Upload
len-horn
View
20
Download
0
Tags:
Embed Size (px)
DESCRIPTION
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. - PowerPoint PPT Presentation
Citation preview
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.
4 © 2005 Employers Reinsurance Corporation
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)
5 © 2005 Employers Reinsurance Corporation
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
6 © 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
7 © 2005 Employers Reinsurance Corporation
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
8 © 2005 Employers Reinsurance Corporation
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
9 © 2005 Employers Reinsurance Corporation
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 © 2005 Employers Reinsurance Corporation
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)
11 © 2005 Employers Reinsurance Corporation
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% = $13,700K
Steepness of penalty depends on relative difference between (B) Within Capital and (C) Beyond Capital charges
12 © 2005 Employers Reinsurance Corporation
Why is Downside Based on Loss Only?Sticking to the facts:>Earn premium, set up reserve = EP*Plan LR.>Remainder after expenses (if any) goes to
underwriting profit that year. For a LOB with any tail, reserve deterioration beyond Plan LR occurs in future years, and therefore must be funded from future capital.LOB profit shows up not in reducing the capital usage cost but in increasing the EVA, or in comparisons of actual TM versus required TM.Another advantage: avoids recursion in determining required TM
14 © 2005 Employers Reinsurance Corporation
Pricing Demo – Short TailExample 1Property Catastrophe Contract
Comments(1) Premium 1,000,000$ (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)
15 © 2005 Employers Reinsurance Corporation
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)
(9a) Amount Within RC 545,882$ = min[ (4) , (9) ](9b) Amount Beyond RC 6,289,380$ = (9) - (9a)(10) Consumption Charge Within RC 120.0%(11) Within RC Consumption Cost 655,058$ = (10) * (9a)(12) Consumption Charge Beyond RC 240.0%(13) Beyond RC Consumption Cost 15,094,512$ = (12) * (9b)(14) Total Consumption Cost 15,749,570$ = (11) + (13)(15) Expected Consumption Cost 314,991$ = (14) * (7)
EVA(16) Expected NPV 843,295$ = (1) - (7) * (8)(17) Expected Capital Usage Cost 342,285$ = (6) + (15)(18) EVA 501,009$ = (16) - (17)
16 © 2005 Employers Reinsurance Corporation
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)
(9a) Amount Within RC 492,110$ = min[ (4) , (9) ](9b) Amount Beyond RC 6,496,785$ = (9) - (9a)(10) Consumption Charge Within RC 120.0%(11) Within RC Consumption Cost 590,532$ = (10) * (9a)(12) Consumption Charge Beyond RC 240.0%(13) Beyond RC Consumption Cost 15,592,283$ = (12) * (9b)(14) Total Consumption Cost 16,182,815$ = (11) + (13)(15) Expected Consumption Cost 323,656$ = (14) * (7)
EVA(16) Expected NPV 689,662$ = (1) - (7) * (8)(17) Expected Capital Usage Cost 348,262$ = (6) + (15)(18) EVA 341,400$ = (16) - (17)
18 © 2005 Employers Reinsurance Corporation
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
19 © 2005 Employers Reinsurance Corporation
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
20 © 2005 Employers Reinsurance Corporation
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%
22 © 2005 Employers Reinsurance Corporation
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
23 © 2005 Employers Reinsurance Corporation
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
24 © 2005 Employers Reinsurance Corporation
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
25 © 2005 Employers Reinsurance Corporation
At Least One Trent Vaughn Critique Addressed:
RMK Can Reflect Systematic Risk
26 © 2005 Employers Reinsurance Corporation
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
27 © 2005 Employers Reinsurance Corporation
Systematic Risk in an Insurance IRM1. Cost of 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
Economic Scenarios
Equity Indices Yield Curves
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
28 © 2005 Employers Reinsurance Corporation
Systematic Risk in an Insurance IRM2. Market Capacity
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
Economic Scenarios
Equity Indices Yield Curves
FX Rates Inflation
Unemployment
2
Net of Financial Market and Reinsurance Hedging
•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 © 2005 Employers Reinsurance Corporation
Systematic Risk in an Insurance IRM3. Other Connections
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
Economic Scenarios
Equity Indices Yield Curves
FX Rates Inflation
Unemployment
2
Net of Financial Market and Reinsurance Hedging
•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 © 2005 Employers Reinsurance Corporation
Systematic Risk in an Insurance IRM4. Net Income Distribution
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
Economic Scenarios
Equity Indices Yield Curves
FX Rates Inflation
Unemployment
2
Net of Financial Market and Reinsurance Hedging
•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]