CAS Ratemaking Seminar RCM1 Logic Fallacies and Paradoxes

CAS Ratemaking Seminar RCM-1 Logic, Fallacies, and Paradoxes in Risk/Profit Loading in Ratemaking: A Socratic Dialogue Introductory Remarks by Glenn Meyers ISO Innovative Analytics March 17, 2008

Insurer Risk and Capital Management Perspective • Risk based capital – The insurer's risk, as measured by its stochastic distribution of outcomes, provides a meaningful yardstick that can be used to set capital requirements. • Insurer risk management – The insurer manages its business to get the best return on its cost of capital.

Steps for Insurer Capital Management in Ratemaking • • Determine total capital for insurer Determine rate of return on that capital Allocate capital to business segment Calculate cost of business segment holding that allocated capital – My remarks today address this part of the problem.

Insurer Risk Management • Reserve Risk contributes to the need for capital and hence it contributes to the ($) cost of capital. • How long you need to hold capital is a consideration in determining an acceptable price.

The Cash Flow for Underwriting Insurance • Investors provide capital – Through the insurer they: • Receive premium income • Pay losses and other expenses • Receive investment income – Invested at interest rate i% • Release capital as liabilities become certain.

Net out the loss and expense payments • Investors provide capital – Through the insurer they: • Receive profit provision in the premium • Receive investment income from capital as it is being held. • Release capital as liabilities become certain. • We want the present value of the income to be equal to the capital invested at the rate of return for equivalent risk

Define Terms • Allocated Capital invested in year t • Provision for Profit • Insurer’s return on invested assets • Insurer’s target return on capital Ct P i r

Calculating the Profit Provision

Calculating the Profit Provision Another Formula

Sample Calculation Profit = 1, 348 = 2. 2% of Initial Liability

Prediction This how actuaries will include the cost of capital in future insurance costing. Main Obstacles to Overcome • Fuzzy relationship between risk and capital – Insurers are starting to build internal capital models – Examples EU Solvency II, British FSA, S&P • Quantification of all risks – – Underwriting risk and reserving risk Asset risk - Several commercial models Operational risk Other • Consensus – Will not come until above issues are substantially settled.