What Did We Learn? Conclusions from the Risk Premium Project Presentation made at the 2005 Casualty Actuarial Society’s Ratemaking Seminar March 2005 New Orleans, LA Richard D. Phillips Bruce A. Palmer Professor of Risk Management and Insurance Georgia State University (EDITED EXCERPT by RAD)

Risk Premium Project ( )  Participants –Robert Butsic, Firemans Fund (Allianz) –David Cummins, Wharton School, U of Pennsylvania –Richard Derrig, Auto Insurers Bureau of Massachusetts –Richard Phillips, Georgia State University  Funding –Casualty Actuarial Society, Committee of the Theory of Risk

Risk Premium Project  Overall Research Objective –Identify appropriate risk adjustments for insurer liabilities to determine equilibrium prices for insurance  Milestones –Phase 1 – Literature Review »Actuarial literature »Finance literature –Phase 2 – Analysis and Theoretical Conclusions »Report CAS Forum Fall 2000 –Phase 3 – Empirical Research »Estimate equity cost of capital by-line of insurance »Prices reflect allocations of capital

Theory Review: Prices in Perfect Capital Markets  With perfect and complete markets assumption –No need for capital (Modigliani-Miller) –No default risk (perfect enforceability) –Nothing to allocate –Pricing done under the risk neutral probability measure AssetsLiabilities Investments  P i Claims  PV   L i )

Theory Review: Prices in Perfect Capital Markets with Default Risk  With insurer default still no need to allocate capital (surplus is a pooled asset) –Allocate default costs ala »Black and Cox (1976) »Phillips, Cummins and Allen (1998) –D = Equilibrium value of default option AssetsLiabilities Investments  P i – D i ] + SClaims  PV   L i ) – D i ] Frictional Costs of Capital 0 Equity S

Theory Review: Prices in Perfect Capital Markets with Default Risk and Capital Market Imperfections  With market imperfections and default costs –Allocate default cost by priority rule –Allocate costs of capital to individual lines –Frictional costs are related to capitalization, i.e.,  = f(S) AssetsLiabilities Investments  P i – D i +  S i ] + SClaims  PV   L i ) – D i ] Frictional Costs of Capital  S i Equity S

Pricing Intermediated Risks: Summary  With market imperfections, insurance prices should reflect 1.Expected cash flow with adjustments for systematic risk 2. Production costs (expenses) 3. Default risk 4.Frictional capital costs

Project 1: Estimating Cost of Equity Capital for Property-Liability Insurers Published in Journal of Risk and Insurance, Sept 2005  Primary research questions 1.What is the cost of equity capital for P&L insurers using a.Capital Asset Pricing Model b.Multi-factor model proposed by Professors Fama and French 2.Are there significant differences in the cost of equity capital across different lines of insurance?

Traditional Asset Pricing Model  Dominant model has been Capital Asset Pricing Model –CAPM cost of equity capital reflects only systematic risk E(r i )= r f +  i [E(r m – r f )] –where E(r i ) = expected return for firm i r f = risk-free rate of interest E(r m )= expected return on market portfolio

Failure of the CAPM? What Failure? Source: Cochrane, John H., 1999, “New Facts in Finance,” Economic Perspectives 23(3): Note: Average annual returns vs. beta for 10 size-sorted stock portfolios. Sample period

Fama-French Multifactor Asset Pricing Model  Fama-French 3 Factor Model –Multi-factor asset pricing model –Cost of capital estimate is E(r i )= r f +  i [E(r m – r f )+  s,i E (  s ) +  v,i E (  v ) –where E(r i ) = expected return for firm i r f = risk-free rate of interest E(r m )= expected return on market portfolio E(  s ) = expected market premium for firm size E(  v )= expected market premium for financial distress  i = market beta to adjust for systematic portfolio risk  i = beta to adjust for systematic risk associated with firm size  i = beta to adjust for systematic associated with financial distress

Project 2: Allocating the Costs of Capital “Pricing Financially Intermediated Risks with Costly External Finance: Evidence from the Insurance Industry” by J. David Cummins, Yijia Lin, and Richard D. Phillips  Primary research questions 1.Do insurer prices reflect capital allocation charges specific to the firm? 2.Are the implied capital allocations at least correlated with the method proposed by Myers and Read? 3.What is the implied per unit cost of allocated capital?

Risk Premium Project Conclusions  Primary theoretical predictions Conclusion I –Both systematic and non-systematic risk are relevant factors determining equilibrium prices for insurance Conclusion II –Multifactor asset pricing models empirically more successful than CAPM Conclusion III –Theoretically appealing surplus allocation models now exists

Risk Premium Project Conclusions  Primary empirical results –Cost of equity capital for insurers »CAPM vs. Multi-factor models »In general FF3F model produces higher estimated costs of equity capital vs. the CAPM –Full information industry beta methodology »In general cost of equity capital for property lines appears higher than liability lines –Strong evidence prices vary across insurers as a function of »Overall default risk »Total capital charges »Internal allocation of those capital charges »Prices appear to be a function of a firm’s access to capital markets –Limitations of competition and arbitrage  Implementation issue - Need estimate of equity risk premium for all models!

Suggested Reading Butsic, Robert P, J. David Cummins, Richard A Derrig, and Richard D. Phillips, 2000, "The Risk Premium Project (RPP): Phase I and II Report," Casualty Actuarial Society Forum, Fall 2000: Cochrane, John H., 1999, “New Facts in Finance,” Economic Perspectives 23(3): Cummins, J. David and Richard D. Phillips, 2001, "Financial Pricing of Property-Liability Insurance," in Georges Dionne, ed., Handbook of Insurance (Boston, MA: Kluwer Academic Publishers) Cummins, J. David and Richard D. Phillips, 2005, “Estimating the Cost of Equity Capital for Property & Liability Insurers," Journal of Risk and Insurance, 72(3) Cummins, J. David, Yijia Lin, and Richard D. Phillips, 2005, “Pricing Financially Intermediated Risks with Costly External Finance: Evidence from the Insurance Industry,” Working Paper Georgia State University, Atlanta, GA. Derrig, Richard A.,and Elisha Orr, 2004, "Equity Risk Premium: Expectations Great and Small,“ North American Actuarial Journal, 8(1): Froot, Kenneth A., 2003, "Risk Management, Capital Budgeting and Capital Structure Policy for Insurers and Reinsurers," Harvard Working Paper, Boston MA.

Suggested Reading Froot, Kenneth A. and Jeremy C. Stein, 1998, "Risk Management, Capital Budgeting, and Capital Structure Policy for Financial Institutions: An Integrated Approach," Journal of Financial Economics 47: Kaplan, Paul D. and James D. Peterson, 1998, "Full-Information Industry Betas," Financial Management 27: Merton, Robert C., and Andre F. Perold, 1993, “Theory of Risk Capital in Financial Firms,” Journal of Applied Corporate Finance 6: Myers, Stewart C and James A. Read, Jr., 2001, "Capital Allocation for Insurance Companies," Journal of Risk & Insurance 68: Phillips, Richard D., J. David Cummins, and Franklin Allen, 1998, "Financial Pricing of Insurance in the Multiple Line Insurance Company," Journal of Risk and Insurance 65: Zanjani, George, 2002, “Pricing and Capital Allocation in Catastrophe Insurance,” Journal of Financial Economics 65: