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

New Zealand Society of Actuaries Conference November 2002 Introduction n Problem at Hand n Assessment of methods for determination of profit margins in General Insurance n Motivation n Explore current thinking within actuarial profession n The Pricing Process n Paper’s focus only on profit margin n Theoretical “cost plus” premium n Input to rate setting process n Approach n Critically assess methods to determine profit margin n Consider some fundamental and practical elements of each method

New Zealand Society of Actuaries Conference November 2002 Outline of our Discussion n Types of Risk n Surplus-Return Framework n CAPM to Determine Return n The Myers-Cohn Approach n An Options Pricing Approach n Utility Theory n Proportional Hazards Transforms n Concluding Remarks

New Zealand Society of Actuaries Conference November 2002 Types of Risk n Process Risk (or Diversifiable Risk) n Risk associated with an individual policy n Diversification can minimise Process Risk n Parameter Risk (or Systemic Risk) n Risks affecting many policies simultaneously (e.g. change in claims frequency) n Cannot be diversified away n What risk should be rewarded? n Theories differ

New Zealand Society of Actuaries Conference November 2002 Surplus-Return Framework n Familiar & intuitive n Two key requirements n amount of surplus allocated to a block of business n rate of return earned on this surplus n Surplus allocation - reflect variability of business n Simplistic, notional approaches n Margin above statutory minimum n Standard deviation principle n Methods recognising covariability n Target return on surplus

New Zealand Society of Actuaries Conference November 2002 Surplus-Return Framework (cont.) n Appeal n Intuitive: capital supporting insurance business must earn an appropriate return n Riskier business requires a higher return n Difficulties n Dependent on capital allocation & return approaches n Estimating applicable risk parameters is not easy in practice

New Zealand Society of Actuaries Conference November 2002 CAPM to Determine Return n Fairley’s methodology, the “Insurance CAPM”, uses an underwriting (or liability) beta to describe insurance risk  L = Cov (r L, r m ) / Var (r m ) n Rewards only systemic risk n Insurance profit expected to be nil n Very controversial n Alternative formulation given by Feldblum  F = Cov (r L, r p ) / Var (r p ) n Diversification achieved through holding minimum risk portfolio of insurance business n No investment freedom for assets backing technical liabilities n Cannot achieve Fairley’s minimum risk portfolio

New Zealand Society of Actuaries Conference November 2002 CAPM (cont.) n CAPM theory relies on some quite restrictive assumptions n Difficulty of estimating the liability beta n Inferred v. Accounting betas n Empirical measurement dependant upon: n Time period n “Market” proxy n Insurance companies included in study

New Zealand Society of Actuaries Conference November 2002 The Myers-Cohn Approach n Some appealing aspects n Discounted cash flow approach n Desire to be “fair” to both policyholders and shareholders n Risk-adjusted discount rate key to this model n Difficult to separate from Insurance CAPM n Hence subject to inherent weaknesses of Insurance CAPM n Relatively insensitive to the level of capital

New Zealand Society of Actuaries Conference November 2002 An Options Pricing Approach n Appeal n Parallels between Options as a contingent payment, and Insurance n Compared to other models the Black-Scholes Model parameters appear relatively easy to determine n Reward for inherent risk n Process (and parameter) risk n Major concerns n Difficulty of matching traded option types to the insurance situation n Weakness of the continuous hedging argument in the insurance context

New Zealand Society of Actuaries Conference November 2002 Utility Theory n Appeal n Theory closely aligned with intuitive view of appetite for risk n Higher return required to engage in more uncertain situation n Takes into account insurance company’s current portfolio n Systemic and diversifiable risk rewarded n Practical difficulties n Derivation of utility function n Parameter describing risk aversion is not readily determined n The Exponential utility function leads to profit loading that is independent of wealth

New Zealand Society of Actuaries Conference November 2002 Proportional Hazards Transforms n Appeal n Method to derive margin for uncertainty that does not rely on any financial or economic theory n Numerical methods effective for processing complex loss distributions n Consistent valuation of risk across different categories of business n Reward for inherent risk n Process (and parameter) risk n Difficulties n Risk aversion parameter not readily determined n Difficult to understand and communicate

New Zealand Society of Actuaries Conference November 2002 Concluding Remarks n Insurers must compete for capital n Shareholders require a competitive return n Management is charged with delivering this return to shareholders n Management generally targets a return based on market conditions n Actuary must set rates to meet management objectives n Should challenge and test appropriateness of the required return n Various theoretical frameworks may assist in appropriate circumstances