Using DFA to Optimize the Value of Reinsurance CAS Seminar on Dynamic Financial Analysis Tillinghast – Towers Perrin Robert F. Conger Thomas S. McIntyre Kurt A. Reichle July 19-20, 1999

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Discussion Outline The Challenge: How Much Reinsurance to Buy, and What Mix? General Approach Methodological Details Case Study - XYZ Insurance Company Summary of Key Issues

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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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 Chief Financial Officer    

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, The answers to reinsurance questions must be specific to XYZ Insurance Company 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.

General Approach

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Evaluate reinsurance alternatives by analyzing and comparing their expected effects on key dimensions of a company’s future strength and performance This framework can be applied to multiple alternative reinsurance programs, including programs that involve non-traditional forms of protection Projected Financial Results Gross of Reinsurance Reinsurance Program A Reinsurance Program B Analysis of Financial Performance Projected Financial Results Net of Reinsurance Projected Financial Results Net of Reinsurance Profitability Volatility Capital Requirements Overall Measures of Risk Return Overall Measures of Risk Return Analysis of Financial Performance Profitability Volatility Capital Requirements

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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 Gross Capital Requirement Cost of “Rented” Reinsurance Capital = Cost of Reinsurance Reduction in Required Capital Reinsurance Net Capital Requirement Reduction in Required Capital Expected Ceded Premium Ceding Commission Expected Ceded Losses Cost of Reinsurance

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Reinsurance strategy alternatives can be compared using an Asset/Liability Efficient Frontier (ALEF  ) framework 0% 10% 20% 30% 40% 50% 0.0%0.5%1.0%1.5%2.0% Level of Risk Expected Return M N A G H J O B Q I D C K E L F R P

Methodological Details

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, The 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, To quantify an insurer’s projected financial results, construct a comprehensive multi- year model of the insurer Line of Business A Business volume Business characteristics Pricing Claims Paid and Reserved Expenses Cash flow pattern Reserving patterns Policyholder dividends Line of Business B Line of Business C... Line of Business Z Starting Balance Sheet Financial Calculator *Multiple versions of the model are used to test various alternative strategies Balance Sheet Income Statement GAAP Statutory Economic Year 1 Financial Results Measures of Risk Return Capital Requirements Analyzer Reinsurance Program* Investment Strategy Capital Structure Tax Calculator Non-Insurance Income Affiliate Results Corporate Elements

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Run the model 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Reinsurance alternatives can be modeled using a variety of tools, depending on the nature of the insurer’s risks and the details of the reinsurance program Reinsurance Individual large claims or multi-claim events Catastrophes Quota share Aggregate excess and/or deductibles Blended products Unique combinations Typical Tool Large loss simulator, calibrated using company and/or industry experience Incorporate output file from a standard catastrophe model Parameters of financial model Financial calculator Transfer analytical data between financial calculator and external reinsurance analysis (e.g., spreadsheet) The modeling needs to address key features of the reinsurance, including ceding commissions, swing rating, cash flow timing, and reinstatements

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, The array of reinsurance alternatives to be modeled will vary according to an insurer’s situation Most typically, expect to evaluate  Current reinsurance program  Effects of eliminating various components of current program  No reinsurance at all  Effects of purchasing various additional reinsurance elements relevant to the insurer’s business  Effects of utilizing relevant reinsurance substitutes  Combinations of all the above It may be desirable to model long term reinsurance strategies based on long term reinsurance cost patterns, but also to consider short-term tactical reinsurance choices to take advantage of temporary departures from long term reinsurance pricing

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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 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. Expected Ceded Premium Ceding Commission Expected Ceded Losses Cost of Reinsurance

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, We have explored several illustrative alternatives to traditional statistical measures of risk and variability 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 Target Return Capital Operating Profit Operating Loss Unfunded obligations “Below Target Return” measure “Expected Policyholder Deficit” measure Probability of Operating Result = X$

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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% DETAILED APPROACH

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, While probability of ruin is the simplest form of risk-capital constraint, more complex constraints can be defined 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 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%”

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, The modeling results allow us to characterize each reviewed reinsurance strategy Key characteristics are the effects on  Expected company return  Risk  Required capital Certain reinsurance elements may be eliminated from consideration due to  Risk reduction not commensurate with cost  Constraints, such as minimum capital requirements to satisfy A.M. Best

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Finally, the results will allow examination of key decisions Which reinsurance components provide risk reduction commensurate with their costs? How can we achieve desired relationships of risk and return by  Varying combinations of reinsurance programs  Varying retentions and amounts of coverage  Utilizing substitutes for reinsurance

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, 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.

Case Study

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Case Study: Reinsurance Strategy 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?

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Top 15 Programs by Normative Net Annual Cost Casualty Clash Special Property QS Prof Liab XS Aviation XS Marine XS Casualty High XS Surety QS Std Property Risk XS Umbrella QS Property High Cat Work Comp Working XS E&O Program XS Special Property Fac Property First Cat Casualty Working XS Millions As a first step, we identified the highest cost components of the reinsurance program $

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, We measured each component’s contribution to reducing insolvency risk, and translated that into a reduction in required capital $

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Some program elements appear to add significant value; others may be inefficient

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, In evaluating strategy alternatives, we narrowed our focus to the three least efficient programs Strategy A B C D E F G Casualty Working XS No Change Double Retention Treble Retention Work Comp Working XS No Change Double Retention Treble Retention Aviation XS No Change Double Retention Treble Retention We also can evaluate alternative programs, in addition to changes to the existing program structure

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, Each strategy can be evaluated in terms of its impact on risk and return 10% 11% 12% 0.9%1.0%1.1% Below Target Risk Expected Return A B D C E F G

Summary of Key Issues

G:\ \WPDOC\Reinsurance\CAS Seminar DFA ppt July 19-20, The actuary – and the company – must be attentive to several key issues Define purpose(s) of reinsurance program... And select risk measures to match Select the universe of reinsurance programs to analyze  Current program  More or less coverage  Different structures Measure/model the cost of each reinsurance component Adequately specify  Interactions between lines of business, investment results, inflation, etc.  Distributions of loss ratios, claim sizes, etc. Sensitivity testing Other key decisions (business growth, asset allocation) interact with the reinsurance decisions