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Risk Measures

Risk Measures. CARE Meeting Hamilton, Bermuda June 6-7, 2005. Paul Kneuer, FCAS MAAA, Holborn Corporation Susan Patschak, FCAS MAAA, Endurance Specialty. Risk Measures. Why do different reinsurers often make different decisions when it comes to pricing the same risk?

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Risk Measures

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  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? • 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: • Net Account Quota Share • Umbrella Cessions Facility • Catastrophe XOL • Catastrophe XOL in a Peak Zone 4

  5. Risk Measures Risk Measures used for the first two contracts • Risk Measure: Contract Profit/Contract Premium • Used by companies constrained by premium-to-surplus ratios • Analogous measures: Combined ratio, Operating ratio • 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. • Analogous Measures: Rate on-line, Value at Risk 5

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

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

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

  9. Risk Measures Umbrella Cessions Facility • Risk Measure: Contract Profit/Contract Premium $2Mn/$5Mn = 40% Conclusion: Well above average. Should accept. • 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 • Risk Measure: Contract profit/Consumption of allocated capital = return on allocated capital (ROAC), or = risk adjusted return on capital (RAROC) • Risk Measure: Contract Profit/Contract ROL • Risk Measure: Contract Profit/Contract CR • Company A: uses RM 1 & 3 • Company B: uses RM 2 & 3 10

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

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

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

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

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

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

  17. Risk Measures ObservationsUnderwriters’ Preferences by Risk Measure • Profit/Allocated Capital • Contracts withoutinuring protections • Excess • High layers • Catastrophe Coverage • Profit/SD • Net placements • Pro-Rata • Low layers • Working Coverage 17

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