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Ratemaking and Economic Profit Loads: An Overview of Modeling Approaches. Richard A. Derrig Ph. D. OPAL Consulting LLC Wharton School University of Pennsylvania. CAS Ratemaking Seminar March 13-14, 2006. GO WITH THE FLOW I. AN EGG TO-DAY IS BETTER THAN

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slide1
Ratemaking and Economic Profit Loads:

An Overview of Modeling Approaches

Richard A. Derrig Ph. D. OPAL Consulting LLCWharton SchoolUniversity of Pennsylvania

CAS Ratemaking Seminar

March 13-14, 2006

go with the flow i
GO WITH THE FLOW I

AN EGG TO-DAY

IS BETTER THAN

A HEN TOMORROW

Benjamin Franklin

Poor Richard’s Almanack

slide3
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.

slide4
Table 2ACCIDENT YEAR LOSS PAYMENT PATTERNS

* Fire, Allied Lines, Inland Marine, Earthquake, Glass, Burglary and Theft.

Source: IRS Revenue Ruling 2005-49.

agenda
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
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
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 Line Asset Income by Line Rate of Return or Premium Regulation

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

Surplus

selecting the models
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 models9
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 models10
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
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
allocation of surplus
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
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
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
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.
using the capital asset pricing model
USING THE CAPITAL ASSET PRICING MODEL
  • 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+ bA (rm - rf)

where rf = risk-free ratebA = 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%)
aib irr model 2003 2005
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 200532
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
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.
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