Why do different reinsurers often make different decisions when it comes to pricing the same risk?

Different reinsurers have different have measures of profitability profitability.

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

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

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.
  

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
  

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.

Umbrella Cessions Facility

Terms

• 5Mn expected ceded premium


• $10Mn per policy limit


• Expected profit of $2Mn, after PC


• Standard Deviation of returns is $20Mn

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.

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 B: uses RM 2 & 3

Catastrophe XOL

Terms

• Ceded premium = $390,000


• Limit = $8.2 million


• Losses and Expenses = $318,000


• Profit = $ 72,000


• Allocated capital = $101,000 .


• ROAC = 71.3%


• ROL = 4.7%


• Combined Ratio = 81.5%


• What decision does Company A make versus Company B? Why?

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

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?

What Else Needs Consideration?

• Standalone?


• Perils?


• Claims department vs. Independent claims adjusters?


• Resolution quality of exposure data?


• ITV undervaluation?


• Client relationship to producers?

Catastrophe Quota Share

• Attritional loss ratio


• Catastrophe load factor


• Client operations/structure


• Data quality both exposure and experience

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