Insurance Capital As A Shared Asset – Theory and Practice

Insurance Capital As A Shared Asset – Theory and PracticeDon MangoDirector of R&D, GE Insurance SolutionsCAS Vice President, Research and Development

2005 CARE Seminar

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 NOTICEThe 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.


Theory


Risk Adjusted Cost of CapitalIssue 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

Shared AssetReservoir, 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


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 Ways1. “Rental” Or Non-Consumptive

Returns Meet Or Exceed Expectation

Capacity Is Occupied, Then Returned Undamaged

A.k.a. Room Occupancy

2. Consumptive Results DeteriorateReserve

Strengthening Is Required

A.k.a. Destroy Your Room, Your Floor, Or Even The Entire Hotel

Charge portfolio segments for both uses of Capital


Two Kinds Of Charges:1. Rental = Access fee for LOC

Function of Capacity Usage (i.e., S&P 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


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: Calculation1. Downside = Max(Simulated Loss > Expected

Loss, 0)2. Capital rental charge (access fee)

(Ex: 10% of allocated capital with adj for reserve factor)

3. Charge for damage within your allocation (drawdown on allocated capital)(Ex: 120% of underwriting result)

4. 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 CostTrial 1: +$2M $5M*10% = $500KTrial 2: -$3M $500K + $3M*120% =

$4,100KTrial 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 TailExample 1Property Catastrophe Contract

Comments(1) Premium 1,000,000$ (2) Limit 10,000,000$

Capacity Occupation Cost(3) Required Capital Factor 35.0% Rating Agency(4) Required Capital (RC) 350,000$ = (3) * (1)(5) Opportunity Cost for Capacity 10.0% r Opp(6) Capacity Occupation Fee 35,000$ = (4) * (5)

Capital Call Cost(7) Probability 2.0%(8) Loss 10,000,000$ Full limit loss(9) Capital Consumption Amount 9,000,000$ = (8) - (1)

(9a) Amount Within RC 350,000$ = min[ (4) , (9) ](9b) Amount Beyond RC 8,650,000$ = (9) - (9a)(10) Consumption Charge Within RC 120.0%(11) Within RC Consumption Cost 420,000$ = (10) * (9a)(12) Consumption Charge Beyond RC 240.0%(13) Beyond RC Consumption Cost 20,760,000$ = (12) * (9b)(14) Total Consumption Cost 21,180,000$ = (11) + (13)(15) Expected Consumption Cost 423,600$ = (14) * (7)

EVA(16) Expected NPV 800,000$ = (1) - (7) * (8)(17) Expected Capital Usage Cost 458,600$ = (6) + (15)(18) EVA 341,400$ = (16) - (17)


Pricing Demo – Long TailExample 2Longer Tail Excess of Loss Contract

Comments(1) Premium 1,000,000$ (2) Limit 10,000,000$

Capacity Occupation Cost(3) Required Capital Factor - Premium 35.0% Rating Agency

(3a) Required Capital Factor - Reserves 25.0% Rating Agency(3b) Reserve Amount 156,705$ (3c) Reserve Duration 5.00 Years

(4) Required Capital 545,882$ = (3) * (1) + (3a) * (3b) * (3c)(5) Opportunity Cost for Capacity 5.0% r Opp(6) Capacity Occupation Fee 27,294$ = (4) * (5)

Capital Call Cost(7) Probability 2.0%(8) Loss (NPV @ 5%) 7,835,262$ Full limit loss, discounted(9) Capital Consumption Amount 6,835,262$ = (8) - (1)




Pricing Demo – Long Tail @ Same EVAExample 2a

Longer Tail with Same EVA as Short TailComments

(1) Premium 846,367$ (2) Limit 10,000,000$

Capacity Occupation Cost(3) Required Capital Factor - Premium 35.0% Rating Agency

(3a) Required Capital Factor - Reserves 25.0% Rating Agency(3b) Reserve Amount 156,705$ (3c) Reserve Duration 5.00 Years

(4) Required Capital 492,110$ = (3) * (1) + (3a) * (3b) * (3c)(5) Opportunity Cost for Capacity 5.0% r Opp(6) Capacity Occupation Fee 24,605$ = (4) * (5)

Capital Call Cost(7) Probability 2.0%(8) Loss (NPV @ 5%) 7,835,262$ Full limit loss, discounted(9) Capital Consumption Amount 6,988,895$ = (8) - (1)




Demo Model


Demo Model1) Loss Distributions

LOB 1 LOB 2 LOB 3 TOTALLog Normal Mu 13.771 13.691 13.571

Log Normal Sigma 30.0% 50.0% 70.0%Expected Loss 1,000,000 1,000,000 1,000,000 3,000,000

Profit Margin 10.0% 10.0% 10.0%Premium 1,111,111 1,111,111 1,111,111 3,333,333 Return $ 111,111 111,111 111,111 333,333

3) Capital Usage CalculationLOB 1 LOB 2 LOB 3

Required Capital Charge on Premium 40.0% 40.0% 40.0%Capital Usage Charge Adj Factor Due to Reserves 100.0% 100.0% 100.0%

(A) Rental Fee 10.0%(B) Consumption Charge Within Required Capital 120.0% 12.00

(C) Consumption Charge Beyond Required Capital 240.0% 24.00 Required Premium Capital 500,000 500,000 500,000


Economic Value Added or EVA

EVA = Return – Cost of Capital UsageFactors 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

4) Portfolio Evaluation MetricsLOB 1 LOB 2 LOB 3 TOTAL

Premium 1,250,000 1,250,000 1,250,000 3,750,000 Required Capital 205,950 433,748 860,302 1,500,000

Return 112,500 100,000 87,500 300,000 Expected Capital Usage $ Cost 94,265 198,531 393,768 686,564

EVA $ 18,235 (98,531) (306,268) (386,564) Usage Cost as % of Capital 45.8% 45.8% 45.8% 45.8%

Rental Fee 10.0% 10.0% 10.0% 10.0%Consumption Charge 35.8% 35.8% 35.8% 35.8%

Prob of Exceeding Required Capital 27.0% 15.0% 15.0% 9.0%

4) Portfolio Evaluation MetricsLOB 1 LOB 2 LOB 3 TOTAL

Premium 1,250,000 1,250,000 1,250,000 3,750,000 Required Capital 500,000 500,000 500,000 1,500,000

Return 112,500 100,000 87,500 300,000 Expected Capital Usage $ Cost 110,714 213,850 362,000 686,564

EVA $ 1,786 (113,850) (274,500) (386,564) Usage Cost as % of Capital 22.1% 42.8% 72.4% 45.8%

Rental Fee 10.0% 10.0% 10.0% 10.0%Consumption Charge 12.1% 32.8% 62.4% 35.8%

Prob of Exceeding Required Capital 5.0% 15.0% 17.0% 9.0%


Portfolio Mix Evaluation and Optimization


Calibrate Total Capital Usage Cost to X% of Required CapitalCan control emphasis of the RAROC formula:Capacity-focused: Majority of Usage Cost comes from Capacity ChargesVolatility-focused: Majority of Usage Cost comes from Volatility ChargesBalanced: 50% from each

Portfolio Mix Evaluation


Portfolio Mix Model – Evaluation

Portfolio Mix:Premium, Loss Ratio,

Commission, Overhead

Input

Required Capital Factors:Premium And Reserves

Capital Usage Cost Factors:

Rental And Consumption

Alternative Mix Evaluati

on

Output

Portfolio EVA

Portfolio Capital Usage

Cost

Marginal Comparisons With

Other Mixes:-Required Premium Capital By

Segment- Capital Usage Cost % By

Segment

Perfect For “What-If” Analyses

Portfolio DVS


Portfolio Mix Model – Optimization

Portfolio Mix:Premium, Loss Ratio,

Commission, Overhead

Input

Required Capital Factors:

Premium and Reserves

Capital Usage Cost Factors:

Rental and Consumption

Mix Evaluation

Output

EVA

Risk-Adjusted Required TM by

Segment

Marginal Comparisons with

Other Mixes

Segment Premium

Constraints

Optimizer Target:

E.g., Maximize EVA

Max Required Capital

Constraint

Optimizer Evaluates

Thousands Of Alternative

MixesEvaluation

Metrics For

Optimal Mix:

-EVA- DVS

- Capital Usage CostMarginal

Comparison With

Starting Mix

“Optimal” Portfolio Mix Given Constraint

s

Perfect For Strategic Directional Analysis

Optimizer Inputs

Optimizer

Output


At Least One Trent Vaughn Critique Addressed:

RMK Can Reflect Systematic Risk


Insurer New Exposure Price Levels Reserves

Cost of Risk

Market Capacity

Financial MarketHedging

Investment Result

Operating ResultInsurance UW

Portfolio

Reinsurance MarketHedging

Net IncomeDistribution

Other Connections?

1

4

3

Insurer AssetPortfolio

Economic Scenarios

Equity Indices Yield Curves

FX Rates Inflation

Unemployment

2

Net of Financial Market and Reinsurance

Hedging


Systematic Risk in an Insurance IRM1. Cost of Risk


Cost of Risk

Market Capacity


Investment Result


Portfolio



Other Connections?

1

4

3


Economic Scenarios


FX Rates Inflation

Unemployment

Economic Scenarios


FX Rates Inflation

Unemployment

2

Net of Financial Market and Reinsurance Hedging

•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 IRM2. Market Capacity


Cost of Risk

Market Capacity


Investment Result


Portfolio



Other Connections?

1

4

3


Economic Scenarios


FX Rates Inflation

Unemployment

Economic Scenarios


FX Rates Inflation

Unemployment

2


•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 IRM3. Other Connections


Cost of Risk

Market Capacity


Investment Result


Portfolio



Other Connections?

1

4

3


Economic Scenarios


FX Rates Inflation

Unemployment

Economic Scenarios


FX Rates Inflation

Unemployment

2


•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 IRM4. Net Income Distribution


Cost of Risk

Market Capacity


Investment Result


Portfolio



Other Connections?

1

4

3


Economic Scenarios


FX Rates Inflation

Unemployment

Economic Scenarios


FX Rates Inflation

Unemployment

2


•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 [email protected]

mailto:[email protected]

Insurance Capital As A Shared Asset – Theory and Practice

Documents

Transcript of Insurance Capital As A Shared Asset – Theory and Practice