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?
 Different reinsurers have different
measures of profitability.
2
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
Risk Measures
The following four contracts will be used to
compare different risk measures:
1.
2.
3.
4.
Net Account Quota Share
Umbrella Cessions Facility
Catastrophe XOL
Catastrophe XOL in a Peak Zone
4
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
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.
Analogous Measures: Rate on-line, Value at Risk
5
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
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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
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
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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
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)
3)


Risk Measure: Contract Profit/Contract ROL
Risk Measure: Contract Profit/Contract CR
Company A: uses RM 1 & 3
Company B: uses RM 2 & 3
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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
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Risk Measures
Catastrophe XOL




ROAC = 71.3%
ROL = 4.7%
Combined Ratio = 81.5%
What decision does Company A make versus
Company B? Why?
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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
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?
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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
Risk Measures
Catastrophe Quota Share
• Attritional loss ratio
• Catastrophe load factor
• Client operations/structure
• Data quality both exposure and experience
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Risk Measures
Observations
Underwriters’ Preferences by Risk Measure
Profit/Allocated Capital
Profit/SD
• Contracts without
inuring protections
• Net placements
• Excess
• Pro-Rata
• High layers
• Low layers
• Catastrophe Coverage
• Working Coverage
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