1. FAS 113 Considerations on Risk Transfer Testing Gary Venter & Paul Brehm CLRS 2002

2. Introduction

3. Overview of FAS 113

4. Establishes the conditions required for a Contract with a reinsurer to be accounted for as reinsurance and Prescribes accounting and reporting standards Note “conditions” and “standards” but not methodology

5. Risk Transfer Essence “Contracts that do not result in the reasonable possibility that the reinsurer may realize a significant loss from the insurance risk assumed generally do not meet the conditions for reinsurance accounting and are to be accounted for as deposits.”

6. Key Issues Test is on reinsurer gaining risk, not on insurer reducing risk Reasonable possibility Significant loss These are terms that invite informed judgment VFIC did not look to draw a line, but rather explore different methods of measuring risk to provide a consistent framework for such judgments

7. Reasonable and Significant FASB only defines them through opposites Insignificant = having little or no importance; trivial Reasonable = probability is more than remote (from FAS 5) Test not met if the probability of a significant variation in either the amount or timing of payments by the reinsurer is remote Scheduled payments fail this test Reinsurer loss not required here, only uncertainty

8. Reasonably Possible to Have Significant Loss Based on present value of all cash flows Under reasonably possible outcomes  Seems to ask for a scenario generator Irrelevant if cash flows are identified as premiums, loss shares, profit shares, etc. Interest rates not to vary across outcomes Significance of loss is relative to amounts ceded to reinsurer

9. Evaluating Reasonable, Significant “Reasonable possibility” and “significant loss” appear closely intertwined For a smaller loss to qualify, it would have to be more likely to occur A 5% chance of a 100% loss might be more convincing than a 10% probability of a 25% loss

10. An Exception Substantially all the insurance risk relating to the reinsured portions of the underlying insurance contracts has been assumed by the reinsurer E.g., fronting Possibly any simple quota share  Depends on interpretation of “reinsured portions”

11. Reinsured Portions A percentage of all the writings in a line of business would seem to be a reinsured portion But a capped quota share, such as excluding cat losses, would not appear to take all of the insurance risk for the reinsured portion It could still meet reasonable and significant tests, but not the exception

12. Related Statements

13. Related statements NAIC Accounting Practices and Procedures Manual for Property and Casualty Insurance Companies  Promulgated after FAS 113; draws heavily from GAAP  “Unless the so-called contract contains this essential element of risk transfer, no credit whatsoever shall be allowed on account thereof in any accounting financial statement of the ceding insurer”

14. Related statements SSAP 62  [§12] “Indemnification of the entity company against loss or liability relating to insurance risk in reinsurance requires both of the following:  a. The reinsurer assumes significant risk under the reinsured portions of the underlying insurance agreements; and  b. It is reasonably possible that the reinsurer may realize a significant loss from the transaction.”

15. Related statements IASB  Principles for accounting for insurance contracts (draft only)  Principle 1.2 defines an insurance contract. Reinsurance is simply treated as a sub-set.  Principle 1.3 defines the uncertainty required for a contract to qualify as an (re)insurance contract.  Introduces the word “material” in describing uncertainty  Does not distinguish between underwriting risk and timing

16. Current Risk Transfer Testing

17. Practitioner survey Response 1Response 2Response 3Response 4Response 5 Official Policy? No YesDon’t know Probability5% or 10% 10% or 20% Reasonable worst case chance 20%10% Significance5% or 10% 10% or 20% 10%20%10% Method Probability distribution of E[ NPV losses], compare to the present value of premium. Compare E[NPV loss] to E[NPV premiums] by scenario Scenario testing NA Net present value of all cash flows.

18. Cat example Hypothetical cat exposure (left) Cat program:  $15M retention (1 in 10 years)  $50M layer (1 in 100 years)  Gross AAL = $6M; ceded layer = $1.625 M Assume 50% target loss ratio Distribution used to calculate the distribution of reinsurer profit/loss NPV calculated at 4%, assuming premiums collected at inception and losses paid at year end

19. Cat example

20. Finite example Assume:  E[AY LR] = 75%, with a c.v. = 10%, distributed lognormally  ER = 32%  Payout pattern at right (industry average) Finite Program:  Cede $15M deposit prem.  65% AP  If LR>75%, cede:  (LR-75%)/(1-.65)  S.t. max of 5%/(1-.65)

21. Finite example – sample cash flows

22. Finite example

23. Considerations Burden of proof is on the cedant; “proof” is that the reinsurer can lose money, not that cedant risk is reduced Analysis should include:  Distribution of possible results  Cash flow estimates  Appropriate, common discount rate  Thorough understanding of contract terms Analysis does not include:  Taxes  Reinsurer expenses The 10-10 rule, or VaR tests in general are “sufficient, but not necessary.” Risk assessment could/should consider the whole distribution…other risk metrics can be considered.

24. Alternatives to VaR Tests

25. Alternative Measures of Risk Expected Deficit Tail Value at Risk Other Coherent Measures Exponential Transforms Transforming the 10-10 Rule

26. Expected Deficit Loss x Probability Single loss: 10-10 ~ 5-20 ~ 2-50 etc. Or average deficit: expected value over all scenarios of the reinsurers loss in the losing scenarios = E(P – L) + From examples:  Property Catastrophe = -40%  Quota Share = -3%  Finite = -3%

27. Coherent Risk Measures 1. Sub-additivity:  (X+Y)   (X) +  (Y) 2. Monotonicity: If X  Y,  (X)   (Y) 3. Positive Homogeneity: for 0   ( X) =  (X) 4. Translation Invariance:  (X+a) =  (X)+a Examples:  Means under transformed probabilities, i.e., E * (X) =  xf * (x)dx, where f * is a transformation of f  TVaR

28. Tail Value at Risk TVaR  = E[X |x > VaR  ] =  x(   xf(x)dx/(1–  ) That is, expected losses when loss exceed threshold = E * (X) where f * is 0 below x(  and f/(1–  ) above Examples at 90 th percentile  Property Catastrophe = -319%  Quota Share = -42%  Finite = -23% Distinguishes last two, which deficit did not Maybe 20% – 25% right target range

29. Problems with and Alternatives to TVaR Problems  No risk attributed to losses below the threshold  Linear impact above the threshold Alternatives  E * with some other f *  E.g., F * (x) =  (b  –1 (F(x))+a) = Wang transform where  is the standard normal distribution

30. Example of Wang Transform TransformedOriginal

31. Measuring Risk with Wang Transform Determine transform parameters  Test different parameters with known treaties Look at expected reinsurer profit under transformed distribution If negative, there is risk

32. Risk with Parameters from Example, i.e., 0.7u – 1.3 From examples:  Property Catastrophe = -440% (P = $3.25M)  Property Catastrophe = -2% (P = $25M)  Quota Share = -19% Cat treaty that is too expensive won’t pass risk transfer by this test  Reinsurance premium levels:  Good deal  Bad deal  So bad it doesn’t qualify for risk transfer  No risk at all

33. Van Slyke – Kreps Approach Uses a market pricing approach to find the market risk load to retrocede the entire contract P & L Uses an exponential risk-adjusted value of losses: RAV = c ln{E[exp(X/c)]} with capital c Then they show the risk load  should obey:  = E[Y] + (  /s) ln E[e – sY/  ], where s is an industry parameter (they suggest about 0.4) and Y is return on premium Solve for  and use c =  /s to find RAV Set a cutoff like RAV(Y)>–70% for risk transfer

34. Van Slyke – Kreps Test From examples:  Property Catastrophe = 75% (P = $3.25M)  Property Catastrophe = -67% (P = $25M)  Quota Share = 25% Again if cat pricing gets too high, risk transfer fails Initial cat price looks small by market risk Quota share has a good deal of risk

35. Transformed 10-10 Rule Transforms normal distribution to make rule more applicable for heavy tails Let X be ROP – i.e., ROP if negative, else 0 F is distribution of X; define F * :  1. For a pre-selected security level  =10%, let =   1 (  )=  1.282, which is the  -th percentile of the standard normal distribution  2. Apply the Wang Transform: F*(x) =  [   1 (F(x))  ].  3. Calculate the expected value under F*: WT(  ) = E*[X]  4. If WT(  ) <  10%, it passes the test, otherwise it fails

36. Application For normal distributions this gives the 10-10 rule For the cat example, risk transfer fails at a premium of $35M For the quota share, WT(0.10) =  14.39% <  10%, so it passes

37. Risk Transfer Tests Summary All based on measures of risk All have to be calibrated to judgment level All work on regular and finite deals Can calibrate using contracts where risk transfer can be more confidently judged

38. Conclusions

39. FAS 113 is a standard, not a methodology; requires:  A reasonable possibility  Of a significant loss FAS 113 does dictate some considerations:  Cash flows between parties  Appropriate, common discount rate  Thorough understanding of contract terms Risk associated with “possibility” and “significance” are typically measured with a VaR measure using 10% and 10% as the critical values

40. Conclusions Other risk measures exist and could be applied to the risk transfer question -- EPD, TVaR, and distributional transforms Regardless of risk measure, critical values need to be established – judgment will still be required There is a disconnect between FAS 113 (reinsurer loss) and risk testing for Index Securitization (reduction in cedant risk)