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Pricing the Insurance Product

The Convergence of Actuarial and Financial Perspectives 1921-2008

Richard A. Derrig

President, OPAL Consulting LLC

CAS Ratemaking Seminar

March 7-9, 2007 Atlanta, GA

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AN EGG TODAY

IS BETTER THAN

A HEN TOMORROW

Benjamin Franklin Poor Richard’s Almanac

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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

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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 ->

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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)

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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)

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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 (1972-1975): OP= 3.5%, U is Residual• Stone Age (1975-1980): 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 (1981-2003) : Policyholder NPV• AIBisic Age (2003- ): IRR policyholders/shareholder

Accounts, Cash Subrogation explicit, U is Residual

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Liabilities-Surplus-ProfitAuto Bodily Injury Liability Insurance

Modeling the Asset / Premium / Surplus / Pre-Tax Profit Flow Policy Life / Surplus Flow

(Surplus backs outstanding liabilities)

0.00

1.00

2.00

Years From Effective Date

As

se

ts /

Pre

miu

m

Total Profit at end of period (8.37%)

Surplus (67% * (L+E) )

Underwriting Operation (L+E)

1.67

1.

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Practical Research – Cost of Capital

• Risk Premium Project: CAS funded, 20 years of literature (http://www.aib.org/rpp/rppsearch.asp.)

• 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

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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

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Practical Research: Equity Risk Premium

• Equity Risk Premium Puzzle (1985) - Realized returns above levels arising from risk aversion Research (1985-2004) - 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 1872-2004, predict 1902-2004 & 1965-2004,74-75 oil - Fin Ratios/OLS, predictions poor, last 30 poorer. - Running average predicts as well as any Fin Ratio model

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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

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REFERENCES• Automobile Insurers Bureau of Massachusetts, 2005. Underwriting Profit Filing for 2006

Rates, DOI Docket R2005-09.• Biger, Nahum and Yehuda Kahane 1978. Risk Considerations in Insurance Ratemaking,

Journal of Risk and Insurance, 45:1, 121-132.• Butsic, R.P., 1999. Capital Allocation for Property-Liability Insurers: A Catastrophe

Reinsurance Application, Casualty Actuarial Society Forum, Spring, 1-70.• Cummns, D., Derrig R. and R. Phillips, 2007. A Report on the CAS COTOR Risk Premium

Project, Risk Management Newsletter.• Cummins, D., Harrington, S., 1987. Fair Rate of Return in Property-Liability Insurance.

Kluwer Academic Publishers, Boston.• Cummins, D., Phillips R., 2005. Estimating the Cost of Equity Capital For Property-Liability

Insurers, Journal of Risk and Insurance, 72, 3, 441-478.• Cummins, D., Phillips, R., 2006. 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, 1997. Ratemaking: A Financial Economics Approach,

Proceedings of the Casualty Actuarial Society, Vol. 84, 301-390.• Derrig, R., 1994. Theoretical Considerations of the Effect of Federal Income Taxes on the

Investment Income in Property-Liability Ratemaking, Journal of Risk and Insurance, 61, 691-706.

• Derrig, R., Orr, E., 2004. Equity Risk Premium: Equity Risk Premium: Expectations Great and Small, North American Actuarial Journal, 8, 45-69.

• Derrig, R., 1989. 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., 1986. Price Regulation in Property-Liability Insurance; a Contingent Claims Approach. Journal of Finance, 41, 1031-1050.

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REFERENCES• Fairley, W., 1979. Investment income and profit margins in property-liability insurance: theory and

empirical results. Bell Journal of Economics, 10, 192-210.• Froot, Kenneth A., 2005. Risk Management, Capital Budgeting and Capital Structure Policy for

Insurers and Reinsurers, Working Paper, Harvard Business School, Cambridge, MA.• Goyal, A., Welch, I., 2005. A Comprehensive Look at the Empirical Performance of Equity

Premium Prediction, Yale ICF Working Paper No. 04-11.• Hill, Raymond D., 1979. Profit Regulation in Property-Liability Insurance, Bell Journal of

Economics, Vol. 10, 172-191.• Hill, R., Modigliani, F., 1987. 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., 2004. The U.S. Equity Risk Premium: Framing Reasonable Expectations, Insights, Swiss Re, Zurich.

• Kozik, Thomas J., and Aaron M. Larson, 2001. The n-Moment Insurance CAPM, Proceedings of the Casualty Actuarial Society, LXXXVII, 168-169 (May).

• Kozik, Thomas J., 1994. Underwriting Betas - The Shadows of Ghosts, Proceedings of the Casualty Actuarial Society, LXXXI, 303-329.

• Kraus, A., Ross, S., 1982. The Determination of Fair Profits for the Property-Liability Insurance Firm, Journal of Finance, 37, 1015-1028.

• Merton, R., Perold, A., 1993. Theory of Risk Capital in Financial Firms. Journal of Applied Corporate Finance 6, 16-32.

• Myers, S., Cohn, R., 1987. 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.

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REFERENCES

• Myers, S., Read, J., 2001. Capital allocation for insurance companies, Journal of Risk and Insurance 68, 545-580. • National Association of Insurance Commissions, 1984. Report of the Investment Income Task Force to the NAIC.• Philips, R.D., Cummins, J.D., Allen, F., 1998. Financial Pricing of Insurance in the Multiple-Line Insurance Company, Journal of Risk and Insurance, 65:4, 597-636.• 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, 559-586. • Swiss Re, 2006. Measuring Underwriting Profitability of the Non-Life Industry, Sigma Series, Zurich.• Taylor, G., 1994. Fair Premium Rating Methods and the Relations Between Them, Journal of Risk and Insurance, 61:4, 592-616.• Zanjani, G., 2002. Pricing and Capital Allocation in Catastrophe Insurance, Journal of Financial Economics 65, 283-305.