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## by Louise Francis Louise_francis@msn

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**Fair Value Accounting and Actuaries in the Post-Enron**WorldSepember, 2002 Casualty Loss Reserve Seminar by Louise Francis Louise_francis@msn.com**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.**Fair Value**• For Assets : Fair Value = Market Value • For Liabilities: Market Value generally not available • Fair Value = PV(Liabilities)@rf + risk load+other adjustments**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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.**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**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**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**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**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)**Method 8: Distribution Transform Method**• Based on transforming aggregate probability distribution • Simple example: x -> kx • Where k>1**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**Method 8: Distribution Transform Method Applied to Lognormal**Aggregate Probability Distribution Transform distribution mean 10% higher than original mean**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**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**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**Method 10: Other**• Intended to account for new methods which are developed and reasonable methods not covered here • Risk margin should be positive**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**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