1. RCM-1: Current Research on Risk and Return Methodologies in Ratemaking Donald Mango, FCAS, MAAA Director of R&D, GE Insurance Solutions March 10, 2005

2. © 2005 Employers Reinsurance Corporation 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. © 2005 Employers Reinsurance Corporation Agenda Application of Myers-Read Merton-Perold Latest from COTOR VALCON Insurance Capital As A Shared Asset Q&A

4. © 2005 Employers Reinsurance Corporation Application of Myers-Read

5. © 2005 Employers Reinsurance Corporation Myers-Read in Simulation Ruhm-Mango-Kreps (RMK) Example: 2 independent normal risks: >Risk A:μ = 100, σ = 30 >Risk B: μ = 200, σ = 40 >Total: μ = 300, σ = 50 > Capital = 2σ  97.725 %ile ruin level

6. © 2005 Employers Reinsurance Corporation Myers-Read in Simulation 1) Simulate the variables, sum them to get total portfolio. In example, 10K iterations. 2) Sort by total portfolio result. 3) Take a small sample of iterations on either side of the “ruin point”: These receive weight = 1, all others receive weight = 0. 4) Take weighted averages of each variable to get “funding” amounts. Subtract expected values to get capital allocation.

7. © 2005 Employers Reinsurance Corporation

8. Merton-Perold

9. © 2005 Employers Reinsurance Corporation Merton-Perold – Summary Capital allocation to segments is meaningless Capital is held at the company level Each segment receives a guarantee from the parent company Price of guarantee could be observable in market Cost of guarantee represents risk capital Opposed to allocation exercises: >Guarantee only has meaning at company level >Order dependence

10. © 2005 Employers Reinsurance Corporation Venter: Charge Capital Cost against Profits Instead of return rate, subtract cost of capital from unit profitability Use true marginal capital costs of business being evaluated, instead of an allocation of entire firm capital >If evaluating growing the business 10%, charge the cost of the capital needed for that much growth >If evaluating stopping writing in a line, use the capital that the company would save by eliminating that line This maintains financial principle of comparing profits to marginal costs

11. © 2005 Employers Reinsurance Corporation Venter: Calculating Marginal Capital Costs Could use change in overall risk measure of firm that results from the marginal business – but requires selection of the overall risk measure Or could set capital cost of a business segment as the value of the financial guarantee the firm provides to the clients of the business segment >This could be called capital consumption (stay tuned)

12. © 2005 Employers Reinsurance Corporation Venter: Value of Financial Guarantee Cost of capital for subsidiary is a difference between two put options: >1. The cost of the guarantee provided by the corporation to cover any losses of the subsidiary >2. The cost to the clients of the subsidiary in the event of the bankruptcy of the corporation Economic value added of the subsidiary is value of profit less cost of capital >Value of profit is contingent value of profit stream if positive A pricing method for heavy-tailed contingent claims would be needed (stay tuned)

13. © 2005 Employers Reinsurance Corporation Latest from COTOR VALCON

14. © 2005 Employers Reinsurance Corporation Latest from COTOR VALCON LiabEx (Todd Bault) Old Lloyd's, only more high tech. Insurance buyers (Buyers), capital providers (Names), and the market, which will also act as the liability principal (LiabEx). > Names have been cleared for suitability. Insurance policy comes to market. Names look at the contract, set the initial premium that the buyer will pay. Names are putting up ZERO capital to get their profit load. LiabEx sets margin requirement. THIS is capital, and LiabEx will charge the Names' margin interest to pay for LiabEx's cost of capital. But LiabEx has a very different cost of capital than for the insurance risk--LiabEx is ONLY worried about default by Names. Profit is a function of bearing risk, and "capital" is not necessarily needed. In fact, this framework handles instantaneous risks just fine

15. © 2005 Employers Reinsurance Corporation Latest from COTOR VALCON LiabEx (Todd Bault) Margin requirements for liabilities would be much higher than for short transactions in equities. LiabEx would have to have some liability assessment techniques, faces considerable parameter risk, and would need to be paid for this. (Sounds like Venter) Those who bear the default risk NEED capital, and that capital has a cost. That capital also has a time element, and margin interest captures that. In the real world, insurers are collecting BOTH loads, since they have part of the principal function (or rather, are forced to by rating agencies on behalf of their shareholders).

16. © 2005 Employers Reinsurance Corporation Latest from COTOR VALCON Capacity (Glenn and Don Agree!) i.Desired counterparty rating  implied minimum capital adequacy ratio (CAR) = Actual Capital / Required Capital ii.Given a minimum CAR and Actual Capital, a Maximum Required Capital falls out. iii.Required Capital is a function of (a) assets, (b) reserves, and (c) written premiums iv.For planning purposes, (a) and (b) are ~ fixed. So really facing Maximum Premium Required Capital.

17. © 2005 Employers Reinsurance Corporation Latest from COTOR VALCON Capacity (Glenn and Don Agree!) v.More precisely, allowable portfolio mixes can generate no more than the Maximum Premium Required Capital. This represents a measure of underwriting capacity. vi.Generic axiom: “The more risk (net of all hedging) an insurer takes on in new underwriting, the more underwriting capacity it uses.” vii.More restrictive axiom: "If an insurer is at its max CAR, and wants to take on additional new business, and cannot reduce Required Capital via hedging (reduction or transfer), nor tolerate a lower CAR and possibly a rating downgrade, then it must raise additional capital."

18. © 2005 Employers Reinsurance Corporation Insurance Capital As A Shared Asset

19. © 2005 Employers Reinsurance Corporation Risk Adjusted Cost of Capital IssueHow It Will Be Addressed Rating Agency Required Capital is a Binding Constraint Use Rating Agency Required Capital formula everywhere But Rating Agency Capital Charges do not Reflect My Risks Vary the Target RORC’s instead of varying the capital amounts (RAROC instead of RORAC) Total Capital is really a Shared Asset simultaneously exposed by all P&L’s Capital Usage Cost formula works as if Finance grants the P&L’s Letters of Credit:  Assess a capacity charge (like an access fee), and  A volatility charge (like a draw down of the LOC) “A pricing method for heavy-tailed contingent claims would be needed”

20. © 2005 Employers Reinsurance Corporation Insurer Capital Is A Shared Asset Shared Asset Reservoir, Golf Course, Pasture, Hotel, … Insurer Capital User 1 User 2 User 3 User 4 Asset Owners: Control Overall Access Rights Preserve Against Depletion From Over-Use Consumes On Standalone Basis Tunnel Vision - No Awareness Of The Whole Consumes On Standalone Basis Tunnel Vision - No Awareness Of The Whole

21. © 2005 Employers Reinsurance Corporation Shared Assets Can Be Used Two Different Ways 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 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

22. © 2005 Employers Reinsurance Corporation An Insurer Uses Its Capital Both Ways 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

23. © 2005 Employers Reinsurance Corporation Two Kinds Of Charges: 1.Rental = Access fee for LOC  Function of Capacity Usage (i.e., Rating Agency Required Capital)  Opportunity Cost of Occupying Capacity 2.Consumption = Drawdown fee for LOC  Function of Downside Potential (i.e., IRM Input Distributions)  Opportunity Cost of Destroying Future Capacity Capital Usage Cost Calculation

24. © 2005 Employers Reinsurance Corporation Economic Value Added or EVA EVA = Return – Cost of Capital Usage Factors in: >Capacity Usage >Company Risk Appetite >Product Volatility >Correlation of Product with Portfolio

25. © 2005 Employers Reinsurance Corporation Reconciliation of Meyers and Mango Comes down to RAROC or RORAC >RAROC: vary the returns >RORAC: vary the capital amounts >Both end up with the product of return and capital Depends on your emphasis Similar to Bingham: >Price for Risk (RAROC) >Leverage for Return (RORAC) See Excel Example

26. © 2005 Employers Reinsurance Corporation Advantages of RAROC Use simple, additive, externally-mandated required capital formulas Transparent, high degree of buy-in, works like a budget Guarantee reconciliation with external capital requirement Explicit, objective expression of risk appetite and emphasis Venter: explicit pricing method for heavy-tailed contingent claims Seamless fit with Economic Value Added (EVA) – in fact, may be cleaner than economic capital allocation approaches Consistent with Morgan Stanley approach (Charles Monet)

27. © 2005 Employers Reinsurance Corporation Thank you Q&A For More Information: don.mango@ge.com