Contract Premium $2Mn/$5Mn = 40% Conclusion: Well above average. Should accept. Risk Measure: Contract Profit/Contract Std Dev Risk Measure: Contract Profit/Contract Std Dev $2Mn/$20Mn = 10% Conclusion: Well below average. Should decline. 9

10. Risk Measures Risk Measures used for the next two contracts 1) Risk Measure: Contract profit/Consumption of allocated capital = return on allocated capital (ROAC), or = risk adjusted return on capital (RAROC) 2) Risk Measure: Contract Profit/Contract ROL 3) Risk Measure: Contract Profit/Contract CR Company A: uses RM 1 & 3 Company A: uses RM 1 & 3 Company B: uses RM 2 & 3 Company B: uses RM 2 & 3 10

11. Risk Measures Catastrophe XOL Terms Terms Ceded premium = $390,000 Ceded premium = $390,000 Limit = $8.2 million Limit = $8.2 million Losses and Expenses = $318,000 Losses and Expenses = $318,000 Profit = $ 72,000 Profit = $ 72,000 Allocated capital = $101,000 Allocated capital = $101,000 11

12. Risk Measures Catastrophe XOL ROAC = 71.3% ROAC = 71.3% ROL = 4.7% ROL = 4.7% Combined Ratio = 81.5% Combined Ratio = 81.5% What decision does Company A make versus Company B? Why? What decision does Company A make versus Company B? Why? 12

13. Risk Measures Catastrophe XOL in Peak Zone Terms Terms Ceded premium = $335,000 Ceded premium = $335,000 Limit = $1.675 million Limit = $1.675 million Losses and Expenses = $235,000 Losses and Expenses = $235,000 Profit = $100,000 Profit = $100,000 Allocated capital = $1 million Allocated capital = $1 million 13

14. Risk Measures Catastrophe XOL in Peak Zone (e.g. Japan, Florida, UK) ROAC = 10% ROAC = 10% ROL = 20% ROL = 20% Combined Ratio = 70% Combined Ratio = 70% What decision does Company A make versus Company B? Why? What decision does Company A make versus Company B? Why? 14

15. Risk Measures What else needs consideration? Standalone? Standalone? Perils? Perils? Claims department vs. Independent claims adjusters? Claims department vs. Independent claims adjusters? Resolution quality of exposure data? Resolution quality of exposure data? ITV undervaluation? ITV undervaluation? Client relationship to producers? Client relationship to producers? 15

16. Risk Measures Catastrophe Quota Share Attritional loss ratio Attritional loss ratio Catastrophe load factor Catastrophe load factor Client operations/structure Client operations/structure Data quality both exposure and experience Data quality both exposure and experience 16

17. Risk Measures Observations Underwriters Preferences by Risk Measure Profit/Allocated Capital Contracts without inuring protections Excess High layers Catastrophe Coverage Profit/SD Net placements Pro-Rata Low layers Working Coverage 17