Profit Provisions Should Not Be a Function of the Firm Lee Van Slyke Provisions for Profits and Contingencies Casualty Actuarial Society Ratemaking Conference March, 2000

“Appropriate Standards for Profit Margins” n Book under CAS Book under CAS Book under CAS n Purpose: Highlight the diversity of intellectual activity n Edited by Lee Van Slyke, member of VFAC n Ten authors, led by D’Arcy and McClenahan

CAS Statement of Principles Regarding Ratemaking n 3. A rate provides for the costs associated with an individual risk transfer. n 4. A rate is reasonable and not excessive, inadequate, or unfairly discriminatory if is an actuarially sound estimate of the expected value of all future costs associated with an individual risk transfer.

CAS Statement of Principles Regarding Ratemaking n The rate should include a charge for the risk of random variation from the expected costs. This risk charge should be reflected in the determination of the appropriate total return consistent with the cost of capital and, therefore, influences the underwriting profit provision.

Not a Naïve Approach n Deeply rooted in microeconomic theory u Arrow, Debreu, et al u Borch, n Simple assumptions (axioms) u Do not assume risk is proportional to variance alone u Prices reflect all information

Methods Not Based on the Firm n Chuck McClenahan, “Insurance Profitability” Insurance ProfitabilityInsurance Profitability n Charles Toney, “The Profit Provision” The Profit ProvisionThe Profit Provision n Judy Mintel, “The Confirmed Operating Return Approach” The Confirmed Operating Return ApproachThe Confirmed Operating Return Approach n Rodney Kreps, “Investment-Equivalent Reinsurance Pricing” Investment-Equivalent Reinsurance PricingInvestment-Equivalent Reinsurance Pricing n Lee Van Slyke, “An Axiomatic Basis for Standards of Profit” An Axiomatic Basis for Standards of ProfitAn Axiomatic Basis for Standards of Profit n John Cozzolino, “Capacity”

Profit v. Rate-of-Return. n Profit is a monetary value. In has meaning, even if not expressed as a rate. n Principle: Expected profit is expected cost of capital for a policy. n To determine a rate of profit, the problem is to select the denominator, surplus or sales.

Investment Income: on Policy- Holder Supplied Funds n The real question is the fair-market value of the premiums, losses and expenses n Premiums received to cover sales costs do not provide investments n Premiums received to cover losses do provide investments

Time value of money n Risk-free rate of return is correct. n The fair-market value of liabilities increases, not decreases, with greater uncertainty. n The fair-market value is the present value at the risk-free rate of return plus a charge for the cost of risk.

Problems of ROE n Discounting to reflect risk: Inconsistencies between short-tail lines and long-tail lines. n Basing risk charge on surplus: Strong companies charge less than weak companies n Surplus allocation: How? From what premises? n It is the rates that are regulated, not the rates of return.

Private Passenger Automobile Assumptions (000’s)

Results (000’s)

Rate Equity v. ROE Equity

Rate Regulation

The Real Issues n What is the amount of risk in a given product in a given state per dollar of premium? n What is the capital market's price per unit of risk?

ROS: Not a Naïve Approach n Deeply rooted in microeconomic theory u Arrow, Debreu, et al u Borch, n Simple assumptions u Do not assume risk is proportional to variance alone u Prices reflect all information

The Cost of Risk n Capital has many rewards n One is the reward for putting capital at risk n The reward for risk that capital commands in a competitive market is the cost of risk, or, the risk charge

What Is the Risk of Selling a Policy?

Beta

Leverage n The firm’s financial condition determine its capacity to underwrite risks. n In the book, Cozzolino explores this further.

Solutions for ROE Problems n Return on sales act to clear the market u The proposed margin is right if there is healthy competition u Policy prices reflect policy risks u Capacity is allocated between short-tail and long-tail lines n Return on sales is easy to understand as a mark-up, a charge to the consumer

Problems for ROS n Really understanding risks u Scenarios u Covariation and regression u Catastrophes and other unexperienced losses n Sorting out the Cost of Risk from the other returns on capital n Product pricing - but that’s a different session!

Respect for Diversity n There is a wide diversity of opinions among actuaries and economists who have thought seriously about profit margins. n Most rate regulation surrounds auto insurance, for which all of the models generally get reasonable results. n We should all show a professional attitude towards those whose conclusions are different from our own. n Don’t assume that something that works well in practice is on a weak intellectual foundation!