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
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.
© 2005 Employers Reinsurance Corporation
2
Theory
© 2005 Employers Reinsurance Corporation
3
Risk Adjusted Cost of Capital
Issue
How It Will Be Addressed
Rating Agency Required Capital is a Use Rating Agency Required
Binding Constraint
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
Capital Usage Cost formula works
Asset simultaneously exposed by all as if Finance grants the P&L’s
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)
© 2005 Employers Reinsurance Corporation
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Insurer Capital Is A Shared Asset
Asset Owners:
• Control Overall Access Rights
•Preserve Against Depletion From Over-Use
User 1
Shared Asset
Reservoir, Golf Course,
Pasture, Hotel, …
Insurer Capital
• Consumes On
Standalone Basis
• Tunnel Vision - No
Awareness Of The Whole
User 2
User 3
© 2005 Employers Reinsurance Corporation
User 4
• Consumes On
Standalone Basis
• Tunnel Vision - No
Awareness Of The Whole
5
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
© 2005 Employers Reinsurance Corporation
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An Insurer Uses Its Capital Both
Ways
1. “Rental” Or NonConsumptive
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
© 2005 Employers Reinsurance Corporation
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Capital Usage Cost Calculation
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
© 2005 Employers Reinsurance Corporation
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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”
© 2005 Employers Reinsurance Corporation
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Capital Usage Charges: Calculation
1. 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)
© 2005 Employers Reinsurance Corporation
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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
© 2005 Employers Reinsurance Corporation
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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
© 2005 Employers Reinsurance Corporation
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Examples
© 2005 Employers Reinsurance Corporation
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Pricing Demo – Short Tail
Example 1
Property Catastrophe Contract
Comments
(1) Premium
(2) Limit
Capacity Occupation Cost
(3) Required Capital Factor
(4) Required Capital (RC)
(5) Opportunity Cost for Capacity
(6) Capacity Occupation Fee
Capital Call Cost
(7) Probability
(8) Loss
(9) Capital Consumption Amount
(9a) Amount Within RC
(9b) Amount Beyond RC
(10) Consumption Charge Within RC
(11) Within RC Consumption Cost
(12) Consumption Charge Beyond RC
(13) Beyond RC Consumption Cost
(14) Total Consumption Cost
(15) Expected Consumption Cost
EVA
(16) Expected NPV
(17) Expected Capital Usage Cost
(18) EVA
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
1,000,000
10,000,000
35.0%
350,000
10.0%
35,000
2.0%
10,000,000
9,000,000
350,000
8,650,000
120.0%
420,000
240.0%
20,760,000
21,180,000
423,600
800,000
458,600
341,400
© 2005 Employers Reinsurance Corporation
Rating Agency
= (3) * (1)
r Opp
= (4) * (5)
Full limit loss
= (8) - (1)
= min[ (4) , (9) ]
= (9) - (9a)
= (10) * (9a)
= (12) * (9b)
= (11) + (13)
= (14) * (7)
= (1) - (7) * (8)
= (6) + (15)
= (16) - (17)
14
Pricing Demo – Long Tail
Example 2
Longer Tail Excess of Loss Contract
Comments
(1) Premium
(2) Limit
Capacity Occupation Cost
(3) Required Capital Factor - Premium
(3a) Required Capital Factor - Reserves
(3b) Reserve Amount
(3c) Reserve Duration
(4) Required Capital
(5) Opportunity Cost for Capacity
(6) Capacity Occupation Fee
Capital Call Cost
(7) Probability
(8) Loss (NPV @ 5%)
(9) Capital Consumption Amount
(9a) Amount Within RC
(9b) Amount Beyond RC
(10) Consumption Charge Within RC
(11) Within RC Consumption Cost
(12) Consumption Charge Beyond RC
(13) Beyond RC Consumption Cost
(14) Total Consumption Cost
(15) Expected Consumption Cost
EVA
(16) Expected NPV
(17) Expected Capital Usage Cost
(18) EVA
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
1,000,000
10,000,000
35.0%
25.0%
156,705
5.00
545,882
5.0%
27,294
2.0%
7,835,262
6,835,262
545,882
6,289,380
120.0%
655,058
240.0%
15,094,512
15,749,570
314,991
843,295
342,285
501,009
© 2005 Employers Reinsurance Corporation
Rating Agency
Rating Agency
Years
= (3) * (1) + (3a) * (3b) * (3c)
r Opp
= (4) * (5)
Full limit loss, discounted
= (8) - (1)
= min[ (4) , (9) ]
= (9) - (9a)
= (10) * (9a)
= (12) * (9b)
= (11) + (13)
= (14) * (7)
= (1) - (7) * (8)
= (6) + (15)
= (16) - (17)
15
Pricing Demo – Long Tail @ Same EVA
Example 2a
Longer Tail with Same EVA as Short Tail
Comments
(1) Premium
(2) Limit
Capacity Occupation Cost
(3) Required Capital Factor - Premium
(3a) Required Capital Factor - Reserves
(3b) Reserve Amount
(3c) Reserve Duration
(4) Required Capital
(5) Opportunity Cost for Capacity
(6) Capacity Occupation Fee
Capital Call Cost
(7) Probability
(8) Loss (NPV @ 5%)
(9) Capital Consumption Amount
(9a) Amount Within RC
(9b) Amount Beyond RC
(10) Consumption Charge Within RC
(11) Within RC Consumption Cost
(12) Consumption Charge Beyond RC
(13) Beyond RC Consumption Cost
(14) Total Consumption Cost
(15) Expected Consumption Cost
EVA
(16) Expected NPV
(17) Expected Capital Usage Cost
(18) EVA
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
846,367
10,000,000
35.0%
25.0%
156,705
5.00
492,110
5.0%
24,605
2.0%
7,835,262
6,988,895
492,110
6,496,785
120.0%
590,532
240.0%
15,592,283
16,182,815
323,656
689,662
348,262
341,400
© 2005 Employers Reinsurance Corporation
Rating Agency
Rating Agency
Years
= (3) * (1) + (3a) * (3b) * (3c)
r Opp
= (4) * (5)
Full limit loss, discounted
= (8) - (1)
= min[ (4) , (9) ]
= (9) - (9a)
= (10) * (9a)
= (12) * (9b)
= (11) + (13)
= (14) * (7)
= (1) - (7) * (8)
= (6) + (15)
= (16) - (17)
16
Demo Model
© 2005 Employers Reinsurance Corporation
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Demo Model
1) Loss Distributions
Log Normal Mu
Log Normal Sigma
Expected Loss
Profit Margin
Premium
Return $
LOB 1
13.771
30.0%
1,000,000
10.0%
1,111,111
111,111
LOB 2
13.691
50.0%
1,000,000
10.0%
1,111,111
111,111
LOB 3
13.571
70.0%
1,000,000
10.0%
1,111,111
111,111
TOTAL
3,000,000
3,333,333
333,333
3) Capital Usage Calculation
Required Capital Charge on Premium
Capital Usage Charge Adj Factor Due to Reserves
(A) Rental Fee
(B) Consumption Charge Within Required Capital
(C) Consumption Charge Beyond Required Capital
Required Premium Capital
LOB 1
40.0%
100.0%
10.0%
120.0%
240.0%
500,000
© 2005 Employers Reinsurance Corporation
LOB 2
40.0%
100.0%
12.00
24.00
500,000
LOB 3
40.0%
100.0%
500,000
18
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
© 2005 Employers Reinsurance Corporation
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Demo Model – RAROC vs RORAC
4) Portfolio Evaluation Metrics
Premium
Required Capital
Return
Expected Capital Usage $ Cost
EVA $
Usage Cost as % of Capital
Rental Fee
Consumption Charge
Prob of Exceeding Required Capital
LOB 1
1,250,000
500,000
112,500
110,714
1,786
22.1%
10.0%
12.1%
5.0%
LOB 2
1,250,000
500,000
100,000
213,850
(113,850)
42.8%
10.0%
32.8%
15.0%
LOB 3
1,250,000
500,000
87,500
362,000
(274,500)
72.4%
10.0%
62.4%
17.0%
TOTAL
3,750,000
1,500,000
300,000
686,564
(386,564)
45.8%
10.0%
35.8%
9.0%
LOB 1
1,250,000
205,950
112,500
94,265
18,235
45.8%
10.0%
35.8%
27.0%
LOB 2
1,250,000
433,748
100,000
198,531
(98,531)
45.8%
10.0%
35.8%
15.0%
LOB 3
1,250,000
860,302
87,500
393,768
(306,268)
45.8%
10.0%
35.8%
15.0%
TOTAL
3,750,000
1,500,000
300,000
686,564
(386,564)
45.8%
10.0%
35.8%
9.0%
4) Portfolio Evaluation Metrics
Premium
Required Capital
Return
Expected Capital Usage $ Cost
EVA $
Usage Cost as % of Capital
Rental Fee
Consumption Charge
Prob of Exceeding Required Capital
© 2005 Employers Reinsurance Corporation
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Portfolio Mix Evaluation and
Optimization
© 2005 Employers Reinsurance Corporation
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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
© 2005 Employers Reinsurance Corporation
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Portfolio Mix Model – Evaluation
Output
Input
Portfolio Mix:
Portfolio
EVA
Premium, Loss Ratio,
Commission,
Overhead
Required Capital
Factors:
Premium And
Reserves
Alternative
Mix
Evaluation
Capital Usage
Cost Factors:
Portfolio Capital
Usage Cost
Portfolio
DVS
Marginal Comparisons
With Other Mixes:
Rental And
Consumption
-Required Premium Capital By Segment
- Capital Usage Cost % By Segment
©
Perfect For “What-If”
Analyses
2005 Employers Reinsurance Corporation
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Portfolio Mix Model – Optimization
Optimizer
Inputs
Segment
Premium
Constraints
Optimizer
Target:
E.g., Maximize
EVA
Max
Required
Capital
Constraint
Optimizer
Output
Optimizer Evaluates
Thousands Of
Alternative Mixes
Input
Output
Portfolio Mix:
Premium, Loss Ratio,
Commission, Overhead
Required Capital
Factors:
EVA
Mix Evaluation
Risk-Adjusted
Required TM by
Segment
Premium and Reserves
Capital Usage
Cost Factors:
“Optimal”
Portfolio Mix
Given
Constraints
Marginal
Comparisons with
Other Mixes
Rental and
Consumption
Evaluation
Metrics For
Optimal Mix:
-EVA
- DVS
- Capital Usage Cost
Marginal
Comparison
With Starting
Mix
©
Perfect For Strategic
Directional Analysis
2005 Employers Reinsurance Corporation
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At Least One Trent Vaughn Critique
Addressed:
RMK Can Reflect Systematic Risk
© 2005 Employers Reinsurance Corporation
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1 Cost of Risk
Economic Scenarios
Financial Market
Hedging
2
Market Capacity
Equity Indices
Yield Curves
FX Rates
Inflation
Insurer Asset
Portfolio
Unemployment
Other Connections?
3
Investment Result
Insurer New Exposure
Price Levels
Reserves
Insurance UW
Portfolio
Operating Result
Reinsurance Market
Hedging
© 2005 Employers Reinsurance Corporation
Net Income
Distribution
4
Net of Financial Market
and Reinsurance Hedging
26
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
1
Cost of Risk
Financial Market
Hedging
Economic Scenarios
2
Equity Indices
Yield Curves
FX Rates
Inflation
Market Capacity
Insurer Asset
Portfolio
Unemployment
Other Connections?
3
Investment Result
Insurer New Exposure
Price Levels
Reserves
Insurance UW
Portfolio
Reinsurance Market
Hedging
© 2005 Employers Reinsurance Corporation
Operating Result
Net Income
Distribution
4
Net of Financial Market and
Reinsurance Hedging
27
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
1
Cost of Risk
Financial Market
Hedging
Economic Scenarios
2
Equity Indices
Yield Curves
FX Rates
Inflation
Market Capacity
Insurer Asset
Portfolio
Unemployment
Other Connections?
3
Investment Result
Insurer New Exposure
Price Levels
Reserves
Insurance UW
Portfolio
Reinsurance Market
Hedging
© 2005 Employers Reinsurance Corporation
Operating Result
Net Income
Distribution
4
Net of Financial Market and
Reinsurance Hedging
28
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?
1
Cost of Risk
Financial Market
Hedging
Economic Scenarios
2
Equity Indices
Yield Curves
FX Rates
Inflation
Market Capacity
Insurer Asset
Portfolio
Unemployment
Other Connections?
3
Investment Result
Insurer New Exposure
Price Levels
Reserves
Insurance UW
Portfolio
Reinsurance Market
Hedging
© 2005 Employers Reinsurance Corporation
Operating Result
Net Income
Distribution
4
Net of Financial Market and
Reinsurance Hedging
29
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
1
Cost of Risk
Financial Market
Hedging
Economic Scenarios
2
Equity Indices
Yield Curves
FX Rates
Inflation
Market Capacity
Insurer Asset
Portfolio
Unemployment
Other Connections?
3
Investment Result
Insurer New Exposure
Price Levels
Reserves
Insurance UW
Portfolio
Reinsurance Market
Hedging
© 2005 Employers Reinsurance Corporation
Operating Result
Net Income
Distribution
4
Net of Financial Market and
Reinsurance Hedging
30
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