1. 1 Measuring Risk/Reward Tradeoffs and Financial/Strategic Planning using DFA Session I: Risk / Return Measurement Session II: Risk / Return Management Russ Bingham Vice President and Director of Corporate Research Hartford Financial Services CAS Seminar on Dynamic Financial Analysis June 7, 2001

2. 2 Contents l Session I - Risk/Return Measurement l DFA Objectives and Practical Questions l Project Dimensions l Describing Uncertainty and Risk l Insurance Risk Transfer Processes at Work l Risk / Return Principles l Risk Metrics l Practical Questions l Session II – Risk / Return Management l Two Key Questions – What Price and How Much Capital? l Total Return Model and Example l Determination of Price and Equity Requirements l Risk-Adjusted Return vs Risk-Adjusted Leverage l Underwriting vs Investment Risk / Return l Risk / Return Summary Comments and Concerns

3. 3 Session I – Risk / Return Measurement

4. 4 DFA Risk Based Financial Model Objectives l To develop a financial model which supports senior management strategic decision making by providing a framework for guiding the construction of an optimal portfolio of underwriting businesses and investment classes in which underwriting, investment and financial risk are viewed on an integrated, enterprise-wide basis, subject to operational and financial constraints, ultimately to maximize shareholder value creation. l To initiate steps to instill a greater degree of financial discipline in company operations l Specifically, to address the following needs l ALM - Optimize aggregate company underwriting and investment portfolio l Capital Allocation - Determine surplus requirements and risk adjusted profit targets for underwriting lines of business and investment which reflects aggregate covariance / diversification benefits

5. 5 DFA Objectives (continued) l Pricing - Develop methods which deal consistently with the risk transfer pricing activities within underwriting, investment and finance, including covariance / diversification benefits. –Underwriting risk  Ratemaking and Policy Pricing –Investment risk  Required return on invested assets –Shareholder risk  Cost of capital l Reserving - Integrate loss reserve range of value estimates l Ratings - Provide foundation for ratings (lead emerging trends by rating agency and states and create opportunities to influence same) l Other -

6. 6 Practical Questions l What questions are being asked? l Focus on specific issues l Who is asking the question? Are there other customers? l Present to level of knowledge / sophistication l Who will pass judgment on results? l Educate to level of acceptance / buy-in l Is orientation strategic or operational? l Level of detail / complexity l Quality / credibility of inputs l Relevance / accuracy of results l Who will be running the model? l In-house requires greater customization

7. 7 Practical Questions (Continued) l Is this a one-time or on-going exercise? l Required model timeliness / responsiveness l Is focus on reported earnings or economic value? l Select appropriate metrics l How do metrics relate to those used in other areas, such as planning, measurement of operating performance, and incentive compensation? l Since DFA is all about risk, is an “educational” process needed to establish a risk / return decision framework? l A risk / return discipline is a necessity if the full value of DFA is to be realized

8. 8 Project Dimensions l Balance sheet, income, cash flow statements l Development “triangles” of policy / accident period into calendar period l Accounting valuation - conventional (Stat or GAAP) and Economic (present value in runoff or as ongoing firm)

9. 9 Policy (or Accident) / Calendar Period Development Triangles Balance Sheet, Income, Cash Flow Calendar Period Policy HistoricalFuture Total Policy HistoricalFuture Total Period 19971998199920002001 Ultimate Period 19971998199920002001 Ultimate Prior X X X X X …... --> Sum Prior X X X X X …... --> Sum 1997 X X X X X …... --> Sum 1997 X X X X X …... --> Sum 1998 X X X X …... --> Sum 1998 X X X X …... --> Sum 1999 X X X …... --> Sum 2000 X X …... --> Sum 2001 X …... --> Sum ==== ================ ==== ================ Reported Sum Sum Sum Sum Sum Reported Sum Sum Sum Sum Sum Calendar Calendar Note: Rates and Economic valuation are oriented across the policy period “row” but regulatory review and wall street focus are typically on the calendar “column” sum

10. 10 Project Dimensions (continued) l Distributional outcomes of important metrics l Risk vs Return Principles applicable to Underwriting, Investment and Finance activities l Reflect Covariance / Diversification Benefits and internal / external variable linkages l With external economic factors (e.g. inflation and interest rates) l Among lines of business and investment classes l Across calendar / accident years l Over development time (e.g. loss payout) l Among variables (e.g. loss vs expense, interest rates vs mortgage prepayments)

11. 11 DFA Simulation Models Describing Insurance Uncertainty and Risk l Input Parameters l Expected value of magnitude and timing of all financial variables - premium, loss, expense, tax, investment yield, surplus, etc. l Variability (i.e. distributions) of same financial variables l Correlations among variables l Output Distributions and Use l Rates of return - underwriting, investment, and shareholder total return with respective risk versus return tradeoffs l Surplus and surplus exposure (e.g. ruin probability, expected policyholder deficit, and expected shareholder deficit) l Risk / Return evaluation framework for decision making

12. 12 Insurance Risk Transfer Processes at Work l Modeling the uncertainty (i.e., volatility) and risk / return characteristics embodied in the insurance process is at the core of DFA. l Underwriting risk from policyholders to company l Underwriting risk from company to reinsurers or from company to financial markets via securitization l Investment risk from financial markets to company with respect to investment of company assets l Finance risk from company to shareholders (or bondholders) as capital is raised

13. 13 Risk / Return Principles l Insurance = underwriting, investment and leverage l Volatility is uncertainty of result l Risk is exposure to adverse result l Higher Underwriting and Investment returns are required when volatility is greater l Risk transfer pricing activities (policyholder, company & shareholder) are based on risk parameters l This can be accomplished independently of leverage l Total return is underwriting and investment return leveraged l Leverage simultaneously magnifies total return and volatility in total return, but NOT necessarily risk l Diversification / covariance benefits with respect to underwriting, investment and finance (i.e. surplus) exist in the aggregate beyond the sum of individual businesses and functions.

14. 14 Total Return, Volatility and Risk

15. 15 Risk / Return Decision Framework – Risk Metrics l Policyholder oriented risk metrics l Probability of ruin l Expected policyholder deficit (EPD) l Shareholder oriented risk metrics Variability in total return (  R ) Variability in total return (  R ) l Sharpe Ratio l Value at risk (VAR) l Tail Value at Risk (TVAR) l Expected Shareholder Deficit l Probability of surplus drawdown (PSD) l Risk Coverage Ratio (RCR) l Others … l RBC and other Rating Agency measures In one way or another all risk measures address the likelihood and/or the severity of an adverse outcome

16. 16 Total Return Risk Schematic

17. 17 Comparison of Policyholder and Shareholder Risk Metrics l Shortcomings of Policyholder oriented risk metrics l Narrow focus on loss typically does not reflect variability in loss payment, premium amount and collection, expense amount and payment and the impact of taxes and investment income on float and surplus l Reliability of results is questionable due to basis upon extreme outcomes in tail of loss distribution l Inconsistency between measures of risk and return make management of the risk/return tradeoff difficult l Advantages of Shareholder oriented risk metrics l Reflects all sources of variability l Captures all relevant factors that impact bottom line l Typically embodies more reliability l Shareholder focus is more in tune with broader financial marketplace l Should allow for diversification effects to be incorporated l Addresses policyholder risks l Provides an important link between price adequacy and solvency l Consistency in measures of risk and return

18. 18 Session II – Risk /Return Management

19. 19 Dealing With Uncertainty and Risk - Two Key Questions A critical objective of DFA modeling is to provide a framework for addressing the risk / return tradeoff, specifically addressing the following two questions: l What price should be charged (i.e. what is appropriate risk-adjusted return)? l How much capital is needed (i.e. what is appropriate risk- adjusted leverage)?

20. 20 Total Return Model l Fully integrated balance sheet, income and cash flow statements l Reconciliation of policy / accident period with calendar period l Nominal and economic valuations l Clearly and consistently stated parameter estimates l Premium, loss and expense amount l Timing of premium collection, loss and expense payment l Investment yield rates l Underwriting and investment tax rates l Leverage ratio and method (preferably risk-based) by which surplus flows are controlled, including distribution of profits l ….

21. 21 Total Risk Model Utilization of Return Model adapted to include l Distributional assumptions of all parameters l Risk-based pricing algorithm for underwriting and investment risk l Risk-adjusted leverage algorithm l Quantification of underwriting, investment and leverage risk/return impact

22. 22 Model Example l Initial Underwriting Case l Policy booked at beginning or year l $900 Premium, collected at policy inception l $1000 Loss, single payment after 3 years l No Expense l 5% Investment Rate l 0% Tax Rate l 3 to 1 Liability to Surplus Ratio l Initial Benchmark ROE = 9% l Losses vary with a standard deviation of $200 (20% CV) l Risk/Return Problem l What is correct premium to charge? l What is required benchmark surplus?

23. 23 A. Single Policy Calendarization

24. 24 Determination of Price and Benchmark Equity l A. Step 1: Total return distribution is generated using overall average leverage of 3 to 1. l Risk is defined as the probability that the total return falls below the breakeven, or risk-free rate of return. Same for all lines of business. l B. Step 2: The price is determined which satisfies the specified risk condition. This establishes risk-adjusted return. l Underwriting price expressed as target combined ratio l C. Step 3: Leverage is altered to restate all returns at 15%. This establishes risk-adjusted leverage. l Change in leverage does not affect Premium and Risk determined in Step 2

25. 25 Total Return, Volatility and Risk

26. 26 B. Single Policy Calendarization – Risk-Adjusted Price Determined

27. 27 C. Single Policy Calendarization – Risk-Adjusted Leverage Determined

28. 28 Determination of Benchmark Equity (contd.): Risk-Adjusted Return Step 2 establishes the risk / return tradeoff line

29. 29 Determination of Benchmark Equity (contd.): Risk-Adjusted Leverage Step 3 Restates all businesses to a uniform 15% return with uniform volatility via altered risk-adjusted leverage

30. 30 Risk-Adjusted Return vs Risk-Adjusted Leverage l Two equivalent alternatives which differ in the form of presentationAt same premium & combined ratio - l Maintain a fixed leverage, but vary the total return based on volatility –This avoids allocation of surplus to lines of business l Maintain a fixed total return, but vary leverage to adjust for volatility –This makes regulatory environment less contentious l Introduction of surplus (via the application of a varying leverage ratio) is optional (but helps communication). A leverage ratio (and thus surplus) serves a similar purpose in application as do IBNR factors, yields, expense ratios and tax rates. While they do not exist at the individual policy level, their necessary consideration in ratemaking and performance measurement requires introduction by formula.

31. 31 Pricing for Risk and Volatility of Return l The Risk Pricing “Line” assumes higher returns from underwriting and investment functions needed to compensate for greater volatility (i.e., uncertainty) in order to satisfy desired risk criteria l Risk and Return metrics are consistent in that they are based on the same variable l Risk pricing is independent of Leverage l Leverage magnifies underwriting and investment risk pricing lines, creating a total return line, while maintaining risk profile l Change in leverage causes total returns to move along line l As long as prices are on risk-based line, leverage is irrelevant l YES this means that adequate risk pricing which generates a fair total return connects the interests of the shareholder and the policyholder and is in the best interest of both l Adequate returns directly control solvency risk

32. 32 Underwriting and Investment Income Mix Characteristics Drive Risk / Return l The mix of underwriting and investment income varies in each line of businsess depending on its respective cash flow characteristics - long tail lines generate a greater proportion of income from investment than short tail lines l Underwriting income volatility is generally greater than investment income volatility, especially in lines with catastrophe exposure l Good cholesterol, bad cholesterol l Commercial lines generally derive a greater share of income from the less volatile investment income component l Personal lines depend on a greater share of income from the more volatile underwriting component l This mix favors commercial lines over personal in terms of the risk / return tradeoff

33. 33 Underwriting vs Investment Risk / Return l Underwriting and Investment each contribute to risk and return l While higher risk investments can be used in ratemaking, the risk transfer pricing principles that apply to this added investment risk must still be reflected l Properly separated and priced underwriting and investment risk largely eliminates the disagreement as to what investment strategy should be built into premium rates. Offsetting occurs since higher investment risk requires higher price (yield) and increased surplus to achieve target ROE level

34. 34 Risk/Return Summary Comments and Concerns l Allocation versus attribution l Objective is not simply allocation of given total company capital l Objective is better viewed as the determination of capital required to satisfy desired total company risk/return criteria which reflects the risk/return characteristics of individual underwriting and investment product risks along with the diversification benefits provided by them l The Insurance process l Insurance is a multi-period process l Liabilities, not premium, drive underwriting risk l Claims (i.e. incurred loss) may be the most significant source of underwriting risk, but other underwriting variables and all cash flows matter l Tax and investment income (on float and surplus) also important

35. 35 Summary Comments and Concerns (Continued) l Delineate Underwriting, Investment and Finance risk / return contributions to assure consistency in risk pricing l Underwriting and investment risk addressed through pricing, not capital l Solvency risk is controlled by price adequacy, not capital levels l Accounting and economic value based financials differ l Choice of risk metric from among several available is critical l Capital, investment income, taxes, and IBNR, do not exist at the underwriting product level, yet all are important elements which affect risk/return and must be reflected (by formula) in the product pricing process l Need for consistency in risk and return metrics in order to manage risk/return tradeoff