FAS 113 Considerations on Risk Transfer Testing

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

2. Introduction

3. Overview of FAS 113

4. Overview of FAS 113 • 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. Response 1 Response 2 Response 3 Response 4 Response 5 Official Policy? No No Yes Don’t know Don’t know Probability 5% or 10% 10% or 20% Reasonable worst case chance 20% 10% Significance 5% 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. Practitioner survey

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: r(X+Y)  r(X) + r(Y) 2.Monotonicity: If X  Y, r(X) r(Y) 3.Positive Homogeneity: for 0 l, r(lX) = lr(X) 4. Translation Invariance: r(X+a) = r(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 • TVaRa = E[X |x > VaRa ] = x(a)xf(x)dx/(1–a) • That is, expected losses when loss exceed threshold • = E*(X) where f* is 0 below x(a) and f/(1–a) above • Examples at 90th 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) = F(bF–1(F(x))+a) = Wang transform where F is the standard normal distribution

30. Example of Wang Transform Original Transformed

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 p should obey: p = E[Y] + (p/s) ln E[e – sY/p], where s is an industry parameter (they suggest about 0.4) and Y is return on premium • Solve for p and use c = p/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 underF*: 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. Conclusions • 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)