Use of a DFA Model to Evaluate Reinsurance Programs

1. Use of a DFA Model to Evaluate Reinsurance Programs Case Study 1999 CAS Seminar on Financial Risk ManagementApril 12-13, 1999Denver, Colorado Presented by:Robert F. Conger, FCASTillinghast – Towers Perrin

2. Discussion Outline • The Challenge: How Much Reinsurance to Buy, and What Mix? • Conceptual Framework • Methodological Approach • Case Study: XYZ Insurance • Key Issues

3. The Challenge: How Much Reinsurance to Buy, and What Mix?

4.     Chief Financial Officer Given the behavior of today’s insurance and financial markets, many property/casualty insurers are re-evaluating their reinsurance programs Buy less reinsurance? • We have excess capital • Keep net premiums up • Eliminate unnecessary expenses and transaction costs • Why share profits? • Maximize investable assets Buy more reinsurance? • Regulatory and rating agency pressure • It’s cheap • Everyone else is grabbing this deal • Let the reinsurers share the coming unprofitable results • Predictions of future catastrophes and mass torts • Support the higher limits we’re selling • We can’t lose on this latest reinsurance proposal • Better safe than sorry Buy different protection? • Securitization • Non-P/C reinsurers (e.g., Life/Health for workers compensation) • Contingent debt/equity capital • CAT futures • Blended products that go beyond traditional hazard risk

5. The design of a reinsurance program involves complex issues, and is material to most insurers’ bottom lines • Despite favorable market conditions, reinsurance is still a significant cost item for many insurers • Reinsurance decisions are becoming more challenging • Benefits have always been difficult to evaluate in relation to costs • How does reduction in underwriting volatility affect capital and return requirements? • Decisions are often made at the program level, but need to be placed in overall enterprise context • Need to avoid inefficient reinsurance activity • Proliferation of reinsurance products expands alternatives to consider • Alternatives to reinsurance products are becoming available, but add further to complexity of analysis • Securitization of risk • Contingent debt/equity capital • Reinsurance price volatility creates short-term tactical opportunities that can be more effectively played against a long-term strategy baseline

6. Case Study: Reinsurance Strategy for XYZ Insurance • Large multi-line company, organized into business units • Reinsurance purchasing occurs at corporate and business unit level • Corporate buys major treaties covering enterprise • Business units buy additional coverage to protect their results • Study focuses on three questions: • Which elements of the reinsurance program add value over the long term? • Which elements are good tactical buys today, due to market conditions? • How can the program be restructured to create more value?

7. Conceptual Framework

8. The answers to reinsurance questions must be specific to XYZ Insurance Compared to XYZ Insurance, no other insurance company has exactly the same • Volume and mix of business • Profitability history and outlook • Exposure to large claims, mass torts, and catastrophes • Investment strategy and performance • Capital amount and structure • Loss reserve adequacy • Reinsurance choices • Risk appetite/aversion • Corporate affiliates • Corporate structure • Stakeholder expectations • Rating agency and regulatory considerations Therefore, the “right” choice of reinsurance for XYZ Insurance will be different than for any other company . . . And may be different next year than this year.

9. Reduction in Required Capital Reinsurance Gross CapitalRequirement Net Capital Requirement Cost of Reinsurance ExpectedCededPremium Ceding Commission Cost of Reinsurance Reduction in Required Capital Components of a reinsurance program can be compared to each other, and to other alternatives, by viewing reinsurance as “rented” capital • Is reinsurance a cost effective source of capital? It adds value when this cost of capital is below the cost of alternatives Expected Ceded Losses Cost of “Rented” Reinsurance Capital =

10. 50% 40% L F K 30% J I R H Q C Expected Return O D N E 20% P G B A M 10% 0% 0.0% 0.5% 1.0% 1.5% 2.0% Level of Risk Reinsurance strategy alternatives can be compared using an Asset/Liability Efficient Frontier (ALEF) framework

11. Either conceptual framework begs several questions • How to quantify an insurer’s projected financial results and the potential for variability in these future results? • Gross of reinsurance • Net of reinsurance(for each alternative reinsurance program) • How to measure the Cost of a Reinsurance program and its effect on an insurer’s Expected Returns? • How to translate “the potential for variability” in future results into a usable and meaningful measure of Risk? • What is an insurer’s Required Capital? • With no reinsurance • With current reinsurance • With alternative reinsurance portfolios

12. Methodological Approach

13. Starting Balance Sheet Financial Calculator Non-Insurance Income AffiliateResults TaxCalculator Reinsurance Program Investment Strategy Capital Structure Line of Business Z . . . Line of Business C Line of Business B Year 1Financial Results • Balance Sheet • Income Statement GAAP Statutory Economic Analyzer To quantify projected financial results, XYZ constructed a comprehensive multi-year model • Line of Business A • Business volume • Business characteristics • Pricing • Claims • Paid and Reserved • Expenses • Cash flow pattern • Reserving patterns • Policyholder dividends Corporate Elements • Measures of • Risk • Return • Capital Requirements

14. Modeled financial outcomes are translated into “Risk Measures” specific to the insurer • Control variability of reported financial results • Reduce capital needs • Long-term • Finance growth • Satisfy regulatory or rating agency constraints • Support pricing of primary products • Offer new insurance products • Allow discounting of reserves • Current reinsurance price is below cost • Etc. Identify Key Reasons to Buy Reinsurance Define Risk Measures that capture the key objectives of the reinsurance program

15. We have explored several illustrative alternatives to traditional statistical measures of risk and variability Probability of Operating Result = X$ • Different reinsurance programs result in different distributions of operating results, and therefore different degrees of “risk” • The Risk Measures must be customized to the specific company “Below Target Return” measure “Expected Policyholder Deficit” measure Target Return Unfunded obligations Capital Operating Loss Operating Profit

16. The advantage of Below Target Risk over standard deviation can be illustrated by an example • These two return probability distributions have the same expected return of 13%, and the same standard deviation • Using a target return of 3% (roughly equivalent to a zero real return), the top distribution has a BTR of 17.6%; the bottom distribution has a BTR of 27.7% • The top return distribution is preferable: more upside and less downside 13%

17. Cost of Reinsurance The Cost of Reinsurance may be modeled several ways • Current proposals from reinsurers/intermediaries • Actual • Hypothetical, based on current market conditions and market knowledge • Nature of long-term relationship with reinsurers • Explicit deal • Implicit expectations • Conceptual model of reinsurance pricing • In the current market, where reinsurers are aggressively seeking top-line growth, short term tactical opportunities may lead to different reinsurance buying decisions than in the long run Expected Ceded Premium Ceding Commission Ceding Commission Expected Ceded Losses The choice of methods will depend on the objectives of the analysis, the expected duration of the reinsurance arrangement, and the nature of information available.

18. The definition of “Required Capital” likewise will vary depending on company perspective • Illustrative definitions of required capital with current reinsurance program • Current capital • Estimated capital at threshold of specified A.M. Best rating • Multiple of RBC • Capital that keeps Expected Policyholder Deficit < x% • With alternative reinsurance programs, we can • Model the different amount of Required Capital that would produce the same level of risk, or • Determine the change in level of risk, given the same amount of capital

19. Probability Metric Time Period and Form of Threshold Measurement Basis Perspective Likelihood of occurrence Expected excess severity above threshold Expected excess over threshold Loss from single event or risk factor Annual accounting result Results over multi-period planning horizon Experience on runoff basis Statutory GAAP Economic Absolute result Result relative to peers Result versus rating agency or regulatory norm Result relative to investor expectations While probability of ruin is the simplest form of risk-capital constraint, more complex constraints can be defined Dimensions of Risk-Capital Constraints Examples: “Less than a 1% chance of GAAP operating loss equal to or greater than 25% of reported equity” “Economic capital sufficient to reduce expected unfunded policyholder obligations to less than .25%”

20. Case Study: XYZ Insurance

21. Top 15 Programs by Normative Net Annual Cost Casualty Working XS Property First Cat Special Property Fac E&O Program XS Work Comp Working XS Property High Cat Umbrella QS Std Property Risk XS Surety QS Casualty High XS Marine XS Aviation XS Prof Liab XS Special Property QS Casualty Clash 0 2 4 6 8 10 12 14 16 Millions As a first step, XYZ identified the highest cost components of the reinsurance program $

22. XYZ measured each component’s contribution to reducing insolvency risk, and translated that into a reduction in required capital $

23. Some program elements appear to add significant value; others may be inefficient

24. In evaluating strategy alternatives, the focus was narrowed to the three least efficient programs Strategy A B C D E F G Casualty Working XS No Change Double Retention Double Retention Double Retention Treble Retention Treble Retention Treble Retention Work Comp Working XS No Change No Change Double Retention Double Retention Double Retention Treble Retention Treble Retention Aviation XS No Change No Change No Change Double Retention Double Retention Double Retention Treble Retention • The same framework can be used to evaluate alternative programs, in addition to changes to the existing program structure

25. Each strategy was evaluated in terms of its impact on risk and return 12% 11% G F E D Expected Return C B A 10% 0.9% 1.0% 1.1% Below Target Risk

26. Key Issues

27. An essential feature of the model is the interaction between its components and across time • Correlations between lines of business • “Runs” of good or bad years • Relationships between historical and future results • Macro-economic trends over time • Correlations between inflation, equity returns, and interest rates • Relationships between underwriting results and investment results • Relationship between gross-of-reinsurance results and recoveries • Patterns of reserve inadequacy/redundancy • Patterns of variation in cash flow • Influence of past results on future management strategies and actions • Investment strategy dependent on yield curve and/or asset duration • Shareholder dividends dependent on operating results

28. The model is run in a wide variety of scenarios over multiple future years • Future inflation rates • Future interest rates and investment returns • Catastrophes • Random large losses • Loss ratio movement • Long term patterns • Shocks • Year-to-year variability As with the company model itself, inter-relationships between elements are an essential feature of the modeling

29. Sensitivity testing is an essential step of the process • Some of the elements to be subjected to sensitivity testing include • Alternative choices of Risk Measures • Different definitions of Required Capital • Selected measure of reinsurance cost • Modeling time horizon • Years of business • Years of runoff • Parameters used to model reinsurable losses (e.g., size-of-loss distribution) • Degree of correlation of results across lines of business and across years • Base level of company profitability and growth • Different combinations of reinsurance components • The objective of the sensitivity testing is to satisfy ourselves that the results are robust, and not driven by one of the modeling choices

30. Of course, modeling does not replace management judgment • Modeling results will depend on key management perspectives, such as the choice of Risk Measure • The final trade-off between risk and return is a matter of preference But this modeling approach provides strong support to allow making the key decisions in a well-informed manner.