CAS RISK PREMIUM PROJECT

1. CAS RISK PREMIUM PROJECT Richard A. Derrig - Moderator Auto Insurers Bureau of Massachusetts Richard D. Phillips Georgia State University Robert P. Butsic Fireman’s Fund Insurance CAS Loss Reserve Seminar Minneapolis, MN Sept. 19, 2000

2. THE RISK PREMIUM PROJECT (RPP)Phase I and II Report • Committee on Theory of Risk • Discount Rate for Liabilities • Literature Review • Actuarial: Process and Parameter Risk • Financial: Systematic Risk • Academic: Dave Cummins, Rich Phillips • Industry: Bob Butsic, Rich Derrig

3. THE RISK PREMIUM PROJECT (RPP)Phase I and II Report(www.casact.org/cotor/rpp) 1. Introduction 2. Literature Search 3. Theoretical Conclusion 4. Proposals for Phase III Appendix A. Risk Premium Project Bibliography Appendix B. Implications for Fair Value Accounting

4. THEORETICAL CONCLUSION #1 • The opinions of financial economists and actuaries regarding the role of systematic vs. non-systematic risks in determining the equilibrium insurance prices are converging. Both see a role for non-systematic risk in pricing.

5. THEORETICAL CONCLUSION #2 • A systematic risk adjustment for the duration of the cash flows associated with a line of insurance should be included in the discount rate used to determine the fair value of the insurance premium. The adjustment to the discount rate will be a function of the maturity structure of the liabilities.

6. THEORETICAL CONCLUSION #3 • The average returns of financial assets cannot be adequately explained by the CAPM beta. Researchers have shown extensions of the CAPM which include additional factors significantly enhance the explanatory power of the models. In addition, although research using more sophisticated empirical tests has been published extending the CAPM, similar research focusing on insurance company returns does not currently exist.

7. THEORETICAL CONCLUSION #4 • A theoretically consistent way to allocate the costs of holding equity capital to individual lines of insurance has been identified. Thus, the costs associated with holding capital can now be charged to individual lines of insurance.

8. THEORETICAL CONCLUSION #5 • The risk of insurer default to the policyholder should be recognized in pricing the risk transfer.

9. Fair Value Accounting Implications • Market Value Balance Sheet • Treatment of Insurer Default • Franchise Value • Accounting for the Risk Load • Process Risk and Value Additivity • Risk Management Costs • Allocation of Joint Costs

10. Market Value Balance Sheet • One-period, idealized • No default • B/S at time policy is sold:

11. Default Option • No guaranty fund, limited liability • Fair Premium = P - D • B/S at time policy is sold:

12. Liability Treatment • Liability as reduced amount L -D • Separate liability offset (-D)

13. Default Under Guaranty Fund • Premiums as if no default • Liability to GF offsets expected default

14. Franchise Value for Ongoing Insurer • Surplus includes value of intangibles • Breakup value of surplus is Sf • With no guaranty fund:

15. Consequences of Default with FV • Default and franchise value are inversely related • Effect of increasing firm risk • Owners are worse off if (change in F) > (change in D) • Not showing F as asset creates perverse results

16. Process Risk and Value Additivity • Process risk commands a price • Risk management costs (Stulz) • Reinsurance, capital, diversification • These costs don’t appear in risk loads

17. Types of Residual Risk • Non-priced process risk • Priced process risk • Priced systematic

18. Allocation of Joint Costs • Systematic risk loads have natural value additivity • Finance models such as CAPM, APM • How does market treat cost of residual process risk? • Examples: cost of holding capital, risk load for catastrophes

19. Solution: Economic Allocation Methods • Microeconomic model of joint cost allocation • Look at marginal impact on total of separate (line) inputs • Economic allocations have value additivity

20. EMPIRICAL PROJECTSPhase III #1 • Full Information Beta For Insurance Lines • If Full Information P&C is 0.92 (1998), How Does That Distribute By Line? • DATA: CRSP and NAIC • The FI Equity Beta With Sum Betas (Autocorrelation) Included And/Or Fama-French Model • Industry Level And Firm Level • Relatively Straightforward Datawise; Output Will be Understandable

21. EMPIRICAL PROJECTSPHASE III #2 • Allocation of Surplus by Line of Insurance • Myers-Read Model Applied to Representative Insurer(s) • Calculation of Covariances of Asset and Liability Types • DATA: CRSP and NAIC at Georgia State and More(?) • Output Compared to Real World Data

22. PHASE IIIREFERENCES Butsic, Robert P, (1999), Capital Allocation for Property-Liability Insurers: A Catastrophe Reinsurance Application, Casualty Actuarial Society Forum, Spring. Ibbotson, Roger G, Paul D. Kaplan and James D. Peterson, (1997), Estimates of Small Stock Betas are Much Too Low, Journal of Portfolio Management, Summer. Kaplan, Paul D. and James D. Peterson, (1998), Full-Information Industry Betas, Financial Management, Summer. Myers, Stewart C. and James A. Read, Jr., (1999), Surplus Allocations for Insurance Companies, AIB Working Paper, July.

23. APPENDIX ALITERATURE RECOMMENDATIONS[TOP TEN NON-CAS] Campbell, John Y., Andrew W Lo, and Craig A. MacKinlay (1997), The Econometrics of Financial Markets (RPP 134) Campbell, John Y. (2000), Asset Pricing at the Millennium, NBER Working Paper (RPP238) Cochrane, John H. (1999), New Facts in Finance, NBER Working Paper (RPP188) Cummins, J. David, and Richard D. Phillips, (2000), Applications of Financial Pricing Models in Property-Liability Insurance, The Handbook of Insurance Economics (RPP130) Cornell, Bradford (1999), Risk, Duration and Capital Budgeting: New Evidence on Some Old Questions, Journal of Business, 72:2 (RPP37)

24. APPENDIX ALITERATURE RECOMMENDATIONS[TOP TEN NON-CAS] Froot, Kenneth A., and Jeremy C. Stein (1999), Risk Management, Capital Budgeting, and Capital Structure Policy for Financial Institutions: An Integrated Approach, Journal of Financial Economics, 47:1 (RPP9) Froot, Kenneth A., Jeremy C. Stein, and David S. Scharfstein (1993), Risk Management: Coordinating Corporate Investment and Financing Policies, Journal of finance, 48:1 (RPP10) Merton, Robert C. and Andre F. Perold, (1993), Theory of Risk Capital in Financial Firms, Journal of Applied Corporate Finance,6:3 (RPP177) Babbel, David F. (1999), Components of Insurance Firm Value, and the Present Value of Liabilities, Investment management for Insurers (RPP225) Barberis, Nicholas, Ming Huang, and Tano Santos (1999), Prospect Theory and Asset Prices, NBER Working Paper (RPP218)

25. EMPIRICAL PROJECTSFUTURE • Equity Beta for Insurer via Multifactor Asset Pricing Models • Campbell-Mei, Fama-French and other Multifactor Models Estimated for Insurers • Alternative Factors Relating to Insurance Tested for Additional Explanatory Power • DATA: CRSP and NAIC at Georgia State and More • Output Compared to Standard and Other Equity Betas for Insurers

26. EMPIRICAL PROJECTSFUTURE • Risk Load and Pricing via Cummins, Allen and Phillips Model • Insolvency Put, Growth and Company • Type Variables are Calculated to Estimate The Economic Premium Inclusive of Risk, Tax and Friction Loadings • DATA: CRSP and NAIC at Georgia State • Relatively Straightforward Datawise; Output Will be Understandable