Insurance Capital As A Shared Asset – Theory and Practice

1. Insurance Capital As A Shared Asset – Theory and Practice Don Mango Director of R&D, GE Insurance Solutions CAS Vice President, Research and Development 2005 CARE Seminar

2. GE Insurance Solutions protects people, property and reputations. With over $50bn in combined assets, the GE Insurance Solutions group of companies is one of the world’s leading providers of commercial insurance, reinsurance and risk management services. Life, Health, Property and Casualty PROPRIETARY INFORMATION NOTICE The information contained in this document is the property of Employers Reinsurance Corporation, a member of the GE Insurance Solutions group of companies. It should not be reprinted, redistributed or disclosed to others without the express written consent of ERC.

3. Theory

5. Insurer Capital Is A Shared Asset • Asset Owners: • Control Overall Access Rights • Preserve Against Depletion From Over-Use Shared AssetReservoir, Golf Course,Pasture, Hotel, … Insurer Capital User 1 User 4 • Consumes On Standalone Basis • Tunnel Vision - No Awareness Of The Whole • Consumes On Standalone Basis • Tunnel Vision - No Awareness Of The Whole User 2 User 3

6. Consumptive Use Example: RESERVOIR Permanent Transfer To The User Non-Consumptive Use Example: GOLF COURSE Temporary Grant Of Partial Control To User For A Period Of Time Shared Assets Can Be Used Two Different Ways • Both Consumptive and Non-Consumptive Use • Example: HOTEL • Temporary Grant Of Room For A Period Of Time • Guest could destroy room or entire wing of hotel, which is Permanent Capacity Consumption

7. 1. “Rental” Or Non-Consumptive Returns Meet Or Exceed Expectation Capacity Is Occupied, Then Returned Undamaged A.k.a. Room Occupancy 2. Consumptive Results Deteriorate Reserve Strengthening Is Required A.k.a. Destroy Your Room, Your Floor, Or Even The Entire Hotel An Insurer Uses Its Capital Both Ways Charge portfolio segments for both uses of Capital

8. Two Kinds Of Charges: Rental= Access fee for LOC Function of Capacity Usage (i.e., S&P Required Capital) Opportunity Cost of Occupying Capacity Consumption = Drawdown fee for LOC Function of Downside Potential (i.e., IRM Input Distributions) Opportunity Cost of Destroying Future Capacity Capital Usage Cost Calculation

9. Why Two Levels of Consumption Fee? • If we treat all downsides as equivalent, we would charge them X% regardless if -$1 or -$100M. • But there should be a "kurtosis penalty" -- penalty for heavy tails. • We could introduce it with a fancy downside transform or Wang transform. • Rating Agency Required Capital is a convenient means to introduce a tail penalty. • Supporting organizational argument: Rating Agency Required Capital is calculated at any level of detail • Penalty for exceeding your allocation ~ additional charge for “destroying other rooms”

10. Capital Usage Charges: Calculation • Downside = Max(Simulated Loss > Expected Loss, 0) • Capital rental charge (access fee)(Ex: 10% of allocated capital with adj for reserve factor) • Charge for damage within your allocation (drawdown on allocated capital)(Ex: 120% of underwriting result) • Charge for damage beyond your allocation (drawdown of other segments’ capital)(Ex: 240% of u/w result beyond capital allocation)

11. Capital Usage Charge Calculation Example • Charges: (A) Rental = 10%(B) Within Capital = 120% (C) Beyond Capital = 240% • Required Capital = $5M • Loss – Exp Loss Capital Usage Cost • Trial 1: +$2M $5M*10% = $500K • Trial 2: -$3M $500K + $3M*120% = $4,100K • Trial 3: -$8M $500K + $5M*120% + $3M*240% = $13,700K • Steepness of penalty depends on relative difference between (B) Within Capital and (C) Beyond Capital charges

12. Why is Downside Based on Loss Only? • Sticking to the facts: • Earn premium, set up reserve = EP*Plan LR. • Remainder after expenses (if any) goes to underwriting profit that year. • For a LOB with any tail, reserve deterioration beyond Plan LR occurs in future years, and therefore must be funded from future capital. • LOB profit shows up not in reducing the capital usage cost but in increasing the EVA, or in comparisons of actual TM versus required TM. • Another advantage: avoids recursion in determining required TM

13. Examples

14. Pricing Demo – Short Tail

15. Pricing Demo – Long Tail

16. Pricing Demo – Long Tail @ Same EVA

17. Demo Model

18. Demo Model

19. Economic Value Added or EVA • EVA = Return – Cost of Capital Usage • Factors in: • Capacity Usage (finite supply, driven by external capital requirements) • Company Risk Appetite • Product Volatility • Correlation of Product with Portfolio Powerful Decision Metric for our Consideration

20. Demo Model – RAROC vs RORAC

21. Portfolio Mix Evaluation and Optimization

22. Calibrate Total Capital Usage Cost to X% of Required Capital Can control emphasis of the RAROC formula: Capacity-focused: Majority of Usage Cost comes from Capacity Charges Volatility-focused: Majority of Usage Cost comes from Volatility Charges Balanced: 50% from each Portfolio Mix Evaluation

23. Portfolio Mix Model – Evaluation Output Input Portfolio Mix: Premium, Loss Ratio, Commission, Overhead Portfolio EVA Alternative Mix Evaluation Portfolio Capital Usage Cost Required Capital Factors: Premium And Reserves Portfolio DVS Capital Usage Cost Factors: Rental And Consumption • Marginal Comparisons With Other Mixes: • Required Premium Capital By Segment • Capital Usage Cost % By Segment Perfect For “What-If” Analyses

24. Portfolio Mix Model – Optimization Optimizer Inputs Optimizer Output Optimizer Evaluates Thousands Of Alternative Mixes “Optimal” Portfolio Mix Given Constraints Segment Premium Constraints • Evaluation Metrics For Optimal Mix: • EVA • DVS • Capital Usage Cost Optimizer Target: E.g., Maximize EVA Max Required Capital Constraint Marginal Comparison With Starting Mix Perfect For Strategic Directional Analysis

25. At Least One Trent Vaughn Critique Addressed: • RMK Can Reflect Systematic Risk

26. Economic Scenarios Equity Indices Yield Curves FX Rates Inflation Unemployment 1 Cost of Risk Financial Market Hedging 2 Market Capacity Insurer Asset Portfolio 3 Other Connections? Investment Result Insurer New Exposure Price Levels Reserves Insurance UW Portfolio Net Income Distribution Operating Result 4 Net of Financial Market and Reinsurance Hedging Reinsurance Market Hedging

27. Systematic Risk in an Insurance IRM1. Cost of Risk • Market price for absorbing Downside potential • Function of risk appetite • Fluctuates widely over time • Consistent across traded and untraded, complete and incomplete • Van Slyke, Wang, CAPM

28. Systematic Risk in an Insurance IRM2. Market Capacity • Function of insurance sector performance, correlation with market, level of pricing cycle, etc. • Impacts price attainable in market by increasing apparent aggregate risk appetite (demand) • Needs further research

29. Systematic Risk in an Insurance IRM3. Other Connections • How are insurance portfolio operating results related to economic variables? • How much of that variance is explainable by movements in these macro variables? • Are there financial market hedging instruments (existing or new) that could reduce this risk?

30. Systematic Risk in an Insurance IRM4. Net Income Distribution • Theory: insurance prices should only compensate for systematic risk • Whatever portion of insurance risk is hedgeable by financial market instruments should be eliminated from the Net Income Distribution • If it remains in the Net Distribution, it should result in a Risk Premium

31. Thank you for your attention This material has been submitted to both PCAS and ASTIN Bulletin Copies of working paper, presentations, and demo model available from Don.Mango@GE.com