DFA and Reinsurance Structuring Presented by Joseph W. Wallen, FCAS General Re Capital Consultants

1. DFA and Reinsurance Structuring Presented by Joseph W. Wallen, FCAS General Re Capital Consultants CAS Ratemaking Seminar March 9-10, 2000 General Reinsurance

2. Topics • I. How Are We Using DFA? • II. Using DFA to Evaluate Reinsurance Structure • III. Reinsurance Applications • The Business Manager’s View • The CFO’s View IV. Conclusion

3. How Are We Using DFA?

4. How Do We Use DFA Models for Clients in the Reinsurance Context? • As business consultants to our clients we use DFA to: • Evaluate appropriate retentions • Evaluate and choose “optimal” reinsurance structures • Independent appraisal of different reinsurance proposals • As a part of the General Re team we use DFA to: • Design effective reinsurance programs for reinsurance clients • Help General Re model the underwriting risk it is taking • e.g., mix of business questions

5. Why Use DFA to Evaluate Reinsurance Structure? • Traditionally evaluated using intuition/rules of thumb • Retentions as a percent of PHS • Assumptions about riskiness of certain lines/layers • DFA Can: • Confirm traditional rules of thumb • Add quantitative analysis to the process • Expand the evaluation criteria to include other items • e.g. asset allocation issues • Incorporate additional factors • Between line correlations/diversification • Asset/Liability correlations

6. Using DFA to Evaluate Reinsurance Structure

7. Steps Involved in Evaluating Reinsurance Structures Determine Risk/Return Metrics Decompose AY Risk Into Line/Layer Additional Considerations Generate R/I Opportunity Set and Generate DFA Output Evaluate DFA Output versus Risk/Return Metrics

8. What Are Some Steps in Evaluating Reinsurance Structure? • Step 1 - Determine Management Objectives for Reinsurance • Depends on who answers the question • Business Unit/Underwriting Manager • Incentive compensation based • Possibly based on U/W Income or Combined Ratio • Other qualitative issues • CFO • Enterprise decisions • Public vs. Mutual company issues • More focused on balance sheet/income statement • Capital adequacy

9. What Are the Steps in Evaluating Reinsurance Structure? • Step 2 - Determine Appropriate Metrics and Constraints • How do they measure risk? • Uncertainty (e.g. Standard Deviation) • Loss (e.g., Value at Risk or Surplus Decline) • Mean Excess Loss • What return metric is used to evaluate reinsurance? • Don’t pre-suppose one correct method • Different business models • Loss Ratios/Combined Ratios • Accident Year/Calendar Year • Book Income • Total Return • Earnings Per Share

10. What Are the Steps in Evaluating Reinsurance Structure? • Step 3 - Decompose Accident Year results by Line/Layer • Reinsurance generally starts with impact on Accident Year • Additional impact on other items • Investment Income • Reserves • Examine how U/W results covary with Lines/Layers • Will indicate where the u/w risk is • Might lead to the relative value of reinsured lines/ layers • Still need to evaluate in the context of DFA Model

11. What Are the Steps in Evaluating Reinsurance Structure? • Step 4 - Create Set of Reinsurance Choices • Need to be reasonable and defined • Unlike asset allocation issues • Generally looking at discrete choices • Based on examination of losses by layer in previous step • Evaluate where reinsurance dollars are best allocated

12. What Are the Steps in Evaluating Reinsurance Structure? • Step 5 - Evaluate Alternative Reinsurance Structures Using the DFA Model • Based on original risk/return metrics • Need to consider additional evaluation criteria outside the DFA Model • claims • underwriting • financial strength • production of business

13. The Underwriting Manager’s Perspective

14. Examples of Evaluating Reinsurance Structure • Example 1 - The Underwriting Manager’s Perspective • Senior management mandates: • Target 95% Combined Ratio • Maximize underwriting profit dollars • Measure on an annual basis for accident year • Manager’s objectives: • Grow business • Maximize bonus • Minimize underwriting “risk” • Probability of CR > 105%, < 5%

15. Evaluating Reinsurance Structure • Within the DFA Model • Capture information for all underwriting accounts • Look at losses by potential reinsurance layer • Should include correlations between lines • Decompose accident year underwriting risk by line/layer • Identify areas of greatest “risk” • Normalize for expected ceded profit • Select line/layer combinations of cessions to design program • Compare resulting program to risk/return metrics

16. Where is the underwriting risk?

17. Where is the underwriting risk?

18. Where is the underwriting risk? Covariance of Layer Loss with U/W Profit Line Layer CAL GL PPAL APD Grand Total 250 xs 0 (5,056,680) (1,451,143) (166,236) (390,639) (7,117,259) 250 xs 250 (1,259,468) (454,840) (6,391) 0 (1,720,699) 500 xs 500 (1,268,704) (579,009) 0 0 (1,847,713) 4 xs 1 (568,757) (805,518) 0 0 (1,374,275) Total (8,153,609) (3,290,510) (172,627) (390,639) (12,059,946)

19. Where is the underwriting risk? Ratio of Covariance to Ceded Profit Dollars Line Layer CAL GL PPAL APD Grand Total 1,009 3,823 250 xs 0 5,360 5,177 662 - 7,627 250 xs 250 8,041 7,162 3,908 500 xs 500 7,179 7,849 - - 7,234 4 xs 1 9,811 19,076 - - 15,455

20. Evaluating Reinsurance Based on Risk Metrics Combined Ratio - Worst 25% of Outcomes 115.0% 113.0% 111.0% 109.0% Combined Ratio 107.0% 105.0% 103.0% 101.0% 99.0% 75% 77% 79% 81% 83% 85% 87% 89% 91% 93% 95% 97% 99% Percentile Gross Business 1M Retn 250k Retn 500k Retn

21. Underwriting Manager’s Perspective • Based on these criteria manager may choose an across the board 500k retention • Meets Combined Ratio tolerance • Cedes approximately 350k annual nominal u/w profit • Also need to examine on an economic basis • Will increase ceded profits • Ignores further diversification benefits on balance sheet • Assets and Underwriting not perfectly correlated • There may be additional natural hedges against income uncertainty • For example: • Ceding a layer/line negatively correlated with assets may increase income risk

22. Optimization Results - Efficient Frontier • Can construct an “efficient frontier” of retentions by line or unit • Currently done in a brute force fashion via simulations • Requires us to be restrictive in developing our opportunity set • Provides a useful framework for evaluating risk/return tradeoff of retention as it impacts the underwriting account

23. Reinsurance from the CFO’s Perspective

24. Examples of Evaluating Reinsurance Structure • Example 2 - The CFO’s Perspective • Goal for reinsurance is to: • Reduce likelihood of missing EPS by > $0.50/share • Minimize probability of 10% PHS Loss • Maximize profit/ROE • Generally want to minimize reinsurance use • Subject to earnings volatility constraints

25. Evaluating Reinsurance Structure at the Enterprise Level • Other factors beyond AY underwriting results • Asset category risk and return • Reserve runoff • Correlations between Liabilities and Assets • Similar process to the Underwriting Manager’s perspective • Consider U/W contribution to income/ROE/Capital risk • Reinsurance only affects a portion of risk components

26. Where is the return risk?

27. Impact of Reinsurance on EPS • Traditional Excess of Loss Reinsurance: • Has minimal impact on EPS downside risk except at tails • Diversification of earnings stream • Leads to use of stop loss if available

28. Impact of Reinsurance on Likelihood of PHS Decline • Unlike EPS protection this metric shows real value: • Choice depends on risk tolerance • Places more value on Excess of Loss

29. Conclusion

30. DFA and Reinsurance Structure • DFA can be useful in evaluating reinsurance • Identifies areas of risk from underwriting that might benefit from reinsurance • Indicates potential value of reinsurance as it impacts: • Accident Year results • Balance Sheet/Earnings • A tool to evaluate potential structures • Exploring alternatives such as: • Underwriting risk versus asset risk • Using reinsurance to change mix of risk across balance sheet

31. Thank You.