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DISCOUNTED CASH FLOW MODELSDISCOUNTED CASH FLOW MODELS

Casualty Actuarial Society Annual MeetingCasualty Actuarial Society Annual Meeting

San Francisco, CASan Francisco, CA Russ BinghamRuss Bingham

November 15-17, 1999November 15-17, 1999 Hartford Financial ServicesHartford Financial Services

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ContentsContents ““Building Blocks”: The Fundamentals Building Blocks”: The Fundamentals Rate of Return Models: Reaching a Common GroundRate of Return Models: Reaching a Common Ground Dealing with Accounting Conventions:Dealing with Accounting Conventions: Economics Rule Economics Rule Equivalency in Rates of Return: Equivalency in Rates of Return: Do Do

it “Right” and all Models can be Reconciledit “Right” and all Models can be Reconciled The Fundamental Insurance Total Return ModelThe Fundamental Insurance Total Return Model The Components of Total Return: The Components of Total Return:

Underwriting, Investment & LeverageUnderwriting, Investment & Leverage Equivalency in Rates of ReturnEquivalency in Rates of Return Aspects of Insurance Total ReturnAspects of Insurance Total Return Exhibits: Balance Sheet, Income, Cash Flow & ReturnsExhibits: Balance Sheet, Income, Cash Flow & Returns

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““Building Blocks”: The FundamentalsBuilding Blocks”: The Fundamentals

Balance Sheet, Income and Cash Flow StatementsBalance Sheet, Income and Cash Flow Statements

Accounting Valuation: Conventional (statutory or Accounting Valuation: Conventional (statutory or GAAP) and Economic (present value) GAAP) and Economic (present value)

Development “Triangles” of Marketing/Policy/Accident Development “Triangles” of Marketing/Policy/Accident Period into Calendar PeriodPeriod into Calendar Period

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Policy (or Accident) / Calendar Period Policy (or Accident) / Calendar Period Development TrianglesDevelopment Triangles

Balance Sheet, Income, Cash Flow

Calendar Period Policy Historical Future Total Period 1996 1997 1998 1999 2000 Ultimate Prior X X X X X …... --> Sum 1996 X X X X X …... --> Sum 1997 X X X X …... --> Sum

1998 X X X …... --> Sum1999 X X …... --> Sum2000 X …... --> Sum

==== ==== ==== ==== ==== Reported Sum Sum Sum Sum Sum Calendar

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Rate of Return Models:Reaching a Common Rate of Return Models:Reaching a Common Ground - Structural ModificationsGround - Structural Modifications

To Convert Myers-Cohn Into a Rate of Return Model To Convert Myers-Cohn Into a Rate of Return Model Inclusion of surplusInclusion of surplus Economic value with after-tax discountingEconomic value with after-tax discounting NPV income formulation (with risk adjustment)NPV income formulation (with risk adjustment) NPV income formulation (without risk adjustment)NPV income formulation (without risk adjustment) Development of NPV balance sheet liabilitiesDevelopment of NPV balance sheet liabilities Policyholder and shareholder rate of return calculationsPolicyholder and shareholder rate of return calculations

To Align Internal Rate of Return Model With Both To Align Internal Rate of Return Model With Both Policyholder and Shareholder PerspectivesPolicyholder and Shareholder Perspectives Separation of operating (i.e. policyholder) cash flowsSeparation of operating (i.e. policyholder) cash flows Policyholder and shareholder rate of return calculationsPolicyholder and shareholder rate of return calculations

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Rate of Return Models: Reaching a Common Rate of Return Models: Reaching a Common Ground - Parameter and Model ConsistencyGround - Parameter and Model Consistency

Dealing with RiskDealing with Risk IRR cost of capital based total returnIRR cost of capital based total return MC risk-adjusted NPV total return equal to risk-free rateMC risk-adjusted NPV total return equal to risk-free rate MC NPV total return (without risk-adjustment) equal to cost MC NPV total return (without risk-adjustment) equal to cost

of capitalof capital Beta of Equity versus Beta of LiabilitiesBeta of Equity versus Beta of Liabilities

Surplus FlowsSurplus Flows Controlling amount required and timing of flowsControlling amount required and timing of flows

– Liability / surplus relationshipLiability / surplus relationship

– Multi-period aspectMulti-period aspect Surplus flow componentsSurplus flow components

– Surplus contribution and its releaseSurplus contribution and its release

– Investment income on contributed surplusInvestment income on contributed surplus

– Release of operating earningsRelease of operating earnings

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Dealing With Accounting Conventions: Dealing With Accounting Conventions: Economics RuleEconomics Rule

Retained earnings Retained earnings Not relevant to economic accountingNot relevant to economic accounting

Unearned premium reserveUnearned premium reserve If it’s not cash, it’s not economicIf it’s not cash, it’s not economic

Reported income and returns (and other financials as well)Reported income and returns (and other financials as well) Potentially misleading basis for rating, regulation & financial analysisPotentially misleading basis for rating, regulation & financial analysis

Leverage constraintsLeverage constraints Concessions to the raters, non-economic constraintsConcessions to the raters, non-economic constraints

Realizing economic valueRealizing economic value Economic value realization takes time, unless liabilities are “sold”Economic value realization takes time, unless liabilities are “sold”

ROE calculation -ROE calculation - Change the formula (income / beginning period contributed surplus)Change the formula (income / beginning period contributed surplus)

– Do not include retained earningsDo not include retained earnings– Do not average the equityDo not average the equity

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Equivalency in Rates of Return: Do it “Right” Equivalency in Rates of Return: Do it “Right” and All Models Can Be Reconciledand All Models Can Be Reconciled

For Single PolicyFor Single Policy (1) IRR(1) IRR (2) Net present value ROE(2) Net present value ROE (3) Total policy ultimate nominal ROE(3) Total policy ultimate nominal ROE (4) Shareholder annual dividend yield realized(4) Shareholder annual dividend yield realized

For Multiple Policy Ongoing (steady state, no growth)For Multiple Policy Ongoing (steady state, no growth) (5) IRR(5) IRR (6) Annual nominal ROE while at steady state (income / (6) Annual nominal ROE while at steady state (income /

beginning contributed surplus)beginning contributed surplus) (7) Shareholder annual dividend yield realized(7) Shareholder annual dividend yield realized

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The Fundamental InsuranceThe Fundamental Insurance

Total Return ModelTotal Return Model (1) Total Return = Operating Return X Operating Leverage(1) Total Return = Operating Return X Operating Leverage + Investment Rate of Return on Surplus+ Investment Rate of Return on Surplus

Operating Return = Underwriting Rate of ReturnOperating Return = Underwriting Rate of Return + Investment Rate of Return on+ Investment Rate of Return on Policyholder Liability “Float”Policyholder Liability “Float”

OROR (2) Total Return = Underwriting Return X Operating Leverage(2) Total Return = Underwriting Return X Operating Leverage + Investment Return X Asset Leverage+ Investment Return X Asset Leverage

Operating Leverage = Net Liabilities / SurplusOperating Leverage = Net Liabilities / Surplus Asset Leverage = Invested Assets / SurplusAsset Leverage = Invested Assets / Surplus

Insurance Consists of Underwriting, Investment & Financial LeverageInsurance Consists of Underwriting, Investment & Financial Leverage

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The Components of Insurance Total Return -The Components of Insurance Total Return -

Underwriting, Investment & Leverage Underwriting, Investment & Leverage Underwriting ReturnUnderwriting Return is the price for the transfer of risk to the company is the price for the transfer of risk to the company

associated with the policyholder related cash flows. When positive associated with the policyholder related cash flows. When positive the company is being paid for the transfer of risk. When negative the the company is being paid for the transfer of risk. When negative the company is incurring a cost to acquire the funds from the policyholder company is incurring a cost to acquire the funds from the policyholder and must depend on the investment spread to generate a profit. and must depend on the investment spread to generate a profit.

Investment ReturnInvestment Return represents the yield on invested assets (from both represents the yield on invested assets (from both policyholder supplied funds and surplus). The spread between the policyholder supplied funds and surplus). The spread between the Investment Return applicable to policyholder supplied funds and the Investment Return applicable to policyholder supplied funds and the Underwriting Return must be positive if the company is to generate a Underwriting Return must be positive if the company is to generate a net operating profit from underwriting.net operating profit from underwriting.

LeverageLeverage (based on surplus requirements needed to meet specified (based on surplus requirements needed to meet specified underwriting, investment and financial risk tolerances) creates a underwriting, investment and financial risk tolerances) creates a magnifying effect on both return and risk.magnifying effect on both return and risk.

Total ReturnTotal Return reflects the shareholder oriented return, comprised of reflects the shareholder oriented return, comprised of levered operating return plus the investment return on surplus.levered operating return plus the investment return on surplus.

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Aspects of Insurance Total Return Aspects of Insurance Total Return The Total Rate of Return, as well as the Underwriting and Investment The Total Rate of Return, as well as the Underwriting and Investment

Rates of Return, can be determined on either Rates of Return, can be determined on either a cash flow basis, via the Internal Rate of Return (IRR) ora cash flow basis, via the Internal Rate of Return (IRR) or as a Return on Equity formed by the ratio of Income to Equity in which the as a Return on Equity formed by the ratio of Income to Equity in which the

financials are in EITHER Nominal or Present Valued termsfinancials are in EITHER Nominal or Present Valued terms The present value rate of return using a risk-adjusted discount rate will The present value rate of return using a risk-adjusted discount rate will

equal the risk-free rate, since by definition risk has been eliminated.equal the risk-free rate, since by definition risk has been eliminated. Leverage is controlled by specifying rules governing the flow of surplus Leverage is controlled by specifying rules governing the flow of surplus

and dividend (distribution of earnings) to maintain a uniform risk profile and dividend (distribution of earnings) to maintain a uniform risk profile over the life of the policyover the life of the policy Contributed surplus governed by constant liability / surplus ratioContributed surplus governed by constant liability / surplus ratio Investment income on surplus dividended as earnedInvestment income on surplus dividended as earned Operating earnings distributed in proportion to per period liability exposureOperating earnings distributed in proportion to per period liability exposure

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Total Return Model ExampleTotal Return Model Example Total Return = Oper Return X Oper Levg + Invest Rate of Return on SurplusTotal Return = Oper Return X Oper Levg + Invest Rate of Return on Surplus

14.9% = 3.7% X 3.0 + 3.9% not risk-adjusted14.9% = 3.7% X 3.0 + 3.9% not risk-adjusted 6.0% = 0.7% X 3.0 + 3.9% risk-adjusted basis6.0% = 0.7% X 3.0 + 3.9% risk-adjusted basis Oper Return = Und Rate of Return + Invest Rate of Return on PH “Float”Oper Return = Und Rate of Return + Invest Rate of Return on PH “Float”

3.7% = -0.2% + 3.9% not risk-adjusted3.7% = -0.2% + 3.9% not risk-adjusted 0.7% = -0.2% + 3.9% - 3.0% risk-adjusted basis0.7% = -0.2% + 3.9% - 3.0% risk-adjusted basis

CAPM Reference Data:CAPM Reference Data: Risk-Free interest rateRisk-Free interest rate 6.0%6.0% 3.9% after-tax3.9% after-tax Risk PremiumRisk Premium 8.9%8.9% Equity BetaEquity Beta 1.001.00 Indicated cost of capitalIndicated cost of capital 14.9%14.9% Liability BetaLiability Beta -0.52-0.52 Indicated risk adjustmentIndicated risk adjustment 4.6%4.6% 3.0% after-tax3.0% after-tax Indicated risk-adjusted discount rateIndicated risk-adjusted discount rate 1.4%1.4% 0.9% after-tax0.9% after-tax

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Simplified Ratemaking SpreadsheetSimplified Ratemaking Spreadsheet