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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

Risk Measures

CARE Meeting

Hamilton, Bermuda

June 6-7, 2005

Paul Kneuer, FCAS MAAA, Holborn Corporation

Susan Patschak, FCAS MAAA, Endurance Specialty


Risk measures1

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 measures2

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 measures3

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


Risk measures4

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

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Risk measures5

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


Risk measures6

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 measures7

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


Risk measures8

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 measures9

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


Risk measures10

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 measures11

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 measures12

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 measures13

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


Risk measures14

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?

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Risk measures15

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 measures16

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

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