Profit Margins In General Insurance Pricing (A Critical Assessment of Approaches)

1
Profit Margins In General Insurance Pricing(A
Critical Assessment of Approaches)

• Nelson Henwood, Caroline Breipohl and Richard
  Beauchamp
• New Zealand Society of Actuaries Conference,
  Rotorua
• 13 November 2002

2
Introduction

• Problem at Hand
• Assessment of methods for determination of profit
  margins in General Insurance
• Motivation
• Explore current thinking within actuarial
  profession
• The Pricing Process
• Papers focus only on profit margin
• Theoretical cost plus premium
• Input to rate setting process
• Approach
• Critically assess methods to determine profit
  margin
• Consider some fundamental and practical elements
  of each method

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Outline of our Discussion

• Types of Risk
• Surplus-Return Framework
• CAPM to Determine Return
• The Myers-Cohn Approach
• An Options Pricing Approach
• Utility Theory
• Proportional Hazards Transforms
• Concluding Remarks

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Types of Risk

• Process Risk (or Diversifiable Risk)
• Risk associated with an individual policy
• Diversification can minimise Process Risk
• Parameter Risk (or Systemic Risk)
• Risks affecting many policies simultaneously
  (e.g. change in claims frequency)
• Cannot be diversified away
• What risk should be rewarded?
• Theories differ

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Surplus-Return Framework

• Familiar intuitive
• Two key requirements
• amount of surplus allocated to a block of
  business
• rate of return earned on this surplus
• Surplus allocation - reflect variability of
  business
• Simplistic, notional approaches
• Margin above statutory minimum
• Standard deviation principle
• Methods recognising covariability
• Target return on surplus

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Surplus-Return Framework (cont.)

• Appeal
• Intuitive capital supporting insurance business
  must earn an appropriate return
• Riskier business requires a higher return
• Difficulties
• Dependent on capital allocation return
  approaches
• Estimating applicable risk parameters is not easy
  in practice

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CAPM to Determine Return

• Fairleys methodology, the Insurance CAPM, uses
  an underwriting (or liability) beta to describe
  insurance risk
• bL Cov (rL, rm) / Var (rm)
• Rewards only systemic risk
• Insurance profit expected to be nil
• Very controversial
• Alternative formulation given by Feldblum
• bF Cov (rL, rp) / Var (rp)
• Diversification achieved through holding minimum
  risk portfolio of insurance business
• No investment freedom for assets backing
  technical liabilities
• Cannot achieve Fairleys minimum risk portfolio

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CAPM (cont.)

• CAPM theory relies on some quite restrictive
  assumptions
• Difficulty of estimating the liability beta
• Inferred v. Accounting betas
• Empirical measurement dependant upon
• Time period
• Market proxy
• Insurance companies included in study

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The Myers-Cohn Approach

• Some appealing aspects
• Discounted cash flow approach
• Desire to be fair to both policyholders and
  shareholders
• Risk-adjusted discount rate key to this model
• Difficult to separate from Insurance CAPM
• Hence subject to inherent weaknesses of Insurance
  CAPM
• Relatively insensitive to the level of capital

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An Options Pricing Approach

• Appeal
• Parallels between Options as a contingent
  payment, and Insurance
• Compared to other models the Black-Scholes Model
  parameters appear relatively easy to determine
• Reward for inherent risk
• Process (and parameter) risk
• Major concerns
• Difficulty of matching traded option types to the
  insurance situation
• Weakness of the continuous hedging argument in
  the insurance context

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Utility Theory

• Appeal
• Theory closely aligned with intuitive view of
  appetite for risk
• Higher return required to engage in more
  uncertain situation
• Takes into account insurance companys current
  portfolio
• Systemic and diversifiable risk rewarded
• Practical difficulties
• Derivation of utility function
• Parameter describing risk aversion is not readily
  determined
• The Exponential utility function leads to profit
  loading that is independent of wealth

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Proportional Hazards Transforms

• Appeal
• Method to derive margin for uncertainty that does
  not rely on any financial or economic theory
• Numerical methods effective for processing
  complex loss distributions
• Consistent valuation of risk across different
  categories of business
• Reward for inherent risk
• Process (and parameter) risk
• Difficulties
• Risk aversion parameter not readily determined
• Difficult to understand and communicate

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Concluding Remarks

• Insurers must compete for capital
• Shareholders require a competitive return
• Management is charged with delivering this return
  to shareholders
• Management generally targets a return based on
  market conditions
• Actuary must set rates to meet management
  objectives
• Should challenge and test appropriateness of the
  required return
• Various theoretical frameworks may assist in
  appropriate circumstances