1 / 33

by Louise Francis Louise_francis@msn

Fair Value Accounting and Actuaries in the Post-Enron World Sepember, 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

Télécharger la présentation

by Louise Francis Louise_francis@msn

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  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

More Related