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Measuring Risk/Reward Tradeoffs andMeasuring Risk/Reward Tradeoffs and Financial/Strategic Planning using DFA Financial/Strategic Planning using DFA

Session I: Risk / Return Measurement Session I: Risk / Return Measurement Session II: Risk / Return ManagementSession II: Risk / Return Management

Russ BinghamRuss Bingham

Vice President and Director of Corporate ResearchVice President and Director of Corporate Research

Hartford Financial ServicesHartford Financial Services

CAS Seminar on Dynamic Financial AnalysisCAS Seminar on Dynamic Financial Analysis

June 7, 2001June 7, 2001

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ContentsContents Session I - Risk/Return MeasurementSession I - Risk/Return Measurement

DFA Objectives and Practical QuestionsDFA Objectives and Practical Questions Project DimensionsProject Dimensions Describing Uncertainty and RiskDescribing Uncertainty and Risk Insurance Risk Transfer Processes at WorkInsurance Risk Transfer Processes at Work Risk / Return PrinciplesRisk / Return Principles Risk MetricsRisk Metrics Practical QuestionsPractical Questions

Session II – Risk / Return ManagementSession II – Risk / Return Management Two Key Questions – What Price and How Much Capital?Two Key Questions – What Price and How Much Capital? Total Return Model and ExampleTotal Return Model and Example Determination of Price and Equity RequirementsDetermination of Price and Equity Requirements Risk-Adjusted Return vs Risk-Adjusted LeverageRisk-Adjusted Return vs Risk-Adjusted Leverage Underwriting vs Investment Risk / ReturnUnderwriting vs Investment Risk / Return Risk / Return Summary Comments and Concerns Risk / Return Summary Comments and Concerns

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Session I – Risk / Return MeasurementSession I – Risk / Return Measurement

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DFA Risk Based Financial Model ObjectivesDFA Risk Based Financial Model Objectives

To develop a financial model which supports senior management To develop a financial model which supports senior management strategicstrategic decision making by providing a framework for guiding the decision making by providing a framework for guiding the construction of an optimal construction of an optimal portfolioportfolio of underwriting businesses and of underwriting businesses and investment classes in which underwriting, investment and financial investment classes in which underwriting, investment and financial riskrisk are viewed on an integrated, enterprise-wide basis, subject to are viewed on an integrated, enterprise-wide basis, subject to operational and financial operational and financial constraintsconstraints, ultimately to maximize , ultimately to maximize shareholder shareholder value creationvalue creation..

To initiate steps to instill a greater degree of financial discipline in To initiate steps to instill a greater degree of financial discipline in company operations company operations

Specifically, to address the following needsSpecifically, to address the following needs ALMALM - Optimize aggregate company underwriting and investment - Optimize aggregate company underwriting and investment

portfolioportfolio Capital AllocationCapital Allocation - Determine surplus requirements and risk adjusted - Determine surplus requirements and risk adjusted

profit targets for underwriting lines of business and investment which profit targets for underwriting lines of business and investment which reflects aggregate covariance / diversification benefitsreflects aggregate covariance / diversification benefits

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DFA Objectives (continued)DFA Objectives (continued)

PricingPricing - Develop methods which deal consistently with the - Develop methods which deal consistently with the risk transfer pricing activities within underwriting, investment risk transfer pricing activities within underwriting, investment

and finance, including covariance / diversification benefits.and finance, including covariance / diversification benefits. – Underwriting risk Underwriting risk Ratemaking and Policy PricingRatemaking and Policy Pricing

– Investment risk Investment risk Required return on invested assetsRequired return on invested assets

– Shareholder risk Shareholder risk Cost of capital Cost of capital ReservingReserving - Integrate loss reserve range of value estimates - Integrate loss reserve range of value estimates RatingsRatings - Provide foundation for ratings (lead emerging trends - Provide foundation for ratings (lead emerging trends

by rating agency and states and create opportunities to by rating agency and states and create opportunities to influence same)influence same)

Other - Other -

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Practical QuestionsPractical Questions

What questions are being asked?What questions are being asked? Focus on specific issuesFocus on specific issues

Who is asking the question? Are there other customers?Who is asking the question? Are there other customers? Present to level of knowledge / sophisticationPresent to level of knowledge / sophistication

Who will pass judgment on results?Who will pass judgment on results? Educate to level of acceptance / buy-in Educate to level of acceptance / buy-in

Is orientation strategic or operational?Is orientation strategic or operational? Level of detail / complexityLevel of detail / complexity Quality / credibility of inputsQuality / credibility of inputs Relevance / accuracy of resultsRelevance / accuracy of results

Who will be running the model?Who will be running the model? In-house requires greater customizationIn-house requires greater customization

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Practical Questions (Continued)Practical Questions (Continued)

Is this a one-time or on-going exercise?Is this a one-time or on-going exercise? Required model timeliness / responsiveness Required model timeliness / responsiveness

Is focus on reported earnings or economic value?Is focus on reported earnings or economic value? Select appropriate metricsSelect appropriate metrics

How do metrics relate to those used in other areas, such How do metrics relate to those used in other areas, such as planning, measurement of operating performance, and as planning, measurement of operating performance, and incentive compensation?incentive compensation?

Since DFA is all about risk, is an “educational” process Since DFA is all about risk, is an “educational” process needed to establish a risk / return decision framework?needed to establish a risk / return decision framework? A risk / return discipline is a necessity if the full value A risk / return discipline is a necessity if the full value

of DFA is to be realizedof DFA is to be realized

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Project DimensionsProject Dimensions

Balance sheet, income, cash flow statementsBalance sheet, income, cash flow statements

Development “triangles” of policy / accident Development “triangles” of policy / accident period into calendar periodperiod into calendar period

Accounting valuation - conventional (Stat or Accounting valuation - conventional (Stat or GAAP) and Economic (present value in runoff or GAAP) and Economic (present value in runoff or as ongoing firm)as ongoing firm)

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Policy (or Accident) / Calendar PeriodPolicy (or Accident) / Calendar PeriodDevelopment TrianglesDevelopment Triangles

Balance Sheet, Income, Cash FlowBalance Sheet, Income, Cash Flow

Calendar PeriodCalendar Period Policy Policy Historical Historical FutureFuture Total Total PeriodPeriod 19971997 19981998 19991999 20002000 20012001 UltimateUltimate PriorPrior X X X X X X X X X …... --> Sum X …... --> Sum 19971997 X X X X X X X X X …... --> Sum X …... --> Sum 19981998 X X X X X X X …... --> Sum X …... --> Sum

19991999 X X X X X …... --> Sum X …... --> Sum2000 2000 X X X …... --> Sum X …... --> Sum2001 2001 X …... --> Sum X …... --> Sum

======== ==== ==== ======== ======== ======== ReportedReported Sum Sum Sum Sum Sum Sum Sum Sum Sum Sum CalendarCalendar

Note: Rates and Economic valuation are oriented across the policy period “row” Note: Rates and Economic valuation are oriented across the policy period “row” but regulatory review and wall street focus are typically on the calendar but regulatory review and wall street focus are typically on the calendar “column” sum“column” sum

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Project Dimensions (continued)Project Dimensions (continued)

Distributional outcomes of important metricsDistributional outcomes of important metrics Risk vs Return Principles applicable to Underwriting, Risk vs Return Principles applicable to Underwriting,

Investment and Finance activitiesInvestment and Finance activities Reflect Covariance / Diversification Benefits and internal / Reflect Covariance / Diversification Benefits and internal /

external variable linkagesexternal variable linkages With external economic factors (e.g. inflation and interest With external economic factors (e.g. inflation and interest

rates)rates) Among lines of business and investment classesAmong lines of business and investment classes Across calendar / accident yearsAcross calendar / accident years Over development time (e.g. loss payout)Over development time (e.g. loss payout) Among variables (e.g. loss vs expense, interest rates vs Among variables (e.g. loss vs expense, interest rates vs

mortgage prepayments)mortgage prepayments)

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DFA Simulation ModelsDFA Simulation ModelsDescribing Insurance Uncertainty and RiskDescribing Insurance Uncertainty and Risk

Input ParametersInput Parameters Expected value of Expected value of magnitudemagnitude and and timingtiming of all financial of all financial

variables - premium, loss, expense, tax, investment yield, variables - premium, loss, expense, tax, investment yield, surplus, etc.surplus, etc.

Variability (i.e. distributions) of same financial variablesVariability (i.e. distributions) of same financial variables Correlations among variablesCorrelations among variables

Output Distributions and UseOutput Distributions and Use Rates of return - underwriting, investment, and shareholder Rates of return - underwriting, investment, and shareholder

total return with respective risk versus return tradeoffstotal return with respective risk versus return tradeoffs Surplus and surplus exposure (e.g. ruin probability, Surplus and surplus exposure (e.g. ruin probability,

expected policyholder deficit, and expected shareholder expected policyholder deficit, and expected shareholder deficit) deficit)

Risk / Return evaluation framework for decision makingRisk / Return evaluation framework for decision making

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Insurance Risk Transfer Processes at WorkInsurance Risk Transfer Processes at Work

Modeling the uncertainty (i.e., volatility) and risk / return Modeling the uncertainty (i.e., volatility) and risk / return characteristics embodied in the insurance process is at the characteristics embodied in the insurance process is at the core of DFA.core of DFA.

Underwriting risk from policyholders to companyUnderwriting risk from policyholders to company Underwriting risk from company to reinsurers or from Underwriting risk from company to reinsurers or from

company to financial markets via securitizationcompany to financial markets via securitization Investment risk from financial markets to company with Investment risk from financial markets to company with

respect to investment of company assetsrespect to investment of company assets Finance risk from company to shareholders (or Finance risk from company to shareholders (or

bondholders) as capital is raisedbondholders) as capital is raised

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Risk / Return PrinciplesRisk / Return Principles Insurance = underwriting, investment and leverageInsurance = underwriting, investment and leverage Volatility is uncertainty of resultVolatility is uncertainty of result Risk is exposure to adverse resultRisk is exposure to adverse result Higher Higher UnderwritingUnderwriting and and InvestmentInvestment returns are required when returns are required when

volatility is greatervolatility is greater Risk transfer pricing activities (policyholder, company & Risk transfer pricing activities (policyholder, company &

shareholder) are based on risk parametersshareholder) are based on risk parameters This can be accomplished independently of leverageThis can be accomplished independently of leverage

TotalTotal return is underwriting and investment return leveraged return is underwriting and investment return leveraged Leverage simultaneously magnifies total return and volatility Leverage simultaneously magnifies total return and volatility

in total return, but NOT necessarily riskin total return, but NOT necessarily risk Diversification / covariance benefits with respect to underwriting, Diversification / covariance benefits with respect to underwriting,

investment and finance (i.e. surplus) exist in the investment and finance (i.e. surplus) exist in the aggregateaggregate beyond the sum of individual businesses and functions.beyond the sum of individual businesses and functions.

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Total Return, Volatility and RiskTotal Return, Volatility and Risk

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Risk / Return Decision Framework – Risk MetricsRisk / Return Decision Framework – Risk Metrics Policyholder oriented risk metricsPolicyholder oriented risk metrics

Probability of ruinProbability of ruin Expected policyholder deficit (EPD)Expected policyholder deficit (EPD)

Shareholder oriented risk metricsShareholder oriented risk metrics Variability in total return (Variability in total return (RR)) Sharpe RatioSharpe Ratio Value at risk (VAR)Value at risk (VAR) Tail Value at Risk (TVAR)Tail Value at Risk (TVAR) Expected Shareholder Deficit Expected Shareholder Deficit Probability of surplus drawdown (PSD)Probability of surplus drawdown (PSD) Risk Coverage Ratio (RCR)Risk Coverage Ratio (RCR) Others …Others …

RBC and other Rating Agency measuresRBC and other Rating Agency measuresIn one way or another all risk measures address theIn one way or another all risk measures address the

likelihood and/or the severity of an adverse outcome likelihood and/or the severity of an adverse outcome

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Total Return Risk SchematicTotal Return Risk Schematic

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Comparison of Policyholder and Shareholder Risk MetricsComparison of Policyholder and Shareholder Risk Metrics

Shortcomings of Policyholder oriented risk metricsShortcomings of Policyholder oriented risk metrics Narrow focus on loss typically does not reflect variability in loss payment, Narrow focus on loss typically does not reflect variability in loss payment,

premium amount and collection, expense amount and payment and the premium amount and collection, expense amount and payment and the impact of taxes and investment income on float and surplusimpact of taxes and investment income on float and surplus

Reliability of results is questionable due to basis upon extreme outcomes Reliability of results is questionable due to basis upon extreme outcomes in tail of loss distributionin tail of loss distribution

Inconsistency between measures of risk and return make management of Inconsistency between measures of risk and return make management of the risk/return tradeoff difficult the risk/return tradeoff difficult

Advantages of Shareholder oriented risk metricsAdvantages of Shareholder oriented risk metrics Reflects all sources of variabilityReflects all sources of variability Captures all relevant factors that impact bottom lineCaptures all relevant factors that impact bottom line Typically embodies more reliabilityTypically embodies more reliability Shareholder focus is more in tune with broader financial marketplaceShareholder focus is more in tune with broader financial marketplace Should allow for diversification effects to be incorporated Should allow for diversification effects to be incorporated Addresses policyholder risksAddresses policyholder risks Provides an important link between price adequacy and solvencyProvides an important link between price adequacy and solvency Consistency in measures of risk and returnConsistency in measures of risk and return

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Session II – Risk /Return Management Session II – Risk /Return Management

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Dealing With Uncertainty and Risk -Dealing With Uncertainty and Risk -Two Key QuestionsTwo Key Questions

A critical objective of DFA modeling is to provide a A critical objective of DFA modeling is to provide a framework for addressing the risk / return tradeoff, framework for addressing the risk / return tradeoff, specifically addressing the following two questions:specifically addressing the following two questions:

What price should be charged (i.e. what is appropriate What price should be charged (i.e. what is appropriate risk-adjusted return)?risk-adjusted return)?

How much capital is needed (i.e. what is appropriate risk-How much capital is needed (i.e. what is appropriate risk-adjusted leverage)?adjusted leverage)?

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Total Return ModelTotal Return Model

Fully integrated balance sheet, income and cash flow Fully integrated balance sheet, income and cash flow statementsstatements

Reconciliation of policy / accident period with calendar periodReconciliation of policy / accident period with calendar period Nominal and economic valuationsNominal and economic valuations Clearly and consistently stated parameter estimatesClearly and consistently stated parameter estimates

Premium, loss and expense amountPremium, loss and expense amount Timing of premium collection, loss and expense paymentTiming of premium collection, loss and expense payment Investment yield ratesInvestment yield rates Underwriting and investment tax ratesUnderwriting and investment tax rates Leverage ratio and method (preferably risk-based) by which Leverage ratio and method (preferably risk-based) by which

surplus flows are controlled, including distribution of profitssurplus flows are controlled, including distribution of profits ……..

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Total Risk ModelTotal Risk Model

Utilization of Return Model adapted to include Utilization of Return Model adapted to include

Distributional assumptions of all parametersDistributional assumptions of all parameters Risk-based pricing algorithm for underwriting and Risk-based pricing algorithm for underwriting and

investment riskinvestment risk Risk-adjusted leverage algorithmRisk-adjusted leverage algorithm Quantification of underwriting, investment and Quantification of underwriting, investment and

leverage risk/return impact leverage risk/return impact

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Model ExampleModel Example Initial Underwriting CaseInitial Underwriting Case

Policy booked at beginning or yearPolicy booked at beginning or year $900 Premium, collected at policy inception$900 Premium, collected at policy inception $1000 Loss, single payment after 3 years$1000 Loss, single payment after 3 years No ExpenseNo Expense 5% Investment Rate 5% Investment Rate 0% Tax Rate0% Tax Rate 3 to 1 Liability to Surplus Ratio3 to 1 Liability to Surplus Ratio Initial Benchmark ROE = 9%Initial Benchmark ROE = 9% Losses vary with a standard deviation of $200 (20% CV)Losses vary with a standard deviation of $200 (20% CV)

Risk/Return ProblemRisk/Return Problem What is correct premium to charge?What is correct premium to charge? What is required benchmark surplus?What is required benchmark surplus?

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A. Single Policy CalendarizationA. Single Policy Calendarization

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Determination of Price and Benchmark EquityDetermination of Price and Benchmark Equity

A. Step 1: Total return distribution is generated using overall A. Step 1: Total return distribution is generated using overall average leverage of 3 to 1.average leverage of 3 to 1. Risk is defined as the probability that the total return falls Risk is defined as the probability that the total return falls

below the breakeven, or risk-free rate of return. Same for below the breakeven, or risk-free rate of return. Same for all lines of business.all lines of business.

B. Step 2: The price is determined which satisfies the B. Step 2: The price is determined which satisfies the specified risk condition. This establishes risk-adjusted return.specified risk condition. This establishes risk-adjusted return. Underwriting price expressed as target combined ratio Underwriting price expressed as target combined ratio

C. Step 3: Leverage is altered to restate all returns at 15%. C. Step 3: Leverage is altered to restate all returns at 15%. This establishes risk-adjusted leverage. This establishes risk-adjusted leverage. Change in leverage does not affect Premium and Risk Change in leverage does not affect Premium and Risk

determined in Step 2 determined in Step 2

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Total Return, Volatility and RiskTotal Return, Volatility and Risk

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B. Single Policy Calendarization – Risk-Adjusted Price DeterminedB. Single Policy Calendarization – Risk-Adjusted Price Determined

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C. Single Policy Calendarization – Risk-Adjusted Leverage DeterminedC. Single Policy Calendarization – Risk-Adjusted Leverage Determined

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Determination of Benchmark Equity (contd.): Determination of Benchmark Equity (contd.): Risk-Adjusted ReturnRisk-Adjusted Return

Step 2 establishes the risk / return tradeoff lineStep 2 establishes the risk / return tradeoff line

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Determination of Benchmark Equity (contd.):Determination of Benchmark Equity (contd.):Risk-Adjusted LeverageRisk-Adjusted Leverage

Step 3 Restates all businesses to a uniform 15% return withStep 3 Restates all businesses to a uniform 15% return with

uniform volatility via altered risk-adjusted leverageuniform volatility via altered risk-adjusted leverage

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Risk-Adjusted Return vs Risk-Adjusted LeverageRisk-Adjusted Return vs Risk-Adjusted Leverage

Two equivalent alternatives which differ in the form of Two equivalent alternatives which differ in the form of presentationpresentation At same premium & combined ratioAt same premium & combined ratio - - Maintain a fixed leverage, but vary the total return based Maintain a fixed leverage, but vary the total return based

on volatility on volatility – This avoids allocation of surplus to lines of businessThis avoids allocation of surplus to lines of business

Maintain a fixed total return, but vary leverage to adjust Maintain a fixed total return, but vary leverage to adjust for volatilityfor volatility– This makes regulatory environment less contentiousThis makes regulatory environment less contentious

Introduction of surplus (via the application of a varying Introduction of surplus (via the application of a varying leverage ratio) is optional (but helps communication).leverage ratio) is optional (but helps communication).

A leverage ratio (and thus surplus) serves a similar purpose in A leverage ratio (and thus surplus) serves a similar purpose in application as do IBNR factors, yields, expense ratios and tax application as do IBNR factors, yields, expense ratios and tax rates. While they do not exist at the individual policy level, rates. While they do not exist at the individual policy level, their necessary consideration in ratemaking and performance their necessary consideration in ratemaking and performance measurement requires introduction by formula. measurement requires introduction by formula.

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Pricing for Risk and Volatility of ReturnPricing for Risk and Volatility of Return

The Risk Pricing “Line” assumes higher returns from underwriting The Risk Pricing “Line” assumes higher returns from underwriting and investment functions needed to compensate for greater and investment functions needed to compensate for greater volatility (i.e., uncertainty) in order to satisfy desired risk criteriavolatility (i.e., uncertainty) in order to satisfy desired risk criteria

Risk and Return metrics are consistent in that they are based on Risk and Return metrics are consistent in that they are based on the same variablethe same variable

Risk pricing is independent of LeverageRisk pricing is independent of Leverage Leverage magnifies underwriting and investment risk pricing Leverage magnifies underwriting and investment risk pricing

lines, creating a total return line, while maintaining risk profilelines, creating a total return line, while maintaining risk profile Change in leverage causes total returns to move along lineChange in leverage causes total returns to move along line

As long as prices are on risk-based line, leverage is irrelevantAs long as prices are on risk-based line, leverage is irrelevant YES this means that adequate risk pricing which generates a fair YES this means that adequate risk pricing which generates a fair

total return connects the interests of the shareholder and the total return connects the interests of the shareholder and the policyholder and is in the best interest of bothpolicyholder and is in the best interest of both Adequate returns directly control solvency riskAdequate returns directly control solvency risk

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Underwriting and Investment Income Mix Underwriting and Investment Income Mix Characteristics Drive Risk / ReturnCharacteristics Drive Risk / Return

The mix of underwriting and investment income varies in each The mix of underwriting and investment income varies in each line of businsess depending on its respective cash flow line of businsess depending on its respective cash flow characteristics - long tail lines generate a greater proportion of characteristics - long tail lines generate a greater proportion of income from investment than short tail linesincome from investment than short tail lines

Underwriting income volatility is generally greater than Underwriting income volatility is generally greater than investment income volatility, especially in lines with catastrophe investment income volatility, especially in lines with catastrophe exposureexposure

Good cholesterol, bad cholesterolGood cholesterol, bad cholesterol Commercial lines generally derive a greater share of income Commercial lines generally derive a greater share of income

from the less volatile investment income componentfrom the less volatile investment income component Personal lines depend on a greater share of income from Personal lines depend on a greater share of income from

the more volatile underwriting component the more volatile underwriting component This mix favors commercial lines over personal in terms of This mix favors commercial lines over personal in terms of

the risk / return tradeoff the risk / return tradeoff

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Underwriting vs Investment Risk / ReturnUnderwriting vs Investment Risk / Return

Underwriting and Investment each contribute to risk and returnUnderwriting and Investment each contribute to risk and return

While higher risk investments can be used in ratemaking, the While higher risk investments can be used in ratemaking, the risk transfer pricing principles that apply to this added risk transfer pricing principles that apply to this added investment risk must still be reflectedinvestment risk must still be reflected

Properly separated and priced underwriting and investment risk Properly separated and priced underwriting and investment risk largely eliminates the disagreement as to what investment largely eliminates the disagreement as to what investment strategy should be built into premium rates. Offsetting occurs strategy should be built into premium rates. Offsetting occurs since higher investment risk requires higher price (yield) and since higher investment risk requires higher price (yield) and increased surplus to achieve target ROE levelincreased surplus to achieve target ROE level

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Risk/Return Summary Comments and ConcernsRisk/Return Summary Comments and Concerns Allocation versus attributionAllocation versus attribution

Objective is not simply allocation of given total company Objective is not simply allocation of given total company capitalcapital

Objective is better viewed as the determination of capital Objective is better viewed as the determination of capital required to satisfy desired total company risk/return criteria required to satisfy desired total company risk/return criteria which reflects the risk/return characteristics of individual which reflects the risk/return characteristics of individual underwriting and investment product risks along with the underwriting and investment product risks along with the diversification benefits provided by them diversification benefits provided by them

The Insurance processThe Insurance process Insurance is a multi-period processInsurance is a multi-period process Liabilities, not premium, drive underwriting riskLiabilities, not premium, drive underwriting risk

Claims (i.e. incurred loss) may be the most significant source of Claims (i.e. incurred loss) may be the most significant source of underwriting risk, but other underwriting variables and all cash underwriting risk, but other underwriting variables and all cash flows matter flows matter

Tax and investment income (on float and surplus) also importantTax and investment income (on float and surplus) also important

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Summary Comments and Concerns (Continued)Summary Comments and Concerns (Continued)

Delineate Underwriting, Investment and Finance risk / return Delineate Underwriting, Investment and Finance risk / return contributions to assure consistency in risk pricingcontributions to assure consistency in risk pricing

Underwriting and investment risk addressed through pricing, not Underwriting and investment risk addressed through pricing, not capitalcapital

Solvency risk is controlled by price adequacy, not capital levelsSolvency risk is controlled by price adequacy, not capital levels Accounting and economic value based financials differAccounting and economic value based financials differ Choice of risk metric from among several available is criticalChoice of risk metric from among several available is critical Capital, investment income, taxes, and IBNR, do not exist at the Capital, investment income, taxes, and IBNR, do not exist at the

underwriting product level, yet all are important elements which underwriting product level, yet all are important elements which affect risk/return and must be reflected (by formula) in the affect risk/return and must be reflected (by formula) in the product pricing processproduct pricing process

Need for consistency in risk and return metrics in order to Need for consistency in risk and return metrics in order to manage risk/return tradeoffmanage risk/return tradeoff