1

CAS Ratemaking Seminar, Salt Lake, UtahMarch 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/ RefereeRobert F. Wolf, FCAS, MAAADirector, Navigant Consulting, Inc.

PanelLouise Francis, Consulting Principal, Francis Analytics & Actuarial Data Mining, Inc.Glenn G. Meyers, Chief of Actuarial Research and Assistant Vice President, ISORuss Bingham, Director of Research, The Hartford Financial Services Group

2

Common Basis

Robert F. Wolf, FCAS, MAAADirector, Navigant Consulting Inc.

3

• 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.”

What is Our Goal?

4

• 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?

What is Our Goal?

5

Assets Liabilities

Capital

Let K = Policyholder Supplied Funds = Premiums Less Loss Payments

Let S = Shareholder Supplied Funds= Capital to Support Insurance Operations

K

S

K+S

Supplied Funds

6

Marginal Balance Sheet Impact

Let RA = Return on Assets whichsupplied by both policyholders and shareholders.

RL = Cost of Float. Investing policyholderSupplied funds until needed.

RE = Cost of Capital. Shareholders Returnon their investment

K+S K

S

Returns RA

Costs RL

Costs RE

7

Marginal Balance Sheet ImpactThis relationship developsinto the generally acceptedview that an insurance companyis a levered trust.

K+S K

S

Returns RA

Costs RL

Costs RE

Levered Trust

(K+S)RA = KRL + SRE

Re-Arranging

S(RE –RA) = K(RA –RL)

Let P = Premium

RU = - (K/P) RL

(S/P)(RE –RA) = (K/P)RA+RU

8

Cost of Capital

9

Niche 1

Niche 2

Niche 3

PremiumDiscounted Combined Ratio

Ru=1-Disc CR

xxx

xxx

xxx

Total xxx

xxx

xxx

xxx

xxx

xxx

xxx

xxx xxx

Needed Capital

xxx

REQ CAPITAL

MarginalCapital

Who Cares?

Now we are talking

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.

10

• 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?

The “Allocating Capital “ Paradox

11

• 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?

12

Myers-Read

13

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…

14

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

15

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

16

Myers-Read – Critiques

• G. Venter:1) Time period for option = ?2) Sensitive to extreme tail – difficult to estimate3) Seems like other additive methods (see RMK)4) Aimed at allocating frictional costs of holding

capital, but used as denominator in RORC formula

17

Merton-Perold

18

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

19

Mango

20

Shared Asset Usage

Shared AssetReservoir, Golf Course,

Pasture, Forest, …

User Community

Asset owners control access rights to preserve asset, control against over-use

Access

Users have their own interests,

often cannot see larger picture

Uses are classified as either CONSUMPTIVE or NON-CONSUMPTIVE

21

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

22

Typical Insurance Capital Allocation

Required Capital @

t=1@ t=2 @ t=3 @ t=4 @ t=5

Written Premium

Reserves @ t=2 @ t=3 @ t=4 @ t=5

Required Capital Formula

Changes in Required Capital are attributed to imputed capital transfers to and from the Owner

But no such transfers ever take place!

23

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

24

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

25

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 the need for individual company's to establish a financial discipline throughout the organization (a process)

o 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?

o Are we fighting a losing battle in Financial Theory? - Behaviorist Economists (Investors are not rational)

26

EXAMPLES

27

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

28

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

29

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%

30

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?

31

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

32

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.