1 A Stochastic Approach to Recognizing Profits of Finite Products Jeffrey W. Davis, FCAS, MAAA Casualty Actuarial Society Reinsurance Seminar July 2001 Jeffrey W. Davis, FCAS, MAAA Casualty Actuarial Society Reinsurance Seminar July 2001

2 Basic Assumption How do you recognize profits on a finite risk product? Basic Question There are profits to recognize.

3 Outline Review Structure of Finite Products Accounting Guidelines Speed-of-Settlement Example Stochastic Representation of Loss Exposure Questions, Comments Review Structure of Finite Products Accounting Guidelines Speed-of-Settlement Example Stochastic Representation of Loss Exposure Questions, Comments

4 Definition of Finite Risk No single definition of financial/finite reinsurance  Finite reinsurance = financial reinsurance?  Finite reinsurance = limited loss potential?  Finite reinsurance = ending reinsurance? We will define finite in terms of basic characteristics

5 TraditionalAlternative Insurance Markets Capital Markets Financial Reinsurance Finite Risk Reinsurance Integrated Risk Contingent Capital Insurance Securitization Traditional Reinsurance Risk Transfer and Financing Grid Risk Financing Risk Transfer

6 Prospective Covers: Coverage for future loss events - Spread Loss - Accident Year Stop Loss - Financial Quota Share - Speed of Settlement Retrospective Covers: Coverage for loss reserve development - Loss Portfolio Transfer - Adverse Loss Development Cover Major Categories of Finite Risk Products

7 Cedant Reinsurer Experience Fund Premium (= Initial Funding + Margin and Expenses) Additional Premiums ( if necessary) Initial Funding Additional Funding ( if necessary) Loss Payments Fund Balance ( if available) Basic Components of Finite Risk Arrangement Interest ( if Funds Withheld) Interest ( if Funds Transferred)

8 Basic Components of Finite Risk Premium in Actuarial Terms Funding Amount Present Value of Expected Losses to be paid from Fund, Assumed to be needed to cover expected loss payments If not needed, then amount returned to cedant with interest credit Margin Appropriate Risk Load to cover variability of Losses between Retention and Limit Reduce for impact of additional premiums If not needed, then amount becomes profit to reinsurer

9 Multi-year / multi-line Pre- and post-funding Loss and profit sharing mechanisms Consideration of time value of money Structured insurance risk elements Integrate non-insurance risks Main features Characteristics of Finite Risk Products

10 Finite Risk ReinsuranceTraditional Reinsurance Temporary and/or limited risk transfer Full consideration of time value of money Multi-year stability in capacity and pricing Contractual loss/profit participation Self-reinsurance concept Full and permanent risk transfer Limited consideration of time value of money Annual renewal/review of capacity and price Understanding of a long- term risk partnership Law of large numbers Comparison with Traditional Reinsurance

11 The differences between traditional reinsurance and finite risk reinsurance lead to different results monitoring and reserving considerations for finite risk products. Question remains: When do you recognize margin as profits? Up front? At commutation? Somewhere in between? Reserving Implications for Finite Risk Products

12 Underlying Loss Exposure (Actuarial Inputs) Expected net loss & ALAE ratio Distribution of forecasted results Estimated payout patterns Underlying Loss Exposure (Actuarial Inputs) Expected net loss & ALAE ratio Distribution of forecasted results Estimated payout patterns Finite Contract Features (Underwriter Inputs) Attachment point Limits (annual and aggregate) Pre and post funding features Discount rate Margin (expenses & profit) PRICE Inputs to Pricing (Prospective)

13 Underlying Loss Exposure (Actuarial Inputs) Expected net loss & ALAE ratio Distribution of forecasted results Estimated payout patterns Underlying Loss Exposure (Actuarial Inputs) Expected net loss & ALAE ratio Distribution of forecasted results Estimated payout patterns Finite Contract Features (Underwriter Inputs) Attachment point Limits (annual and aggregate) Pre and post funding features Discount rate Margin (expenses & profit) Results => Reserves Inputs to Reserving

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15 FAS 5 (Profit Recognition) An estimated loss…shall be accrued by a charge to income if: It is probable that a liability has been incurred, and The amount of loss can be reasonably estimated. Accounting Guidelines

16 Original Cedant Offshore Reinsurer Experience Fund Basic Components of Speed of Settlement (SOS) Retro Reinsurer Premium(= Part of Margin) Additional Funding (if necessary)

17 Original Cedant E[L] = $500 Offshore Reinsurer Experience Fund Attachment = $650 Limit = $100 $25 $15 Basic Components of Speed of Settlement (SOS) Retro Reinsurer $10 Additional Funding (if necessary)

18 Example of Speed of Settlement - Initial Pricing

19 Income Statement Impact - Initial Pricing Premium = Margin = 10 Million Loss Reserve= 100% * Margin (ignoring retro expenses) =100% * 10 million = 10 million UW Income = Premium - Losses = 10 Million - 10 Million = 0 Can be seen as aggressive or conservative.

20 Income Statement Impact - Reduced Variability Variability should decrease with time ==> Pr(loss) decreases ==>Profits more certain ==>Release reserves and realize profits So how do you easily quantify the reduction in variability? Alter initial shape parameters and resimulate distribution

21 Example of Speed of Settlement - Reduced Uncertainty

22 Income Statement Impact - Reduced Variability How do you measure release of reserves and thus underwriting profit? Option 1:Reduction in Probability of Loss = (11% - 13%) / 13% = -17% ==> 17% * 10 million = $1.7 million profit Option 2:Increase in NPV of SOS Cash Flows = ( ) / 5.4 = 54% ==> 54% * 10 million = $5.4 million profit Option 3:Uniform over duration/payment period liabilities Option 4:Judgment / Deterministic

23 Income Statement Impact - Increased Variability Variability can increase with time ==>Usually variability increase is one-sided ==>Expected value of loss increases ==>Profits less certain ==>Hold reserve levels, maybe increase reserves So how do you easily quantify the increase in variability? Alter initial shape parameters and resimulate distribution

24 Example of Speed of Settlement - Increased Uncertainty

25 Income Statement Impact - Increased Uncertainty Maybe no income statement impact, but useful for planning. Option 1:Increase in Probability of Loss = (25% - 13%) / 13% = 95% Option 2:Decrease in NPV of SOS Cash Flows = ( ) / 5.4 = -89% Option 3:Not Applicable Option 4:Judgment / Deterministic

26 Other Considerations Model error Parameter error Variation in Payment Pattern Taxes and Expenses Correlation with other finite contracts Underwriting input Changes in underlying risk exposure Interest rate risk Credit risk

27 Questions, Comments ??