Profit ProvisionsShould Not Be a Function of the

Firm

Profit ProvisionsShould Not Be a Function of the

Firm

Lee Van SlykeLee Van Slyke

Provisions for Profits and ContingenciesCasualty Actuarial Society Ratemaking Conference

March, 2000

“Appropriate Standards for Profit Margins”

“Appropriate Standards for Profit Margins”

Book under CASBook under CAS Purpose: Highlight the diversity of Purpose: Highlight the diversity of

intellectual activityintellectual activity Edited by Lee Van Slyke, member of Edited by Lee Van Slyke, member of

VFACVFAC Ten authors, led by D’Arcy and Ten authors, led by D’Arcy and

McClenahanMcClenahan

CAS Statement of Principles Regarding RatemakingCAS Statement of Principles Regarding Ratemaking 3. A rate provides for the costs associated 3. A rate provides for the costs associated

with an individual risk transfer. with an individual risk transfer. 4. A rate is reasonable and not excessive, 4. A rate is reasonable and not excessive,

inadequate, or unfairly discriminatory if is inadequate, or unfairly discriminatory if is an actuarially sound estimate of the an actuarially sound estimate of the expected value of all future costs associated expected value of all future costs associated with an individual risk transfer.with an individual risk transfer.

CAS Statement of Principles Regarding RatemakingCAS Statement of Principles Regarding Ratemaking The rate should include a charge for the risk The rate should include a charge for the risk

of random variation from the expected of random variation from the expected costs. This costs. This risk chargerisk charge should be should be reflected in the determination of the reflected in the determination of the appropriate appropriate total returntotal return consistent with the consistent with the cost of capitalcost of capital and, therefore, influences and, therefore, influences the underwriting profit provision. the underwriting profit provision.

Not a Naïve ApproachNot a Naïve Approach

Deeply rooted in microeconomic theoryDeeply rooted in microeconomic theory Arrow, Debreu, et al 1945-1960Arrow, Debreu, et al 1945-1960 Borch, 1960-1980Borch, 1960-1980

Simple assumptions (Simple assumptions (axioms)axioms) Do Do notnot assume risk is proportional to assume risk is proportional to

variance alonevariance alone Prices reflect Prices reflect allall information information

Methods Not Based on the FirmMethods Not Based on the Firm

Chuck McClenahan, “Chuck McClenahan, “Insurance ProfitabilityInsurance Profitability”” Charles Toney, “Charles Toney, “The Profit ProvisionThe Profit Provision”” Judy Mintel, “The Confirmed Operating Return Judy Mintel, “The Confirmed Operating Return

Approach”Approach” Rodney Kreps, “Investment-Equivalent Reinsurance Rodney Kreps, “Investment-Equivalent Reinsurance

Pricing”Pricing” Lee Van Slyke, “An Axiomatic Basis for Standards Lee Van Slyke, “An Axiomatic Basis for Standards

of Profit”of Profit” John Cozzolino, “Capacity”John Cozzolino, “Capacity”

Profit v. Rate-of-Return. Profit v. Rate-of-Return.

Profit is a monetary value. In has meaning, Profit is a monetary value. In has meaning, even if not expressed as a rate.even if not expressed as a rate.

Principle: Expected profit is expected cost Principle: Expected profit is expected cost of capital for a policy.of capital for a policy.

To determine a rate of profit, the problem is To determine a rate of profit, the problem is to select the denominator, surplus or sales.to select the denominator, surplus or sales.

Investment Income: on Policy-Holder Supplied Funds Investment Income: on Policy-Holder Supplied Funds The real question is the fair-market value of The real question is the fair-market value of

the premiums, losses and expensesthe premiums, losses and expenses Premiums received to cover sales costs do Premiums received to cover sales costs do

not provide investmentsnot provide investments Premiums received to cover lossesPremiums received to cover losses do do

provide investmentsprovide investments

Time value of money Time value of money

Risk-free rate of return is correct. Risk-free rate of return is correct. The fair-market value of liabilities The fair-market value of liabilities

increases, not decreases, with greater increases, not decreases, with greater uncertainty.uncertainty.

The fair-market value is the present value at The fair-market value is the present value at the risk-free rate of return the risk-free rate of return plusplus a charge for a charge for the cost of risk.the cost of risk.

Problems of ROEProblems of ROE

Discounting to reflect risk: Inconsistencies Discounting to reflect risk: Inconsistencies between short-tail lines and long-tail lines. between short-tail lines and long-tail lines.

Basing risk charge on surplus: Strong Basing risk charge on surplus: Strong companies charge less than weak companiescompanies charge less than weak companies

Surplus allocation: How? From what Surplus allocation: How? From what premises?premises?

It is the rates that are regulated, not the rates It is the rates that are regulated, not the rates of return.of return.

Private Passenger AutomobilePrivate Passenger Automobile

Premium $100,000Loss Ratio 0.65Expense Ratio 0.35

Loss PayoutYear 1 0.25Year 2 0.35Year 3 0.20Year 4 0.12Year 5 0.08

Assumptions (000’s)Assumptions (000’s)

ResultsResults

Time Premium Loss ExpenseTotal Cash

Flow6.0% Present

Value0.0 $100,000 $100,000 $100,0000.5 $(16,250) $(35,000) (51,250) (49,778)1.5 (22,750) (22,750) (20,846)2.5 (13,000) (13,000) (11,238)3.5 (7,800) (7,800) (6,361)4.5 (5,200) (5,200) (4,001)

Total $100,000 $(65,000) $(35,000) $7,776

(000’s)

Rate Equity v. ROE EquityRate Equity v. ROE Equity

0

20

40

60

80

100

120

Company A Company B Company C Company D

Loss & Expense Profit Equity

Rate RegulationRate Regulation

Composition of Private Passenger Rates

Paid Loss & LAE29%

Case Reserves29%

Loss Development8%

Trend14%

Expenses18%

Profit2%

The Real IssuesThe Real Issues

What is the amount of risk in a given What is the amount of risk in a given product in a given state per dollar of product in a given state per dollar of premium?premium?

What is the capital market's price per unit of What is the capital market's price per unit of risk?risk?

ROS: Not a Naïve ApproachROS: Not a Naïve Approach

Deeply rooted in microeconomic theoryDeeply rooted in microeconomic theory Arrow, Debreu, et al 1945-1960Arrow, Debreu, et al 1945-1960 Borch, 1960-1980Borch, 1960-1980

Simple assumptionsSimple assumptions Do Do notnot assume risk is proportional to assume risk is proportional to

variance alonevariance alone Prices reflect Prices reflect allall information information

The Cost of RiskThe Cost of Risk

Capital has many rewardsCapital has many rewards One is the reward for putting capital at riskOne is the reward for putting capital at risk The reward for risk that capital commands The reward for risk that capital commands

in a competitive market is in a competitive market is the cost of riskthe cost of risk,,or,or, the risk charge the risk charge

What Is the Risk of Selling a Policy?What Is the Risk of Selling a Policy?

1

10

100

1,000

10,000

100,000

1,000,000

10,000,000

10 100 1,000Cost Per Unit of Risk

Un

its

of

Ris

k

California Earthquake Authority - Reinsurance Layer $2 Billion

Excess of $4 Billion

$2 Million Investment in a Single Issue of Baa Subordinate Bonds

BetaBetaTHE CAPITAL MARKET LINE

THE COST OF RISK PER UNIT OF RISK AS A FUNCTION OF MARKET

80

85

90

95

100

105

110

115

120

-1 -0.5 0 0.5 1 1.5 2 2.5

Composite Variable Measuring Relationship to Market

LeverageLeverage

The firm’s financial condition determine its The firm’s financial condition determine its capacity to underwrite risks. capacity to underwrite risks.

In the book, Cozzolino explores this further.In the book, Cozzolino explores this further.

Solutions for ROE ProblemsSolutions for ROE Problems

Return on sales act to clear the marketReturn on sales act to clear the market The proposed margin is right if there is healthy The proposed margin is right if there is healthy

competitioncompetition Policy prices reflect policy risksPolicy prices reflect policy risks Capacity is allocated between short-tail and Capacity is allocated between short-tail and

long-tail lineslong-tail lines Return on sales is easy to understand as a Return on sales is easy to understand as a

mark-upmark-up, a charge to the consumer, a charge to the consumer

Problems for ROSProblems for ROS

Really understanding risksReally understanding risks ScenariosScenarios Covariation and regressionCovariation and regression Catastrophes and other unexperienced lossesCatastrophes and other unexperienced losses

Sorting out the Cost of Risk from the other Sorting out the Cost of Risk from the other returns on capitalreturns on capital

Product pricing - but that’s a different Product pricing - but that’s a different session!session!

Respect for DiversityRespect for Diversity

There is a wide diversity of opinions among actuaries There is a wide diversity of opinions among actuaries and economists who have thought seriously about profit and economists who have thought seriously about profit margins.margins.

Most rate regulation surrounds auto insurance, for Most rate regulation surrounds auto insurance, for which all of the models generally get reasonable results.which all of the models generally get reasonable results.

We should all show a professional attitude towards We should all show a professional attitude towards those whose conclusions are different from our own.those whose conclusions are different from our own.

Don’t assume that something that works well in Don’t assume that something that works well in practice is on a weak intellectual foundation!practice is on a weak intellectual foundation!