CAS Ratemaking Seminar, Salt Lake, Utah

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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, MAAADirector, 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, The Hartford Financial Services Group
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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
• Whats 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
KS
K
Capital
S
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Marginal Balance Sheet Impact
Let RA Return on Assets which supplied by both
policyholders and shareholders. RL Cost of
Float. Investing policyholder Supplied funds
until needed. RE Cost of Capital.
Shareholders Return on their investment
KS
K
S
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Marginal Balance Sheet Impact
This relationship develops into the generally
accepted view that an insurance company is a
levered trust.
Levered Trust (KS)RA KRL SRE
KS
Re-Arranging S(RE RA) K(RA RL) Let P
Premium RU - (K/P) RL
K
S
(S/P)(RE RA) (K/P)RARU
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Cost of Capital
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Discounted Combined Ratio
Ru1-Disc CR
Premium
Needed Capital
MarginalCapital
Now we are talking
xxx
xxx
xxx
Niche 1
Who Cares?
Niche 2
xxx
xxx
xxx
Niche 3
xxx
xxx
xxx
xxx
xxx
xxx
Total
xxx
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 insurers return on marginal
capital will be equal for all risks.
REQ CAPITAL
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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 companys 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
  (prize-winner)
• Buckle up

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Myers-Read Summary

• Focus on Value of Default Option of Insurer
• gtFunction 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

• 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
Shared AssetReservoir, Golf Course,Pasture,
Forest,
User Community
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 over-depletion
• 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
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

Shared AssetReservoir, Golf Course,Pasture,
Hotel, Insurer Capital
User 1
User 4

• Consumes On Standalone Basis
• Tunnel Vision - No Awareness Of The Whole

• Consumes On Standalone Basis
• Tunnel Vision - No Awareness Of The Whole

User 2
User 3
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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

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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 AB 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
• As ROE 30/75 40
• Bs 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.