profit margins in general insurance pricing (a critical assessment of approaches) nelson henwood,...

Profit Margins In General Insurance Pricing

(A Critical Assessment of Approaches)

Nelson Henwood, Caroline Breipohl and Richard Beauchamp

New Zealand Society of Actuaries Conference, Rotorua13 November 2002

New Zealand Society of Actuaries Conference November 2002

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

Paper’s 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


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


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


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


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


CAPM to Determine Return

Fairley’s methodology, the “Insurance CAPM”, uses an underwriting (or liability) beta to describe insurance risk

L = Cov (rL, rm) / Var (rm)

Rewards only systemic risk

Insurance profit expected to be nil

Very controversial

Alternative formulation given by Feldblum

F = 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 Fairley’s minimum risk portfolio


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


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


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


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 company’s 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


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


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

profit margins in general insurance pricing (a critical assessment of approaches) nelson henwood,...

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