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. Life, Health, Property and Casualty
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

4. Risk Adjusted Cost of Capital How It Will Be Addressed
Issue
How 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 Our Risks
Vary the Target RORC’s instead of varying the capital amounts (RAROC)
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)

5. Insurer Capital Is A Shared Asset
Asset Owners:
Control Overall Access Rights
Preserve Against Depletion From Over-Use
Shared Asset Reservoir, 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. 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

7. 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
Charge portfolio segments for both uses of Capital

8. Capital Usage Cost Calculation
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

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. Powerful Decision Metric for our Consideration
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. Portfolio Mix Evaluation
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

23. Portfolio Mix Model – Evaluation
Input
Output
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. Net of Financial Market and Reinsurance Hedging1
Cost of Risk
Economic Scenarios
Equity Indices
Yield Curves
FX Rates
Inflation
Unemployment
Financial Market
Hedging 2
Market Capacity
Insurer Asset
Portfolio
Other Connections? 3
Investment Result
Insurer New Exposure
Price Levels
Reserves
Insurance UW
Portfolio
Operating Result
Net Income
Distribution 4
Net of Financial Market and Reinsurance Hedging
Reinsurance Market
Hedging

27. Systematic Risk in an Insurance IRM 1. 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 IRM 2. 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 IRM 3. 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 IRM 4. 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