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

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Theory

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)

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

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

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

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

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”

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)

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

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

Examples

Pricing Demo – Short Tail

Pricing Demo – Long Tail

Pricing Demo – Long Tail @ Same EVA

Demo Model

Demo Model

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

Demo Model – RAROC vs RORAC

Portfolio Mix Evaluation and Optimization

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

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

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

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

Net of Financial Market and Reinsurance Hedging 1 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

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

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

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?

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

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