Richard A. Derrig Ph. D. OPAL Consulting LLC Wharton School University of Pennsylvania
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Transcript of Richard A. Derrig Ph. D. OPAL Consulting LLC Wharton School University of Pennsylvania
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.