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DFA and Reinsurance Structuring Presented by Joseph W. Wallen, FCAS General Re Capital Consultants CAS Ratemaking Seminar March 9-10, 2000. General Reinsurance. Topics. I. How Are We Using DFA? II. Using DFA to Evaluate Reinsurance Structure III. Reinsurance Applications
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DFA and Reinsurance Structuring Presented by Joseph W. Wallen, FCAS General Re Capital Consultants CAS Ratemaking Seminar March 9-10, 2000 General Reinsurance
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
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
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
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
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
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
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
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
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
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%
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
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)
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
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
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
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
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
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
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
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
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