Transcript Capital Consumption Don Mango, FCAS, MAAA Director of R&D GE Insurance Solutions 2004 CAS Annual Meeting.

Capital Consumption
Don Mango, FCAS, MAAA
Director of R&D
GE Insurance Solutions
2004 CAS Annual Meeting
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.
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.
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Goals for Today
Demonstrate: alternative evaluation
framework to capital
allocation/release/IRR
Shared Asset: unifying it with capital
allocation (PCAS submission)
Portfolio: two methods to allocate a
portfolio risk charge to segment
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Demonstrate
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Allocation vs Consumption
Three questions:
What do you do with the total capital?
How do you evaluate business segments?
What does it mean to be in a portfolio?
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Allocation vs Consumption
Question 1: What happens to the total capital?
Allocation
Consumption
 Divided up among the
 Left intact
segments.
 Each segment has the right
 Either by explicit
to “call” upon the total capital
allocation, or assignment
to pay its operating deficits
of the marginal change in
or shortfalls
the total capital
requirement from adding
the segment to the
remaining portfolio
Simultaneous, Overlapping Rights to a Single Capital Pool
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Allocation vs Consumption
Question 2: How are the segments evaluated?
Allocation
Consumption
 Give the allocations to
 Give each segment “access
each segment
rights” to the entire capital
 Evaluate each segment’s  Evaluate each segment’s
return on their allocated
potential calls (both
capital
likelihood and magnitude) on
the total capital
 Must clear their hurdle
rate
 Must pay for the likelihood
and magnitude of their
potential calls
Decentralized vs Centralized Capital Management
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This is THE CRITICAL SLIDE!
Allocation vs Consumption
Question 3: What does being in a portfolio mean?
Allocation
Consumption
 Being standalone with
 Being standalone with
less capital
potential access to all the
capital
 But still having access to
all the capital if
 But all other segments have
necessary, although it is
similar access rights
unclear how this is
reflected
The difference between having a kiddie pool in your
backyard and joining a swim club
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Details of the Framework
1. Scenario analysis and capital
consumption
2. Default-free discounting
3. Capital Call Cost Function
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1. Scenario Analysis and Capital
Consumption
Experience fund
> From Finite Reinsurance
> Fund into which goes all revenue, from which
comes all payments
> Reflects investment income
When the fund is exhausted, but further payments
still need to be made, exercise the Call Option for
capital
That capital gets spent  CONSUMED
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Experience Fund
Long-Tailed LOB
Example 1
Experience Fund for Long-tailed Contract
120% Loss Ratio Scenario
Investment Rate
1
Time
0
1
2
3
4
5
6
7
8
9
10
TOTAL
NPV
$
$
$
$
$
$
$
$
$
$
$
2
Beginning
Fund
Balance
88,305
30,570
615
-
8.0%
3
4
$
$
$
$
$
$
$
$
$
$
$
Premiums
103,305
-
$
$
$
$
$
$
$
$
$
$
$
$
$
103,305
103,305
$
$
Expenses
15,000
15,000
15,000
Probability
10.0%
Loss Ratio
116.2%
5
Payment
Pattern
0.0%
50.0%
25.0%
12.0%
6.0%
4.0%
2.0%
1.0%
0.0%
0.0%
0.0%
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$
$
$
$
$
$
$
$
$
$
$
100.0% $
86.2% $
Paid
Losses
60,000
30,000
14,400
7,200
4,800
2,400
1,200
120,000
103,479
Ultimate
Loss
120,000
7
8
Investment
Income
$
$
2,264
$
46
$
$
$
$
$
$
$
$
-
Ending Fund
Balance
$
88,305
$
30,570
$
615
$ (13,785)
$
(7,200)
$
(4,800)
$
(2,400)
$
(1,200)
$
$
$
$
9
-
$
$
$
$
$
$
$
$
$
$
$
Capital
Call
13,785
7,200
4,800
2,400
1,200
-
$
$
29,385
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Experience Fund
Short-Tailed LOB
Example 1A
Experience Fund for Short-tailed Contract
120% Loss Ratio Scenario
Investment Rate
1
Time
0
1
2
3
4
5
6
7
8
9
10
TOTAL
NPV
$
$
$
$
$
$
$
$
$
$
$
2
Beginning
Fund
Balance
85,000
-
8.0%
3
4
$
$
$
$
$
$
$
$
$
$
$
Premiums
100,000
-
$
$
$
$
$
$
$
$
$
$
$
$
$
100,000
100,000
$
$
Expenses
15,000
15,000
15,000
Loss Ratio
120.0%
5
Payment
Pattern
0.0%
80.0%
15.0%
5.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
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$
$
$
$
$
$
$
$
$
$
$
100.0% $
90.9% $
Paid
Losses
96,000
18,000
6,000
120,000
109,084
Ultimate
Loss
120,000
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8
Investment
Income
$
$
$
$
$
$
$
$
$
$
$
-
Ending Fund
Balance
$
85,000
$ (11,000)
$ (18,000)
$
(6,000)
$
$
$
$
$
$
$
-
9
$
$
$
$
$
$
$
$
$
$
$
Capital
Call
11,000
18,000
6,000
-
$
$
35,000
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Chart 1: Capital Consumption Profile Over Time
Short versus Long Tail with 120% Loss Ratio
$20,000
$18,000
$16,000
Short Tail
Long Tail
$14,000
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
1
2
3
4
5
6
7
8
9
10
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Property Cat Example
Example 4
Property Catastrophe Contract
Premium $
Limit $
Probability
Premiums
Expenses
Losses
Capital Call Amount
Capital Call Factor
Capital Call Charge
Expected NPV
Expected Capital Call Cost
Expected Risk-adjusted NPV
$
$
$
$
$
$
$
$
1,000,000
10,000,000
No Loss Scenario
98.0%
1,000,000
0.0%
800,000
720,000
80,000
$
$
$
$
$
Loss Scenario
2.0%
1,000,000
10,000,000
9,000,000
400.0%
36,000,000
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2. Default-Free Discounting
Conditional on its occurrence, a given scenario’s
outcome is certain  discount at the default-free
rate
Risk-adjusted discounting is too clumsy
> Overloaded operator
> Try splitting out default probability from price
of risk in risky debt spreads
Reflect uncertainty between scenarios, not within
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3. Capital Call Cost Function
Risk-based overhead expense loading
Pricing decision variable
Application of utility theory
Borch (1961):
To introduce a utility function which the company
seeks to maximize, means only that such
consistency requirements (in the various
subjective judgments made by an insurance
company) are put into mathematical form.
Transparent, Explicit Formulation of Risk-Reward Appetite
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3. Capital Call Cost Function
Make the implicit explicit
Express your preferences explicitly, in
mathematical form, and apply them via a
utility function
The mythical “Risk Appetite”
Enforce consistency in the many judgments
being made
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Implicit Preferences
Preferences buried in Kreps’ “Marginal Standard Deviation”
risk load approach:
> The marginal impact on the portfolio standard deviation is
our chosen functional form for transforming a given
distribution of outcomes to a single risk measure.
> Risk is completely reflected, properly measured and
valued by this transform.
> Upward deviations are treated the same as downward
deviations.
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Shared Asset
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Problem Statement
Capital Allocation is
necessary
The best way to make
risk-based portfolio
composition decisions
Critical element of
financial product pricing
Standard language of
management
Capital Allocation makes
no sense
All of the company’s
capital is available to
support each policy
No capital is transferred
at policy inception
Capital is transferred via
reserve strengthening
How can we resolve this paradox and move forward?
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Allocation Has Two Definitions
1. Transfer
Distributing, moving
This applies to flows
We transfer assets all the
time, a.k.a. claims
payments
2. Earmarking
Categorizing, bucketing,
setting aside
This applies to balances
We earmark assets all the
time, a.k.a. reserves
Resolution May Lie in the Theory of Shared Assets
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Shared Asset Usage
User
Community
Users have their
own interests,
often cannot see
larger picture
Access
Shared Asset
Reservoir, Golf Course,
Pasture, Forest, …
Asset owners control access
rights to preserve asset,
control against over-use
Uses are classified as either
CONSUMPTIVE or NON-CONSUMPTIVE
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Consumptive and Non-Consumptive
Consumptive
•Permanent transfer of control
of a portion of the asset to the
user
•Aggregation risk from overdepletion
•Examples:
> Water from reservoir
> Fisheries
> Timber
Non-Consumptive
•Temporary partial transfer of
control of a portion of the
asset to the user
•Aggregation risk from
exceeding capacity
•Examples:
> Golf course
> Campsites
> Hotel
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Typical Insurance Capital Allocation
Written
Premium
Reserves @
t=2
@ t=3
@ t=4
@ t=5
Required Capital Formula
Required
Capital @
t=1
@ t=2
@ t=3
@ t=4
@ t=5
Changes in Required Capital are attributed to
imputed capital transfers to and from the Owner
But no such transfers ever take place!
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Must We Assume a Capital Transfer?
Changes in the level of required capital are
attributable to changes in the balances that generate
required capital
> Not to transfers of required capital
> Technically a mis-imputation
Amounts of required capital could be thought of as
generated balances, like the amount of rooms
rented in a hotel
Occupancy of the firm’s finite capacity
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The Capital Hotel
Occupancy has a time dimension and an
amount dimension
Return is equivalent of rental fees  should
also be linear with time and amount
There are also clearly opportunity costs, since
occupancy of capacity (rooms) precludes it
from use by others
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The Bi-Polar Capital Hotel
Two distinct different types of insurance capital
usage:
1. Non-Consumptive or “Rental”
> Returns are at or above expectation
> Capital is occupied, then returned undamaged
> A.k.a. Benign room occupancy
2. Consumptive
>Results deteriorate
> Reserve strengthening is needed
> A.k.a. Destroy your room, your floor, the
entire hotel
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Different types of capital usage at different parts of the spectrum
Spectrum of Outcomes
50.00
Region 1: Occupation
0
0.1
0.2
0.3
0.4
0.5
Better Outcomes
0.6
0.7
0.8
0.9
1
Region 2: Destroy Your Room
(50.00)
Outcome
Capital Allocation (Your Room)
(100.00)
Worse Outcomes
Non-Consumptive
(150.00)
Destroy Your Room
Region 3: Destroy the Hotel
Destroy the Hotel
(200.00)
Your Room
(250.00)
Cumulative Prob
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Advantages of Shared Asset
Approach
1. Clear demonstration of dual modes of
insurance capital usage
2. Handles simultaneous claim of any policy
to lay claim to all the company’s assets
3. Inclusive not divisive: from slicing the pie to
simultaneous, competing usage of a
common capital pool
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Portfolio Allocation
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Capital Consumption
Capital Consumption Allocation Methodology Flowchart
Step 1: Generate
Operating and U/W
Results
Underwriting Results
Iteration
1
2
3
4
LOB 1
(100)
100
(300)
(200)
LOB 2
10
(200)
50
(500)
LOB 3
(200)
(400)
(200)
100
TOTAL
(290)
(500)
(450)
(600)
Inv Inc
350
350
350
350
Company
Operating
Result
60
(150)
(100)
(250)
Total Risk
Charge
(122.67)
(48.94)
(426.87)
Step 2: Apply Risk
Adjustment Formula to
Operating Result
Step 3: Allocate Total Risk Charge to LOB
Iteration
1
2
3
4
Neg U/W Results - Shares
LOB 1
LOB 2
33.3%
0.0%
0.0%
33.3%
60.0%
0.0%
28.6%
71.4%
LOB 3
66.7%
66.7%
40.0%
0.0%
Allocated Risk Charges
LOB 1
LOB 2
(41)
(29)
(122)
(305)
Expected Risk Charges
(38)
(86)
LOB 3
(82)
(20)
-
Total
(123)
(49)
(427)
(25)
(150)
Step 4: Calculate the Expected Risk Charges
Expected Losses
LOB 1
LOB 2
1,000
800
LOB 3
1,300
Expected Risk Charges
LOB 1
LOB 2
3.8%
10.8%
Calibrate with Overall
Cost of Capital
PHS
Expected Risk
Charge as % of PHS
1,000
15.0%
LOB 3
1.9%
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Shared Asset Portfolio Mix Model
Key Inputs
•Plan Expected Loss
•Plan Profit Margin, expressed as percent of
expected loss
•Mean Loss and Margin (ex expenses) gives you
Plan Premium
•Actual Profit Margin (will be changed by Solver)
•Demand Curve (see below)
•Max Required Capital = input constraint
•Capital Usage Charges (aka Hotel charges)
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Shared Asset Portfolio Mix Model
Key Calculations
•Actual/Plan Profit Margin = Price Deviation off Plan
(feeds Volume Impact formula)
> Assumes Plan [ Profit Margin, Premium Volume ] is
achievable
> Volume Impact = based on Demand Curve
> Increase or decrease in Exposure Units as a
function of deviation of Actual price deviation off
Plan
•Actual Premium = Exp Loss * Actual Profit Margin *
Volume Impact
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Shared Asset Portfolio Mix Model
Key Calculations
•Required Capital = X% * Actual Premium (simplified
approximation of rating agency formula)
•Hotel formula is calculated using Loss Distribution
only (excluding Profit Margin), scaled for Volume
Impact as well
•Capital Usage Charges are therefore Required
Profit Margin, which can be expressed as % of
Expected Loss
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Shared Asset Allocation
Calculation
1. Given: Scenarios of underwriting income by
product segment
2. Capital rental charge
(Example uses 7% of allocated capital)
3. Charge for damage within your allocation
Example uses 14% of underwriting result
4. Charge for damage beyond your allocation
Example uses 112% of underwriting result
beyond capital alloc
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Shared Asset Allocation
Calculation Example
Charges
0.070
0.140
1.120
Positive Outcomes
0 > Outcome > -Alloc Capital
-Alloc Capital > Outcome
Capital Allocation = $5M
Underwriting Result
+$2M
-$3M
-$8M
Capital Usage Cost
$5M*7% = $350K
$350K + $3M*14% = $770K
$350K + $5M*14% +
$3M*112% = $4,050K
Steepness of penalty depends on relative difference in charges
between “within capital” and “beyond capital” usages
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Shared Asset Portfolio Mix Model
Key Calculations
•Solver minimizes sum of squared differences
between Actual and Required Profit Margin by
modifying the price changes, which impact volume
•Constraints:
> Required Capital cannot exceed maximum
required capital;
> Actual profit margin must not be less than
Required profit margin for all Products.
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References
Shared Asset – working paper draft and Excel demo
model, send me an email: [email protected]
Capital Consumption Allocation – see Appendix B of
www.casact.org/pubs/forum/03wforum/03wf351.pdf
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Thank You
Questions?
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June 7, 2004