Using DFA to Allocate Capital: Extending the Traditional Approach

1. Swiss Re Investors, Inc.Z Using DFA to Allocate Capital: Extending the Traditional Approach Dan Isaac & Stephen Philbrick 2000 Casualty Loss Reserve Seminar: September 19, 2000

2. Note to CLRS Participants • Some changes have been made to this presentation subsequent to the CLRS on September 19. • Additional informational slides has been added to both supplement the original presented output and to improve the overall flow. • There have been no substantive changes to the conclusions. • Also, please review the notes attached to some of the slides to achieve a fuller understanding of that particular slide.

3. Agenda • Introduction to Capital Allocation • Why is Capital Allocated • Controversies • Metrics and Issues Associated with the Metrics • Traditional Capital Allocation Approach • Introduction to DFA • Introduction to CUFFS, a sample Insurance Company • Extending Traditional Capital Allocation Approaches using DFA • Shapley Illustration • Conclusions

4. Capital • Capital Allocation vs. Capital Adequacy • This presentation only address issues relating to Capital Allocations

5. Introduction to Capital Allocation

6. Why Allocate Capital? “The underlying economic point of view taken is that of a reinsurer considering a new contract. The reinsurer has committed surplus to support the variability of his existing book; the new contract will require additional surplus to support its variability.” (Kreps, Reinsurer Risk Loads from Marginal Surplus Requirements)

7. Why Allocate Capital? Capital allocation serves three primary purposes: • to compare managerial performance across business units • to provide a risk indicator for regulators and other stakeholders • and to develop a common basis for major decisions, including investment and underwriting strategies, and setting the corporate structure (Mulvey, Belfatti and Madsen, Integrated Financial Risk Management: Capital Allocation Issues 1999)

8. Capital Allocation is Controversial “In this paper we have demonstrated that meaningful allocation is a mathematical impossibility…” (Bass & Khury, 1992 Discussion Papers on Insurer Financial Solvency) “A policy written with a monoline automobile insurance company with $100 million of surplus is not as well protectedas a policy written with a large multiline insurance company with $100 million allocated to its automobile line of business”(Charles McClenahan, as quoted by Glenn Meyers, Contingencies, September/October 2000) “I agree with Chuck’s statement.”Glenn Meyers

9. Yet Even the Detractors Note: “In other words, surplus allocation may be useful as a management tool to help improve the overall return on equity that is of interest to investor-owners…” (Bass & Khury,1992 Discussion Papers on Insurer Financial Solvency) “But I also agree with the idea of using capital allocation as an internal management tool…”(Glenn Meyers, Contingencies, September/October 2000)

10. Limits of Use “Furthermore, even greater care must be taken to make sure that such attempts, aimed at the internal management of the enterprise, are not inadvertently extended beyond its natural limited application, to the arena of rate regulation as the sole measure of the soundness of rates.” (Bass & Khury, 1992 Discussion Papers on Insurer Financial Solvency)

11. Combine Risk Variable and Risk Function • RISK VARIABLE: • RISK FUNCTION: Sample Metrics & Allocation Methods METRICS: • Statutory Surplus • Economic Value • RBC Ratio etc. • Probability of Ruin (Value at Risk) • Variance • Standard Deviation • Semi-Variance • Shortfall Measures (Expected Policyholder Deficit, Tail Value at Risk) ALLOCATION METHODS: • First-In Marginal Contribution (Standalone) • Last-In Marginal Contribution (Marginal) • Shapley Values

12. Application of Metrics Issues • Additivity • Parameter Risk/Process Risk (CAPM) • Scope • Time Frame • Liability versus Assets • Symmetry • Not All Failures Are Created Equal

13. Traditional Approach to Capital Allocation • No Existing Reserves • One Year of New Business • No Asset Risk • Full Recognition of Ultimate Results at the End of the Year

14. Possible Extensions Using DFA Multiple Years of New Business: Allow multiple years of new business to be written instead of one year of new business Asset Returns: Allow for volatile asset returns, and allocate capital to assets Existing Reserves: Include existing reserves in addition to one year of new business in capital allocation process

15. Introduction to DFA Z

16. Introduction to DFA Dynamic:Reflects the year-to-year variability and interaction of measurable financial risks. Financial:Projects 1000 or more sets of probabilistic financial statements (GAAP, Statutory, Economic). Analysis:Allows a thorough assessment of both risk and reward, thereby aiding in the evaluation and identification of opportunities to improve expected financial results and/or reduce financial variability.

17. Income Statements Economic Liability & & Asset Business Simulation Simulation Cashflow Statements • By Line of Business • Amount and timing of: reserves and future losses • Reinsurance structure • Expenses • Business Plan • Etc. • By Currency • Inflation • GDP • Interest Rates • Asset class returns • Etc. TM FIRM Optimization Balance Sheets & Valuation • Financial Statements • Economic • GAAP • Statutory • Financial Strategies • Define Strategic Asset Allocation Introduction to DFA Combining the asset and liability simulations and their interactions creates a robust set of a thousand or more prospective year-by-year financial statements to enhance decision-making. I4

18. Introduction to CUFFS Insurance Company Z

19. CUFFS Insurance Company: Existing Reserves Existing Reserves (by line) Duration: 2.5

20. CUFFS Insurance Company: Run-off Cash Flows • Financial Conditions • Existing Reserves $ 5,263 million • Unearned Premium $ 1,729 million

21. CUFFS Insurance Company: Run-off Cash Flows • Financial Conditions • Invested Assets $ 9,867 million • Statutory Surplus $ 3,755 million Duration: 2.7

22. CUFFS Insurance Company: Business Plan Written Premium (by line) Duration: 2.0

23. Mean Loss Ratio: 75.2% CUFFS Insurance Company: Premium Growth & Loss Ratio --- Budget --- • Premium Growth Rate: 1.2% --- Budget ---

24. CUFFS Insurance Company: Asset Portfolio Summary Invested Assets Fixed Income

25. Extending Traditional Capital Allocation Approaches using DFA Z

26. Use Standard Deviation of Statutory Surplus at the end of the time horizon as the Risk Measure Allocating Capital based on the Marginal Impact of a particular variable (e.g. Difference between With and Without Workers Comp) Excluded Business is assumed to be Completely Reinsured Capital Allocation Methodology

27. Possible Extensions Using DFA Multiple Years of New Business: Allow multiple years of new business to be written instead of one year of new business Asset Returns: Allow for volatile asset returns, and allocate capital to assets Existing Reserves: Include existing reserves in addition to one year of new business in capital allocation process

28. Possible Extensions Using DFA Multiple Years of New Business: Allow multiple years of new business to be written instead of one year of new business Asset Returns: Allow for volatile asset returns, and allocate capital to assets Existing Reserves: Include existing reserves in addition to one year of new business in capital allocation process • Existing Reserves • Clearly can be Very Risky (e.g. Asbestos Reserves) • Driven by many of the same factors as the New Business • Need to address both “How Much” and “How Long” • Especially important for Pricing Long-Term Lines

29. Capital Allocation Based on Capital Allocation Based on New Business and Existing New Business Reserves GL - New GL GL - Res Prop Prop - New Prop - Res AL - New AL AL - Res WC - New WC WC - Res Existing Reserves Distribution of Existing Distribution of Written Premium Reserves 100% Other 90% GL 80% GL 70% 60% Prop 50% Prop 40% 30% AL AL 20% 10% WC WC 0%

30. New Business versus Reserves Existing Reserves • Different Risk Characteristics • New Property Business can be very Risky because of Catastrophe exposure • Largely Eliminated in the Property Reserves • Split by line varies dramatically

31. Workers Comp Property New Business Reserves Existing Reserves Risk Allocation by Line

32. Possible Extensions Using DFA Multiple Years of New Business: Allow multiple years of new business to be written instead of one year of new business Asset Returns: Allow for volatile asset returns, and allocate capital to assets Existing Reserves: Include existing reserves in addition to one year of new business in capital allocation process • Multiple Years of New Business • Companies do not Close at the End of One Year • Some Risks take longer than One Year to Develop (e.g. Pollution)

33. Multiple Years of New Business Other

34. Time Diversification changes Impact of Different Risk Factors Reduces Impact of High Severity Claims (e.g. Property) Increases Impact of Inflation Sensitive Lines (e.g. Workers Comp) Reflects ongoing nature of the company Reflects wider range of Risks faced by Insurance Companies Recognition Delay on Reserves Pricing Risk Multiple Years of New Business • Impact of Expanding the Time Frame

35. Possible Extensions Using DFA Multiple Years of New Business: Allow multiple years of new business to be written instead of one year of new business Asset Returns: Allow for volatile asset returns, and allocate capital to assets Existing Reserves: Include existing reserves in addition to one year of new business in capital allocation process • Asset Returns: • Large Source of Volatility • Becoming even more so with dropping Premium to Surplus ratios and increasing Equity allocations • Correlated to Liabilities because of Inflation Sensitivity

36. Issue: Most allocation methods require a “with” and “without” run What About Assets? • Concern: • What should be done for “without” assets?

37. Two options on the liability side: 1. Don’t write the business New Business only 2. Reinsure the business away “Without” Assets Definition

38. Option #1: Assume some fixed rate of return Advantages: Easy to understand Most similar to the “without” a line “Without” Assets Definition Disadvantages: • What should the fixed rate be? • Can’t be achieved in reality

39. Option #2: Invest everything in lowest risk asset class Advantages: Still relatively simple Achievable alternative “Without” Assets Definition Disadvantages: • Can lead to nonsensical results

40. Held Statutory Surplus . RBC Ratio =. Required Regulatory (Risk-Based) Capital “Without” Assets Definition

41. Option #3: Determine asset allocation that minimizes risk measure Advantages: Eliminates possibility of negative capital allocation “Without” Assets Definition

42. Held Statutory Surplus . RBC Ratio =. Required Regulatory (Risk-Based) Capital “Without” Assets Definition

43. Disadvantages: Much more complex Need a solution for each marginal run Very time consuming, especially for Shapley values “Without” Assets Definition Option #3: Determine asset allocation that minimizes risk measure Advantages: • Eliminates possibility of negative capital allocation

44. Other GL Prop AL WC Assets With Asset Returns 100% Other 90% 80% GL 70% 60% 50% Prop 40% 30% AL 20% 10% WC 0% Without

45. Considers Indirect Impacts of Operations e.g. Taxes: Impact of Realizing Gains/Losses on Balance Sheet depends on prior year Gains and Losses Easier to Consider Multiple Basis for Allocation e.g. Statutory Surplus and RBC Ratio Can Consider More Complex Transactions Multi-Year Aggregate Reinsurance Contingent Equity Other Benefits of Using a DFA Model

46. Shapley Values Z

47. Shapley Value Introduction • The Marginal “Last-In” allocation method used thus far only evaluates the marginal risk addition to the business as a whole. • The Shapley Value allocation method expands on the Marginal “Last-In” concept by considering all possible permutations of entry. • Shapley Value evenly splits the mutual covariance between the “With” and “Without” marginal scenarios.

48. Shapley Value Illustration

49. Shapley Value Illustration

50. Shapley Value Illustration