CAS Ratemaking Seminar, Salt Lake, Utah
March 13-14, 2006
RCM-2: Town Hall Session: Logic, Fallacies, and Paradoxes in Risk
and Return Analysis in Ratemaking: Town Hall Meeting
Moderator/Host/Panelist/ Referee
Robert F. Wolf, FCAS, MAAA
Director, Navigant Consulting, Inc.
Panel
Louise Francis, Consulting Principal, Francis Analytics & Actuarial
Data Mining, Inc.
Glenn G. Meyers, Chief of Actuarial Research and Assistant Vice
President, ISO
Russ Bingham, Director of Research,1 The Hartford Financial Services
Group
Common Basis
Robert F. Wolf, FCAS, MAAA
Director, Navigant Consulting Inc.
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What is Our Goal?
• CAS Statement of Principles
“The underwriting profit and
contingency provisions are the
amounts that, when considered with
net investment and other income,
provide an appropriate total after-tax
return.”
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What is Our Goal?
• Two Issues
– What’s appropriate?
• Risk charge for “random variation from the
expected costs” must be “consistent with the
cost of capital”
• Included in underwriting profit provision
– How do you measure return?
• Return on what?
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Supplied Funds
Let K = Policyholder Supplied Funds = Premiums Less
Loss Payments
Let S = Shareholder Supplied Funds= Capital to Support
Insurance Operations
Assets
Liabilities
K+S
K
Capital
S
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Marginal Balance Sheet Impact
Costs
RL
Returns
Let RA = Return on Assets which
RA
supplied by both policyholders
and shareholders.
RL = Cost of Float. Investing policyholder K+S
Supplied funds until needed.
RE = Cost of Capital. Shareholders Return
on their investment
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Costs
RE
K
S
This relationship develops
into the generally accepted
view that an insurance company
is a levered trust.
Marginal Balance Sheet Impact
Costs
RL
Returns
RA
Levered Trust
(K+S)RA = KRL + SRE
K+S
Re-Arranging
S(RE –RA) = K(RA –RL)
K
Let P = Premium
S
RU = - (K/P) RL
(S/P)(RE –RA) = (K/P)RA+RU
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Costs
RE
Cost of Capital
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Premium
Niche 1
xxx
Discounted
Combined
Ratio
Ru=1-Disc CR
Needed
Capital
Marginal
Capital
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Who
Cares?
Now
we are
talking
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Niche 2
xxx
xxx
xxx
Niche 3
xxx
xxx
xxx
Total
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An insurer chooses to write the risks that yields the
greatest return on marginal capital. In the long run, in a
stable underwriting environment, the insurer will make
an adequate return on capital and the insurer’s return on
marginal capital will be equal for all risks.
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REQ CAPITAL
The “Allocating Capital “ Paradox
• 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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• Insurance Capital is a Claims
Paying Reservoir
– Subject to unpredictable
future inflows and outflows
• Likelihood and
magnitude of
drawdowns
• Co-incidence with other
drawdowns
• Systemic shocks
• Huge mismatch:
– Cost of Capital = Current
Expense
– Current underwriting
activities are exposing
future capital
• Capital is a holistic portfolio
phenomenon
– not meaningfully divisible
– Can we allocate life to our
organs?
– Can we allocate the
WhiteSox success to each
player?
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Myers-Read
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Myers-Read
• 2003 ARIA prize winning paper
• Presented at 2003 Spring Meeting
• Also invited discussions by many CAS
researchers
• Butsic applied it to Cat Reinsurance pricing in
1999 Reinsurance Call Paper program (prizewinner)
•
Buckle up…
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Myers-Read – Summary
•
Focus on Value of
Default Option of
Insurer
>Function of surplus,
covariance of losses
and assets
• Marginal default value
for LOB i depends on
required capital for
LOB i, covariance,
portfolio mix
• Covariances all add up,
so marginal default
values all add up under
certain assumptions (stay
tuned)
• Use this to determine
unique allocation
formula
• Elegant mathematics in
a multi-variate
LogNormal
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Myers-Read – Critiques
• G. Meyers:
demonstrates ISO
insurer distributions are
not homogeneous
• Introduces
heterogeneity
multiplier to make
things add up
• A way to “make it
work”
• S. Mildenhall: adds up if
and only if distributions are
homogeneous
– Defined as straight linear
scaling with volume, no
shape change
• Not true for most Insurance
distributions
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Myers-Read – Critiques
•
1)
2)
3)
4)
G. Venter:
Time period for option = ?
Sensitive to extreme tail – difficult to estimate
Seems like other additive methods (see RMK)
Aimed at allocating frictional costs of holding capital, but
used as denominator in RORC formula
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Merton-Perold
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Merton-Perold – Summary
• Capital allocation to
segments is
meaningless
• Capital is held at the
company level
• Each segment receives a
guarantee from the
parent company
• Price of guarantee could
be observable in market
• Cost of guarantee
represents risk capital
• Opposed to allocation
exercises:
– Guarantee only has
meaning at company
level
– Order dependence
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Mango
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Shared Asset Usage
User
Community
Shared Asset
Reservoir, Golf Course,
Pasture, Forest, …
Access
Users have their
own interests,
often cannot see
larger picture
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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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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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
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User 4
• Consumes On
Standalone Basis
• Tunnel Vision - No
Awareness Of The
Whole
Potential Discussion Points




Risk Load = Profit Load = Contingency Load ?????? .. or what??
o Is it a loss element or a profit load element
o CAPM, Diversifiable and Non-diversifiable risk arguments.
o By the way, what is a company’s cost of capital??
o Has anyone defined risk yet? Risk of insolvency? Solvency Put? Hey
if I were CEO, I don’t want to just survive, I want to thrive?
o Risky Investments and Profit Loads?
o The time question? No time, no risk? Less time less risk? More time
more risk?
Correlation? Can anyone get this right???
Capital Allocation
o Main Stream
 Milton/Perold
 Myers/Read
 Lack of Homogeneity Argument Presented in Layman’s
Terms
 Fama/ French
 Other
o Capital Allocation vs. Capital Attribution vs. Capital Consumption
(Why does capital have to be allocated to begin with ?)
o Marginal Capital Consistant with economic theory on marginal costs
o Marginal Capital doesn’t add up to total capital…so what???
General Considerations on Integrated Risk (ERM) Management and
Disciplined Capital Mangement
o
o
the need for individual company's to establish a financial
discipline throughout the organization (a process)
the need to implement a finanical model which incorporates
key concepts and is applied throught the company.
o Has anyone figured out how to reward and punish a silo’d unit from
an integrated result?
25 in Financial Theory? - Behaviorist
o Are we fighting a losing battle
Economists (Investors are not rational)
EXAMPLES
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The George Zanjani Example
• Division A
– Expected return of 30
– Requires capital of 120 as a standalone
• Division B
– Expected return of 15
– Requires capital of 120 as a standalone
• Combine A and B
– Expected return of 45
– Requires total capital of 150
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The George Zanjani Example
• Division A
– Expected return of 30
– Requires capital of 120 as a standalone
• Division B
– Expected return of 15
– Requires capital of 120 as a standalone
Scenario
Probability
Loss - A
Loss - B
1
2/39
60
135
2
7/39
150
45
3
30/39
0
0
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The George Zanjani Example
• It makes sense to combine A and B.
– ROE for A = 30/120 = 25%
– ROE for B = 15/120 = 12.5%
– ROE for A+B = 45/150 = 30%
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The George Zanjani Example
• Marginal capital for A and B is 30
• Gross-Up allocated capital = 75 for both A and
B
• A’s ROE = 30/75 = 40%
• B’s ROE = 15/75 = 20%
• B does not meet overall target of 30%
• Do we “fire” B?
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The George Zanjani Example
• A capital allocation leading to “correct”
economic decision
– Allocate capital of 100 to A
– Allocate capital of 50 to B
• Both allocations are above the marginal
capital “floor.”
• ROE = 30% for both A and B
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Does this example apply to insurance?
• Not really – Insurance decisions are made in smaller
chunks.
• Suppose the Divisions A and B consist of a bunch of
individual insurance policies.
• You can devise a more profitable strategy where you
write a few more polices in Division A, and fewer in
Division B.
• The Zanjani example turns capital allocation upside
down by forcing you to allocate capital in proportion
to the risk load.
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