RCM-1: Current Research on Risk and Return Methodologies in Ratemaking Donald Mango, FCAS, MAAA Director of R&D, GE Insurance Solutions March 10, 2005

RCM-1: Current Research on Risk and Return Methodologies in RatemakingDonald Mango, FCAS, MAAADirector of R&D, GE Insurance Solutions March 10, 2005

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Agenda

Application of Myers-Read

Merton-Perold

Latest from COTOR VALCON

Insurance Capital As A Shared Asset

Q&A


Application of Myers-Read


Myers-Read in SimulationRuhm-Mango-Kreps (RMK)

Example:

2 independent normal risks:

>Risk A: μ = 100, σ = 30

>Risk B: μ = 200, σ = 40

>Total: μ = 300, σ = 50

>Capital = 2σ 97.725 %ile ruin level


Myers-Read in Simulation

1) Simulate the variables, sum them to get total portfolio. In example, 10K iterations.

2) Sort by total portfolio result.3) Take a small sample of iterations on either side of

the “ruin point”: These receive weight = 1, all others receive weight = 0.

4) Take weighted averages of each variable to get “funding” amounts. Subtract expected values to get capital allocation.



Merton-Perold


Merton-Perold – Summary

Capital allocation to segments is meaninglessCapital is held at the company levelEach segment receives a guarantee from the parent companyPrice 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


Venter: Charge Capital Cost against ProfitsInstead of return rate, subtract cost of capital from unit

profitability

Use true marginal capital costs of business being evaluated, instead of an allocation of entire firm capital> If evaluating growing the business 10%, charge the

cost of the capital needed for that much growth> If evaluating stopping writing in a line, use the capital

that the company would save by eliminating that line

This maintains financial principle of comparing profits to marginal costs


Venter: Calculating Marginal Capital Costs

Could use change in overall risk measure of firm that results from the marginal business – but requires selection of the overall risk measure

Or could set capital cost of a business segment as the value of the financial guarantee the firm provides to the clients of the business segment>This could be called capital consumption

(stay tuned)


Venter: Value of Financial GuaranteeCost of capital for subsidiary is a difference between

two put options:>1. The cost of the guarantee provided by the

corporation to cover any losses of the subsidiary>2. The cost to the clients of the subsidiary in the

event of the bankruptcy of the corporationEconomic value added of the subsidiary is value of

profit less cost of capital>Value of profit is contingent value of profit

stream if positiveA pricing method for heavy-tailed contingent claims

would be needed (stay tuned)


Latest from COTOR VALCON


Latest from COTOR VALCONLiabEx (Todd Bault)• Old Lloyd's, only more high tech.

• Insurance buyers (Buyers), capital providers (Names), and the market, which will also act as the liability principal (LiabEx). > Names have been cleared for suitability.

• Insurance policy comes to market. Names look at the contract, set the initial premium that the buyer will pay.

• Names are putting up ZERO capital to get their profit load.

• LiabEx sets margin requirement.

• THIS is capital, and LiabEx will charge the Names' margin interest to pay for LiabEx's cost of capital.

• But LiabEx has a very different cost of capital than for the insurance risk--LiabEx is ONLY worried about default by Names.

• Profit is a function of bearing risk, and "capital" is not necessarily needed.

• In fact, this framework handles instantaneous risks just fine


Latest from COTOR VALCONLiabEx (Todd Bault)

• Margin requirements for liabilities would be much higher than for short transactions in equities.

• LiabEx would have to have some liability assessment techniques, faces considerable parameter risk, and would need to be paid for this. (Sounds like Venter)

•Those who bear the default risk NEED capital, and that capital has a cost. •That capital also has a time element, and margin interest captures that.•In the real world, insurers are collecting BOTH loads, since they have part of the principal function (or rather, are forced to by rating agencies on behalf of their shareholders).


Latest from COTOR VALCONCapacity (Glenn and Don Agree!)i. Desired counterparty rating implied minimum

capital adequacy ratio (CAR) = Actual Capital / Required Capital

ii. Given a minimum CAR and Actual Capital, a Maximum Required Capital falls out.

iii. Required Capital is a function of (a) assets, (b) reserves, and (c) written premiums

iv. For planning purposes, (a) and (b) are ~ fixed. So really facing Maximum Premium Required Capital.


Latest from COTOR VALCONCapacity (Glenn and Don Agree!)v. More precisely, allowable portfolio mixes can generate no

more than the Maximum Premium Required Capital. This represents a measure of underwriting capacity.

vi. Generic axiom: “The more risk (net of all hedging) an insurer takes on in new underwriting, the more underwriting capacity it uses.”

vii. More restrictive axiom: "If an insurer is at its max CAR, and wants to take on additional new business, and cannot reduce Required Capital via hedging (reduction or transfer), nor tolerate a lower CAR and possibly a rating downgrade, then it must raise additional capital."


Insurance Capital As A Shared Asset


Risk Adjusted Cost of CapitalIssue How It Will Be Addressed

Rating Agency Required Capital is a Binding Constraint

Use Rating Agency Required Capital formula everywhere

But Rating Agency Capital Charges do not Reflect My Risks

Vary the Target RORC’s instead of varying the capital amounts (RAROC instead of RORAC)

Total Capital is really a Shared Asset simultaneously exposed by all P&L’s

Capital Usage Cost formula works as if Finance grants the 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)

“A pricing method

for heavy-ta

iled

contingent c

laims

would be needed”


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


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


An Insurer Uses Its Capital Both Ways

1. “Rental” Or Non-Consumptive

Returns Meet Or Exceed Expectation

Capacity Is Occupied, Then Returned Undamaged

A.k.a. Room Occupancy

2. Consumptive Results DeteriorateReserve Strengthening Is

Required A.k.a. Destroy Your

Room, Your Floor, Or Even The Entire Hotel


Two Kinds Of Charges:1. Rental = Access fee for LOC

Function of Capacity Usage (i.e., Rating Agency 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

Capital Usage Cost Calculation


Economic Value Added or EVA

EVA = Return – Cost of Capital UsageFactors in:> Capacity Usage> Company Risk Appetite> Product Volatility> Correlation of Product with Portfolio


Reconciliation of Meyers and Mango

Comes down to RAROC or RORAC>RAROC: vary the

returns>RORAC: vary the

capital amounts>Both end up with the

product of return and capital

Depends on your emphasis

Similar to Bingham:>Price for Risk (RAROC)>Leverage for Return

(RORAC)

See Excel Example


Advantages of RAROC

•Use simple, additive, externally-mandated required capital formulas • Transparent, high degree

of buy-in, works like a budget

•Guarantee reconciliation with external capital requirement•Explicit, objective expression of risk appetite and emphasis

•Venter: explicit pricing method for heavy-tailed contingent claims •Seamless fit with Economic Value Added (EVA) – in fact, may be cleaner than economic capital allocation approaches•Consistent with Morgan Stanley approach (Charles Monet)


Thank youQ&A

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Documents

RCM-1: Current Research on Risk and Return Methodologies in Ratemaking Donald Mango, FCAS, MAAA Director of R&D, GE Insurance Solutions March 10, 2005