1 Pricing the Insurance Product The Convergence of Actuarial and Financial Perspectives Richard A. Derrig President, OPAL Consulting LLC CAS Ratemaking Seminar March 7-9, 2007 Atlanta, GA

2 AN EGG TODAY IS BETTER THAN A HEN TOMORROW Benjamin Franklin Poor Richard’s Almanac

3 Actuarial v Financial View of Pricing Actuarial View: Price Dynamics in Insurance Markets Risk = Volatility of Losses Managed for Risk, e.g. Reinsurance Policy and Accident Year Perspective Financial View: Price Dynamics in Asset Markets Risk = Volatility of Returns Managed for Risk, Capital Allocation Calendar Year Perspective

4 Discussion Items A short history of pricing models – Concepts A short history of pricing models – Comments A short history of pricing models - Regulation Practical Research – Risk Premium Project Going Forward ->

5 A Short History of Pricing - Concepts 1. Budget period – Supply side provision of +5% (+2.5 for WC) 2. Investment offset –Calendar year acct (ISO,Biger-Kahane) 3. CAPM return: Returns offset w income at risk-free (Fairley, Hill) 4. Include taxes, (Myers-Cohn), 2 tax rates (Hill-Modigliani) 5. Perspective: Policyholder, Shareholder (NCCI, Cummins, Taylor) 6. PV taxes independent of risk, (Myers, Derrig) 7. Insurance is an option (Krauss-Ross, Doherty-Garven, Derrig) 8. Insolvency put in prices (Butsic, Cummins-Allen-Phillips) 9. Allocate capital (costs): Insolvency put equal at the margin (Myers-Read); Capital and risk management, catastrophes, (Zanjani); Testing prices for frictional costs, (Cummins-Phillips-Lin)

6 A Short History of Pricing - Comments 1. Budget period – Supply side provision of +5% (Company) 2. Investment Offset- Calendar year pricing (Company) 2. CAPM return: Returns offset w risk-free income (Equilibrium) 3. Include taxes, Myers-Cohn (Policyholder) 4. Perspective: Policyholder, Shareholder (Equilibrium) 5. PV taxes independent of risk, (Myers Theorem) 6. Insurance is an option (Price is exchange option value) 7. Insolvency put in prices (Price is less than fully guaranteed price) 8. Allocate capital (Costs): Insolvency put equal at the margin (Equilibrium); Capital and risk management, catastrophes, (Frictional costs); Testing prices for frictional costs (Taxes, RM, Capital)

7 A Short History of Pricing – Regulation (Massachusetts) Jurassic Period (till 1972): U= +5%; +2.5 for WC. ISOsic Period (1971- ):State X, OP target, U is Residual Cliffisic Period ( ): OP= 3.5%, U is Residual Stone Age ( ): One Period Cash Flow; Target Rate of Return; U is Residual; CAPM Target & Liability Risk Adjustment in Equilibrium NCCIsic Age (1980- ): WC Internal Rate of Return Myerscohnic Age ( ) : Policyholder NPV AIBisic Age (2003- ): IRR policyholders/shareholder Accounts, Cash Subrogation explicit, U is Residual

8 Liabilities-Surplus-Profit

9 Practical Research – Cost of Capital Risk Premium Project: CAS funded, 20 years of literature ( Summary: Risk Management Newsletter, March 2007 Cummins-Phillips (2005) => P&C Average Market Risk (Equity beta = 1) Frictions matter additionally (FF Size and Distress Factors Significant) Line of Insurance Matters for COC Auto WC Average, Other lines above Personal Average, Commercial above average Cap weighted avg, equal weight avg differ

10 Practical Research – Allocation of Capital Merton Perold (1995): Allocation to Divisions, Acquisitions Myers-Read (2001): Fair allocation at the margin retains constant insolvency put and adds up Zanjani (2002): Monitoring, Agency Costs => Economize Capital, Risk Management/Diversification Cummins-Phillips-Lin (2006): Prices inverse to insolvency risk, reflect Myers-Read allocation, underwriting and market risk unrelated, depend on capital structure and downside risk aversion

11 Practical Research: Equity Risk Premium Equity Risk Premium Puzzle (1985) - Realized returns above levels arising from risk aversion Research ( ) - Many approaches using dividend models, analysts, financial economists, behavior economists yield wide range of estimates, -1% to 9%, depending on method & definition. Derrig-Orr (2004) -Compares most of the above; adjusts all to single definition, range narrows to about 5% to 9% (e.g. negative 0.3%->5.5%) Welch–Goyett (2006) - IS and OOS prediction tests 1month,1 year, 5 year ERP - Data , predict & ,74-75 oil - Fin Ratios/OLS, predictions poor, last 30 poorer. - Running average predicts as well as any Fin Ratio model

12 Going Forward  Specification and quantification of “frictions” = non-systematic risk management and capital charges. Actuarial and finance converging still, adopt the central “liquidity” variable? Pricing regulation (when it exists) is stuck in the ’70s. Low returns for P&C? Swiss Re Profitability (2006) Integration of Allocation and ERM

13 REFERENCES Automobile Insurers Bureau of Massachusetts, Underwriting Profit Filing for 2006 Rates, DOI Docket R Biger, Nahum and Yehuda Kahane Risk Considerations in Insurance Ratemaking, Journal of Risk and Insurance, 45:1, Butsic, R.P., Capital Allocation for Property-Liability Insurers: A Catastrophe Reinsurance Application, Casualty Actuarial Society Forum, Spring, Cummns, D., Derrig R. and R. Phillips, A Report on the CAS COTOR Risk Premium Project, Risk Management Newsletter. Cummins, D., Harrington, S., Fair Rate of Return in Property-Liability Insurance. Kluwer Academic Publishers, Boston. Cummins, D., Phillips R., Estimating the Cost of Equity Capital For Property-Liability Insurers, Journal of Risk and Insurance, 72, 3, Cummins, D., Phillips, R., Effects of Capital Allocation on Pricing in Property-Liability Insurance: An Investigation into the Pricing of Intermediated Risks, Working Paper. D’arcy, Stephen P. and Michael Dyer, Ratemaking: A Financial Economics Approach, Proceedings of the Casualty Actuarial Society, Vol. 84, Derrig, R., Theoretical Considerations of the Effect of Federal Income Taxes on the Investment Income in Property-Liability Ratemaking, Journal of Risk and Insurance, 61, Derrig, R., Orr, E., Equity Risk Premium: Equity Risk Premium: Expectations Great and Small, North American Actuarial Journal, 8, Derrig, R., Solvency Levels and Risk Loadings Appropriate for Fully Guaranteed Property-Liability Insurance Contracts: A Financial View, Financial Models of Insurance Solvency, Cummins, D., and Derrig, R., (Eds), Kluwer Academic Publishers, Boston. Doherty, N., Garven, J., Price Regulation in Property-Liability Insurance; a Contingent Claims Approach. Journal of Finance, 41,

14 REFERENCES Fairley, W., Investment income and profit margins in property-liability insurance: theory and empirical results. Bell Journal of Economics, 10, Froot, Kenneth A., Risk Management, Capital Budgeting and Capital Structure Policy for Insurers and Reinsurers, Working Paper, Harvard Business School, Cambridge, MA. Goyal, A., Welch, I., A Comprehensive Look at the Empirical Performance of Equity Premium Prediction, Yale ICF Working Paper No Hill, Raymond D., Profit Regulation in Property-Liability Insurance, Bell Journal of Economics, Vol. 10, Hill, R., Modigliani, F., The Massachusetts model regulation in nonlife insurance: an appraisal and extensions. In: Cummins, D., Harrington. S. (Eds.), Fair Rate of Return in Property- Liability Insurance. Kluwer Academic Publishers, Boston. Kahley, William J. and Halliwell, Leigh J.,1992. The NCCI Internal Rate of Return and Cost of Capital Models, NCCI Digest, 7:4, p.37. Karl, K., Laster, D., The U.S. Equity Risk Premium: Framing Reasonable Expectations, Insights, Swiss Re, Zurich. Kozik, Thomas J., and Aaron M. Larson, The n-Moment Insurance CAPM, Proceedings of the Casualty Actuarial Society, LXXXVII, (May). Kozik, Thomas J., Underwriting Betas - The Shadows of Ghosts, Proceedings of the Casualty Actuarial Society, LXXXI, Kraus, A., Ross, S., The Determination of Fair Profits for the Property-Liability Insurance Firm, Journal of Finance, 37, Merton, R., Perold, A., Theory of Risk Capital in Financial Firms. Journal of Applied Corporate Finance 6, Myers, S., Cohn, R., A discounted cash flow approach to property-liability insurance rate regulation. In: Cummins, D., Harrington, S. (eds.), Fair Rate of Return in Property-Liability Insurance. Kluwer Academic Publishers, Boston.

15 REFERENCES Myers, S., Read, J., Capital allocation for insurance companies, Journal of Risk and Insurance 68, National Association of Insurance Commissions, Report of the Investment Income Task Force to the NAIC. Philips, R.D., Cummins, J.D., Allen, F., Financial Pricing of Insurance in the Multiple-Line Insurance Company, Journal of Risk and Insurance, 65:4, Sherris, M., van der Hoek, J., (2004), Capital Allocation in Insurance: Economic Capital and the Allocation of the Default Option Value, Proceedings of the 14th AFIR International Colloquium, Boston, MA, Swiss Re, Measuring Underwriting Profitability of the Non-Life Industry, Sigma Series, Zurich. Taylor, G., Fair Premium Rating Methods and the Relations Between Them, Journal of Risk and Insurance, 61:4, Zanjani, G., Pricing and Capital Allocation in Catastrophe Insurance, Journal of Financial Economics 65,