Richard A. Derrig Ph. D.

OPAL Consulting LLC

Wharton SchoolUniversity of Pennsylvania

CAS Ratemaking SeminarMarch 13-14, 2006

Ratemaking and Economic Profit Loads:An Overview of Modeling Approaches

GO WITH THE FLOW I

AN EGG TO-DAY

IS BETTER THAN

A HEN TOMORROW

Benjamin Franklin

Poor Richard’s Almanack

Table 1ACCIDENT YEAR LOSS PAYMENT PATTERNS

Multiple Peril Lines incl. Homeowners/Farmowners, Commercial Multiple Peril, Special Liability, Ocean Marine, Aircraft (all perils), and Boiler & Machinery.Source: IRS Revenue Ruling 2005-49.

Private Passenger CommercialAutomobile Auto/Truck Worker's Medical Other International

Year Multiple Peril * Liability/Medical Liability/Medical Compensation Malpractice Liability (Composite)

AY + 0 59.7445 43.1926 28.8244 28.2489 7.3447 14.9618 40.9985

AY + 1 21.2902 29.0082 26.1626 29.6249 21.6744 21.2494 24.8454

AY + 2 6.2978 12.3625 17.8168 13.4260 24.2917 18.0763 11.6583

AY + 3 3.7334 7.3684 12.2533 6.4585 15.8409 9.9288 7.1198

AY + 4 4.1122 3.9413 6.5704 4.1717 12.9464 9.0569 5.6234

AY + 5 0.5824 1.9075 3.3239 1.8437 4.3014 7.3016 2.0325

AY + 6 1.2933 1.0153 2.0938 2.7611 3.3116 7.0452 2.1195

AY + 7 0.5903 0.4535 1.1121 1.9017 2.7577 2.2955 0.8552

AY + 8 1.0596 0.2703 0.5796 1.1559 2.0475 3.4791 1.0266

AY + 9 -0.0821 0.1159 0.3700 2.0515 1.2471 1.2223 0.1531

AY + 10 0.5226 0.1159 0.3700 2.0515 1.2471 1.2223 0.1531

AY + 11 0.5226 0.1159 0.3700 2.0515 1.2471 1.2223 0.1531

AY + 12 0.3332 0.1159 0.1530 2.0515 1.2471 1.2223 0.1531

AY + 13 N/A 0.0171 N/A 2.0515 0.4951 1.2223 0.1531

AY + 14 N/A N/A N/A 0.1501 N/A 0.4936 0.1531

AY + 15 N/A N/A N/A N/A N/A N/A 2.8020

Sum 100.0000 100.0003 99.9999 100.0000 99.9998 99.9997 99.9998

Table 2ACCIDENT YEAR LOSS PAYMENT PATTERNS

* Fire, Allied Lines, Inland Marine, Earthquake, Glass, Burglary and Theft.Source: IRS Revenue Ruling 2005-49.

Year

SpecialProperty

*

Auto Physical Damage

Fidelity, Surety

Financial Guaranty,Mortgage Guaranty

Other (Including

Credit, Accident

and Health)

AY + 0

62.9320

89.6468

38.3328 4.0723

69.1729

AY + 1

25.5631

10.0377

20.5156

36.6916

22.0439

AY + 2

5.7525

0.1578

20.5758

29.6180

4.3916

AY + 3

5.7525

0.1578

20.5758

29.6180

4.3916

Sum100.000

1 100.000

1 100.000

0 99.9999 100.0000

AGENDA

I. Regulatory History

II. Economic Pricing Models

III. Key Parameters

IV. Investment Returns and Taxes

V. Estimating the Cost of Capital

VI. Estimating the Risk Premium

VII. Allocation of Surplus

Regulatory Profit Modeling History

Jurassic Period (till 1972): U= +5%; +2.5 for WC. ISOsic Period (1971- ):State X, OP target, U is Residual Cliffisic Period (1972-1975): OP= 3.5%, U is Residual Stone Age (1975-1980): One Period Cash Flow; Target

Rate of Return; U is Residual; CAPM Target & Liability Risk Adjustment in Equilibrium

NCCIsic Age (1980- ): WC Internal Rate of Return Myerscohnic Age (1981-2003) : Policyholder NPV AIBisic Age (2003- ): IRR policyholders/shareholder

Accounts, Cash Subrogation explicit, U is Residual

THE PROPERTY-CASUALTY INSURANCE INDUSTRY CASE

Income = Underwriting + Investment Underwriting Income = Premiums - (Expenses + Losses)

- Income Taxes Investment Income = Asset Income - Income Taxes Beginning Assets = Capital (Equity and Debt)

= Surplus (Market Value) Property-Casualty Rate of Return is

P/C Rate of Return Regulation is by line of Business (Auto, Workers Comp, Marine,...) by State

Problems: Surplus by LineAsset Income by LineRate of Return or Premium Regulation

Premiums - (Expenses + Losses) + Asset Income - Income TaxesSurplus

SELECTING THE MODELS

IA. Present Value Cash Flow DCF Models Prospective or Demand View Myers-Cohn Model is the Paradigm Only Policyholder Flows are Valued Premium Equals Risk-Adjusted Discounted Value of

Losses, Expenses and Underwriting and Investment Income Taxes

Expected Risk Loading Percentage for Company Calculated From Risk-Adjustment (1 - (Zero Risk Premium/Risk-Adjusted Premium))

Expected Rate of Return to Company Not Calculated; Depends on Investment Portfolio

SELECTING THE MODELS

IB. Internal Rate of Return Models Investor or Supply View NCCI Model is the Paradigm AIB IRR 2003-2006 Model is New Shareholder Flows are Valued Premium is Residual in Solving Target Rate of Return

is Discount Rate of Shareholder Investment and Return Flow with Zero NPV (IRR)

Target Rate of Return to Company is Cost of Equity and Debt Capital

SELECTING THE MODELS

IC. CalendarYearAccounting Models Retrospective or Company View; Value for Prospective

Use Depends on Assumptions (e.g.., steady growth) One-Period Company Balance Sheet is the Paradigm Calendar Year Company Flows are Valued Premium should be Residual in Solving Cost of Capital

Equals After-Tax Investment Plus Underwriting Return Levered on Surplus as Capital for Calendar Year

Rate of Return to Company is Bottom Line. By Line Results Depend on Allocation of Net Worth

SUPPLY AND DEMAND

NPV Models Calculate Fair Value Demand Price and Assume Supply at That Price

IRR Models Calculate Fair Value Supply Price and Assume Demand at That Price

Both Models Depend on the Parametric Input Values Competitive Markets Assume Equality of Model Prices CY Accounting Models Calculate Company Prices Real Incomplete Markets Have a Wide Range of Prices

SELECTING THE PARAMETERS

Key Parameters DCF IRR AcctBasic Structure Policy or Policy Year Cash

FlowsPolicy or Policy Year CashFlows

Calendar Year FlowsStacked Policy Flows

Aggregate Levels Losses Expenses Premiums

Outside ModelOutside ModelOutside Model

Outside ModelOutside ModelOutside Model

Company or IndustryDatabases (Best's)

Cash Flows Premium Commission Co. Expense Loss

ALAE ULAE Surplus Taxes Investment Income

Empirical Study/ModelPremium FlowEmpirical Study (Mass)Empirical Study/Simulation ModelsLoss Flow1/2 Loss, 1/2 Co. Exp.Model/TheoryModel AlgebraTaxes Only

Empirical Study/ModelPremium FlowEmpirical Study (Mass)Empirical Study/Simulation ModelsLoss Flow1/2 Loss, 1/2 Co. Exp.Model/TheoryModel AlgebraAsset Income Less Tax

Company or Industry TimeSeries With or WithoutAdjustments and Allocations(GAAP, SAP)

ALLOCATION OF SURPLUS

All Models Need by Line Surplus (Beginning Assets) Allocation Allocation Methods (NAIC Report, 1984)

– Proportional to Premiums (Book)

– Proportional to Reserves (Book)

– Proportional to Discounted Reserves (Market). Problems:

– How much surplus is “needed”?

– All surplus stands behind all lines.

– How much surplus should be used for Rate or Premium Regulation?

IRR vs. CYAM I

General Issues: CYAM commits and values surplus in the

single year of exposure. IRR commits surplus in proportion to any outstanding liabilities possibly over many years.

CYAM earns a return (profit) at the end of a single year, like a company. IRR earns a return (profit) as liabilities decrease, as risk is resolved, like a policy.

IRR vs. CYAM II

General Issues: CYAM assumes projected policy liabilities

(reserves) will be like calendar year reserves from old policies and some portion will be available for investment for exactly one year.

IRR assumes reserves are exactly as expected in magnitude and timing, and will be available for investment, possibly over many years.

IRR vs. CYAM III

Specific Issue: Physical Damage CYAM assumes projected policy liabilities will

be like calendar year payments net of recoveries and a small portion will be available for investment for exactly one year.

IRR assumes liabilities are exactly as expected in magnitude (gross) and timing, income consists of premium plus (later) subrogation recoveries.

Bodily InjuryModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Calendar Year / Block Surplus (Surplus backs policy exposure year)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.0

0

Years From Effective Date

As

se

ts /

Pre

miu

m

Surplus (67%)

Operating Profit at end of period (3.56%)

Underwriting Operation (L+E)

0.9644

1.67

1

Note: Underwriting Operations flows come from 100H-1A Exhibit 4, Column 3

Bodily InjuryModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Calendar Year / Block Surplus (Surplus backs policy exposure year)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.0

0

Years From Effective Date

As

se

ts /

Pre

miu

m

Surplus Investment Profit (5.13%)

Surplus (67%)

Operating Profit at end of period (3.56%)

Underwriting Operation (L+E)

0.9644

1.67

1

Note: Underwriting Operations flows come from 100H-1A Exhibit 4, Column 3

Bodily InjuryModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Policy Life / Surplus Flow (Surplus backs outstanding liabilities)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.0

0

Years From Effective Date

As

se

ts /

Pre

miu

m

Total Profit at end of period (8.37%)

Surplus (67% * (L+E) )

Underwriting Operation (L+E)

1.67

1.

Note: Underwriting Operations flows come from 100H-1A Exhibit 4, Column 3

Property Damage LiabilityModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Calendar Year / Block Surplus (Surplus backs policy exposure year)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Surplus (67%)

Operating Profit at end of period (3.56%)

Underwriting Operation (L+E)

0.9644

1.67

1.

Note: Underwriting Operations flows come from 100H-1B Exhibit 4, Column 3

Property Damage LiabilityModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Calendar Year / Block Surplus (Surplus backs policy exposure year)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Surplus Investment Profit (5.13%)

Surplus (67%)

Operating Profit at end of period (3.56%)

Underwriting Operation (L+E)

0.9644

1.67

1.

Note: Underwriting Operations flows come from 100H-1B Exhibit 4, Column 3

Property Damage LiabilityModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Policy Life / Surplus Flow (Surplus backs outstanding liabilities)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Total Profit at end of period (8.37%)

Surplus (67% * (L+E) )

Underwriting Operation (L+E)

1.67

1.

Note: Underwriting Operations flows come from 100H-1B Exhibit 4, Column 3

Physical DamageModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Calendar Year / Block Surplus (Surplus backs policy exposure year)

-0.10

1.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Surplus (67%)

Operating Profit at end of period (3.56%)

Underwriting Operation (Net L+E)

0.9644

1.

Note: Underwriting Operations flows come from 100H-1C Exhibit 4, Column 3

1.67

NET

Physical DamageModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Calendar Year / Block Surplus (Surplus backs policy exposure year)

-0.10

1.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Surplus Investment Profit (5.13%)

Surplus (67%)

Operating Profit at end of period (3.56%)

Underwriting Operation (Net L+E)

0.9644

1.

Note: Underwriting Operations flows come from 100H-1C Exhibit 4, Column 3

1.67

NET

Physical DamageModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Policy Life / Surplus Flow (Surplus backs outstanding liabilities)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Total Profit at end of period (8.37%)

Surplus (67% * Gross L+E / 1.31 )

Surplus / Gross L+E Overlap

Underwriting Operation (Gross L+E)

1.

Note: Underwriting Operations flows come from 100H-1C Exhibit 4, Column 3

1.67

Gross L+E / Net L+E = 1.31

GROSS

Physical DamageModeling the Asset / Premium / Surplus / Pre-Tax Profit Flow

Policy Life / Surplus Flow (Surplus backs outstanding liabilities)

0.00

1.00

2.00

0.25

0.50

0.75

1.00

2.00

3.00

4.00

5.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Total Profit at end of period (8.37%)

Surplus (67% * Gross L+E / 1.31 )

Underwriting Operation (Net L+E)

1.

Note: Underwriting Operations flows come from 100H-1C Exhibit 4, Column 3

1.67

Gross L+E / Net L+E = 1.31

NET

SELECTING THE PARAMETERS

Key Parameters DCF IRR Acct

Investment Assets Taxable Bonds Tax-Exp. Bonds Comm. Stock Preferred Stock Other Assets

Company PortfolioBest's, Fed. Flow of Funds

Company PortfolioBest's, Fed. Flow of Funds

Annual Statements

Returns Risk-Free

Historical: Fed. Res. G-13& Ibbotson AssociatesProspective: WSJ Daily,Futures, Options, Models.

Historical: Fed. Res. G-13& Ibbotson AssociatesProspective: WSJ Daily,Futures, Options, Models.

Not Applicable

Returns Risky

Risk-free & Risk PremiumHistorical: IbbotsonAssociatesProspective: Risk-Free &Historical Risk Premium

Risk-free & Risk PremiumHistorical: IbbotsonAssociatesProspective: Risk-Free &Historical Risk Premium

Underwriting Income,Investment Income andCapital Gains

CAPM is a simple descriptive linear model of (all) asset returns. For an Asset A, one period returns rA are expected (^) to be:

rA = rf + A (rm - rf)where rf = risk-free rate

A = asset beta (covariance of asset returns with market) rm - rf = MRP

= market risk premium Market Risk Premium (MRP) is Market Rate of Return - Risk-Free Rate

of Return.

MRP is historically quite variable; prospective MRP is Risk Premium Puzzle (Derrig/Orr, 2004)

Traditional/Ibbotson Estimation uses all data average (1926-2005).

Problems:

Are there Better Estimates? What period of time to use? (All = 8.5%, 30 years = 5.0%)

USING THE CAPITAL ASSET PRICING MODEL

Key Parameters DCF IRR AcctTaxes Underwriting

ProspectivePremium Earned 35% Unearned 20% Losses 35% (Discounted - Revenue Ruling 94-47)

ProspectivePremium Earned 35% Unearned 20% Losses 35% (Discounted - Revenue Ruling 94-47)

Historical

Taxes Investment Taxable Bonds Tax-ExemptBonds Stocks Dividends Cap Gains Other Assets

35%Implicit 25-35% plus Post'86 Tax 35%, 70% exclusion plusPost '86 Proration35%35%

35% Post '86 Tax 35%, 70% exclusion plusPost '86 Proration35% (1-value of deferral)35%

Actual Annual Statement, Underwriting andInvestment TaxesCombined, NOLS, AMT

Taxes Alternate Minimum Tax

? ?

?

SELECTING THE PARAMETERS

SELECTING THE PARAMETERSKey Parameters DCF IRR Acct

Cost of Capital/Risk Adjustment

Underwriting Beta

Market Risk Premium

(Ibbotson Associates) Risk Premium (Insurance Data)

Methods

Dividend Growth

CAPM

(Value Line

Survey Data)

Historical Analysis

Miscellaneous

Finance Charges

Uncollected Premium

Policyholder Dividends

Uninvested Assets

Empirical Study

Empirical Study

Empirical Study

Delayed Prem, Deferred Taxes/ Subrogation Recoveries

Empirical Study

Empirical Study

Empirical Study

Delayed Prem, Deferred Taxes/ Subrogation Recoveries

AIB IRR Model (2003-2005)

Built from first principles by RAD and Kim Scott, VP and Chief Actuary, Auto Insurers Bureau of Massachusetts

Department (State Rating Bureau) proposed several alternative IRR formulations, all were rejected or withdrawn

Features: All Cash Flows, PH account funded at RF discounted liabilities (excess returned to SH proportional to resolved liabilities), PH cash deficiencies funded by SH excess of surplus

Physical Damage has gross payments (PH liabilities) and subrogation recoveries separated with large cash deficiency (disputed by Department).

AIB IRR Model (2003-2005)

Full Model, description and formulas in 2006 Filing Accepted by Department (State Rating Bureau) for

2006 Still disputed Physical Damage treatment of surplus

commitment and subrogation recoveries Solution may be in uninvested assets (subrogation

recoveries & deferred taxes) as countrywide invested assets are (a few percentage points) less than loss and unearned premium reserves (policy liabilities).

References

Automobile Insurers Bureau of Massachusetts, 2005 Underwriting Profit Filing for 2006 Rates, DOI Docket R2005-09.

Cummins, J. David, 1990, “Multi-Period Discounted Cash Flow Ratemaking Models in Property Liability Insurance,” Journal of Risk and Insurance, V. 57, No. 1, 79-109.

Cummins, J. David and Richard D. Phillips, 2005, “Estimating the Cost of Equity Capital for Property-Liability Insurers”, Journal of Risk and Insurance, Vol. 72, No. 3, 441-478

Derrig, Richard A., 1987, “The Use of Investment Income in Massachusetts Private Passenger Automobile and Workers’ Compensation Ratemaking,” Chapter 6, J.D. Cummins and S.E. Harrington, eds. Fair Rate of Return in Property-Liability Insurance, Hingham, MA, Kluwer-Nijhoff

Derrig, Richard A., 1993, “Price Regulation in US Automobile Insurance – A Case Study of Massachusetts Private Passenger Automobile Insurance 1978-1990”, The Geneva Papers on Risk and Insurance No. 67 (April), 158-173.

Derrig, Richard A., 1994, “Theoretical Considerations of the Effect of Federal Income Taxes on Investment Income in Property-Liability Ratemaking”, Journal of Risk and Insurance, V. 61, No. 4, 691-709.

Kahley, William J. and Halliwell, Leigh J., 1992 “The NCCI Internal Rate of Return and Cost of Capital Models”, NCCI Digest, V. 7, Issue 4, p. 37.

National Association of Insurance Commissions, 1984, Report of the Investment Income Task Force to the NAIC.

Taylor, Greg, 1994, “Fair Premium Rating Methods and the Relations Between Them,” Journal of Risk and Insurance, Vol. 61, No. 4, 592-615.