Fair Value Accounting and Actuaries in the Post-Enron World

1. Fair Value Accounting and Actuaries in the Post-Enron WorldSepember, 2002 Casualty Loss Reserve Seminar by Louise Francis Louise_francis@msn.com

2. Fair Valuation Task Force • Much of material is based on work the CAS task force on fair value of liabilities • White paper presenting the task force’s work is on CAS web site • Focus is on valuing liabilities.

3. Fair Value • For Assets : Fair Value = Market Value • For Liabilities: Market Value generally not available • Fair Value = PV(Liabilities)@rf + risk load+other adjustments

4. Some Alternatives to Fair Value • Undiscounted expected values • PV at risk free rate • PV using industry standard risk adjustment • Mixture of fair value and alternative • Entity specific measure

5. Methods Section • PV(Expected Liabilities)@rf considered straightforward to estimate using standard actuarial procedures • Use treasury rate for average duration of liabilities or use a maturity schedule applied to cash flow • This section focuses on a less familiar area: methods of computing risk loads

6. The Methods • CAPM based methods • IRR approach • Single Period RAD • Methods that use historical underwriting data • Methods using probability distributions • Using reinsurance data • Direct Estimation Method • Transformed Distributions • Rules of thumb • Other

7. Two Major Paradigms • Finance Perspective • Only non diversifiable risk included in risk load • Non diversifiable risk used in risk load is systematic risk • Actuarial Perspective • Diversifiable risk matters • Non diversifiable risk used in risk load is parameter risk

8. Method 1: CAPM Based • CAPM for assets: • rA = rf + βA (rM – rf) • CAPM for liabilities • rL = rf + βL (rM – rf) • βA is positive, βL is negative

9. Method 1: CAPM Based • A number of different ways to estimate βL • Compute βe and βA for insurance companies. Get βL by subtraction. • Regress accounting underwriting profitability data on stock market index • Regress accounting underwriting profitability data by line on industry all lines profitability

10. Method 1: CAPM • Method is controversial • Estimates of βL very sensitive to estimates of βA because of leverage • Accounting data biased • CAPM under attack in Finance literature • See Kosick, PCAS, 1991 • Recent research funded by CAS and AERF has addressed some of CAPM problems

11. Method 2: IRR • A pricing based method • Uses the IRR pricing method to back into a risk adjusted discount rate • Internal rate of return on capital contributions and withdrawls equals required rate of return

12. Method 2: IRR • Requires a surplus allocation • Requires an estimate of ROE • Assumes risk load on reserves lies on a continuum with risk load used in pricing

13. Method : Risk Adjusted Discount Method • A pricing based method • Discount = risk free rate minus a risk adjustment • Uses relationship between required ROE, expected investment return, income tax rate and ROE

14. Method 3: Risk Adjusted Discount Method Example • Leverage (S/L) =.5, ROE =.13 • E(rI) = .07, E(rF) = .06 • E(t) = 0, E(L) = $100 • Risk Adj = (S/L)*(ROE - E(rI)) +E(rF) -E(rI) = .5* (.13 - .07) + .06 - .07 = .02

15. Method 4: Based on Underwriting Data • Bases risk adjustment on long term averages of profitability observed in underwriting data. • Method first published by Butsic (1988) to compute risk adjusted discount rates • Uses industry wide data, possibly for all lines • Unless data for very long periods is used, results could be unstable

16. Method 4: Based on Underwriting Data • c = (1+rF)-u – e(1+rF)-w – l(1+rA)-t • c is ratio of PV(profit) to premium • rF is risk free rate, rA is risk adjusted rate • e is expense ratio • l is loss and LAE ratio • u is duration of premium, w is duration of expenses, t is duration of liabilities

17. Method 5: Loss Distribution Based Risk Loads • Three classical actuarial risk load formulas • Risk load = λ (sd Loss) • Risk load = λ (var Loss) • U(Equity) = E[U(Equity + Premium - Loss)] • A recent actuarial risk load formula • Risk Load =  Surplus Requirement, Surplus requirement from Expected Policyholder Deficit calculation

18. Method 5: Distribution Based Risk Loads • All four formulas require a probability distribution for aggregate losses • Simulation and Heckman-Meyers are common methods for deriving probability distribution • Probability distribution includes process and parameter risk • Risk load may not be value additive • Typically gives a risk load that is applied to PV(liabilities), not an adjustment to discount rate.

19. Method 5: Distribution Based Methods

20. Method 5: Distribution Based Methods • The aggregate losses displayed in the graph have a mean of $4.7M, and sd of $.14M and a variance of 1.9*1012. • A variance based risk load might have a λ of 10-7 • Risk load = 10-7*1.9*10-12=190,000

21. Method 5: Distribution Based Methods • Standard deviation based risk loads often use the sd to derive a theoretical surplus: • Surplus (S) = z.999*sd = 3.1* 1.4M = 4,340,000 • Philbrick’s method for converting this into a risk load: • Risk Margin=(ROE-rf)/(1+ROE)*S • If ROE = .13 and rf =.06 • Risk Margin =(.13-.06)/1.13*4,340,000=230,442

22. Method 5: Distribution Based Methods • This result is about 5% of liabilities. • The risk margin might be 5% of liabilities discounted at the risk free rate • A more complicated formula for liabilities paying out over several years • RM=Σ(ROE-rf)St/(1+ROE)t

23. Method 6: Using the Reinsurance Market • Reinsurance surveys • Conceptually similar to PCS Cat options • Extrapolate from companies’ own reinsurance program • Compare price charged by reinsurers to PV(liabilities)@rF to get risk load • Might need to make adjustments for riskiness of layers

24. Method 7: Direct Estimation • Directly uses market values of companies’ equity and assets to derive market value of liabilities • MV(Liabilities) = MV(Assets) – MV(Equity) • Ronn-Verma method used to compute MV(Assets)

25. Method 8: Distribution Transform Method • Based on transforming aggregate probability distribution • Simple example: x -> kx • Where k>1

26. Method 8: Distribution Transform Method • Power transform • S*(x)->S(x)p • S(x) is survival distribution of x (1 – F(x)) • p is between 0 and 1 • The tail probabilities increase • Mean also increases • Choice of p depends on riskiness of business

27. Method 8: Distribution Transform Method Applied to Lognormal Aggregate Probability Distribution Transform distribution mean 10% higher than original mean

28. Method 8: Distribution Transform Method • Let F(x)=1-(b/(b+x))q, S(x)=b/(b+x)q • S*(x) = (b/(b+x))qp • E(x) =b/(q-1) • E*(x)=b/(qp-1) • ILF(L)*=1-(b/(b+L))qp-1/(1-b/(b+100000))qp-1

29. Method 9: Rules of Thumb • In some situations there may not be adequate data or other resources to develop risk loads from scratch • Rules of thumb may provide a quick and dirty by adequate approach • Might require an industry committee to develop the rules

30. Method 9: Rules of Thumb • Examples • Compute the risk adjusted discount rate by subtracting 3% from the risk free rate • The risk load should be 10% of the present value of liabilities in the General Liability line and 5% of liabilities in the Homeowners line

31. Method 10: Other • Intended to account for new methods which are developed and reasonable methods not covered here • Risk margin should be positive

32. Method 10: Other • Research on this subject is ongoing • One method recently discussed is based on utility theory • Risk load based on stochastic analysis of program and surplus used in adverse scenarios. A or charge is applied to surplus useage

33. Credit Standing and Fair Values • Adjustment would recognize that a financially weak company would be less likely to satisfy its obligations in full than a financially strong company • Reduce expected liabilities by expected amount not to be paid because of default • A number of methods for estimating presented in white paper