1. Risk Premium Project Phase III: Final Report Academic InvestigatorsIndustry Investigators J. David Cummins University of Pennsylvania Richard A. Derrig Automobile Insurers Bureau Richard D. Phillips Georgia State University Robert P. Butsic Fireman’s Fund Casualty Actuarial Society Meeting Colorado Springs, CO, May 17, 2004 Copyright 2004, J. David Cummins and Richard D. Phillips, all rights reserved. Not to be reproduced without permission.

3. Plan of Presentation  Introduction and Summary: Risk-Premium Project  Richard A. Derrig  Cost of Capital Estimation  J. David Cummins  Capital Allocation  Richard D. Phillips  Discussion

4. Risk Premium Project Overview  Overall Research Objective  Identify appropriate risk adjustments for insurer liabilities to determine equilibrium prices for insurance and fair valuation of reserves  Milestones  Phase 1 – Literature Review  Actuarial literature  Finance literature  Phase 2 – Analysis and Theoretical Conclusions  Report CAS Forum Fall 2000  Phase 3 – Empirical Research  By-line costs of capital estimates  Report CAS Forum Winter 2003  Parameterization of recent capital allocation models

5. Primary Theoretical Conclusions Conclusion I Both systematic and non-systematic risk are relevant factors determining equilibrium prices for insurance Conclusion II A linkage exists between systematic risk and duration Conclusion III Multifactor asset pricing models are superior to the CAPM Conclusion IV Theoretically appealing surplus allocation model now exists, and Insurer default should be recognized in pricing risk transfer

6. Estimating the Cost of Equity Capital For Property-Liability Insurers

7. Objective of Study  Estimate overall costs of capital for P-L insurers  Capital asset pricing model (CAPM)  Fama-French three factor method (FF3F)  Estimate costs of capital by line of insurance  Full information beta (FIB) approach

8. Cost of Capital: Defined  The cost of capital is the rate of return a firm must earn on projects to avoid destroying firm value  Cost of equity capital  Cost of debt capital  Overall cost of capital  Consequences of erroneous cost of capital estimates  Underpricing – lose money on policies underwritten  Overpricing – lose business to competitors

9. Uses of the Cost of Capital  Project decision making – accept or reject projects  Product pricing  Entry or exit lines of business or geographical markets  Mergers and acquisitions

10. Estimating Cost of Capital By Line  Cost of capital is known to vary  By industry  By firm within an industry  By line of business within a firm  Little or no prior research on cost of capital by line for insurance

11. Estimating the Divisional Cost of Capital  Divisional cost of capital or project cost of capital is the required rate of return on project that will not destroy firm value  Adjusted present value method – each cash flow has its own cost of capital  Financial pricing models utilize cost of capital for individual lines of business  Cost of capital for diversified (conglomerate) firms  Overall cost of capital can be estimated using market data  However, the overall cost of capital may over or under- estimate the cost of capital for lines of business (divisions)

12. Estimating Divisional Cost of Capital: Traditional Methodology  Pure play approach:  Identify publicly traded firms that specialize in the same product as the division (i.e., that have a “pure play” in that product)  Approximate the divisional cost of capital as the average cost of capital for the pure play firms.

13. Pure Play Approach: Limitations  Few specialist firms may be available  Most P-L insurance written by multiple line firms  Specialized subs of conglomerates are not publicly traded  Specialist firms in many industries may not be representative of divisions of conglomerate firms (e.g., may be smaller)  Because the cost of capital is higher for small firms, using pure play estimates of the cost of capital for the divisions of a conglomerate may yield biased results

14. The Full-Information Industry Beta Method  The full-information industry beta (FIB) method provides a promising alternative to the pure play approach (Kaplan and Peterson 1998).  The FIB approach  Uses a sample of conglomerate and specialist firms to estimate cost of capital by line (division)  Fundamental insight: the observable beta for the conglomerate is a weighted average of the unobservable betas of the underlying lines of business

15. The Full Information Industry Beta Method II  Regress the firm’s observable cost of capital parameters on variables measuring the firm’s participation in various industries and business lines  Coefficients of the line of business participation variables are then interpreted as the full-information beta coefficients for the business lines  Firms outside of the estimation sample (e.g., mutuals or non-traded stock firms) can estimate the cost of capital for their own line of business compositions

16. FIB Estimation Outline  Estimate the FIB costs of capital using all firms in the Compustat data base for the period 1997-2000  Regression analyses  All insurance and non-insurance firms based on 2-digit industry categories from the North American Industry Classification System (NAICS)  All insurance and non-insurance firms with P-L insurance lines subdivided based on National Association of Insurance Commissioners database  Industry participation based on revenue measures

17. Betas Used As Dependent Variables  Capital asset pricing model (CAPM) betas  Fama-French 3-factor betas  Responds to the criticism that the CAPM gives inaccurate estimates of the cost of capital because it omits important financial risk-factors  Fama-French risk factors  CAPM systematic market risk factor  Firm size (total market capitalization)  Financial distress (book value (BV) of equity/market value (MV) of equity

18. Capital Asset Pricing Model (CAPM) Capital asset pricing model (CAPM) cost of capital: Where E(r i ) = cost of capital for firm I r f = the risk-free rate of interest r m = the return on the “market” portfolio β mi = Cov(r m,r f )/Var(r m ) = beta for systematic market risk of firm I

19. Fama-French 3-Factor (FF3F) Model FF3F cost of capital: E(r i ) = cost of capital for firm i β mi = beta for systematic market risk of firm i β si = size beta for firm i β vi = financial distress beta for firm i π s = the expected market risk premium for firm size π h = the expected market risk premium for financial distress risk

20. Why the Fama-French 3 Factor Model?  Extensive research shows CAPM fails to capture accurately the cross-sectional differences in expected stock returns  Various multi-factor models have been proposed  Arbitrage pricing theory  Wei model  FF3F model  FF3F has been extensively tested and has become the dominant multi-factor model in practical finance applications.

21. FF3F Model: What Do the Factors Represent?  Market risk factor, E(r m ) – r f  Market systematic risk – same rationale as CAPM  Market risk premium for firm size, π s  “Small stock premium” – small stocks tend to have higher expected returns than large stocks  Market risk premium for financial distress, π h  Firms in financial distress (low growth prospects) have higher expected returns than healthier firms  Measured by the ratio of book to market equity, BE/ME  Shown by FF to do better than the P/E ratio

22. Estimating Cost of Capital: Implementation  Implementing the cost of capital methodologies  Estimate betas for each firm by regressing stock returns on risk factor variable(s)  Estimate expected market risk premia  Plug beta coefficients and expected market risk premia into cost of capital equations to estimate cost of capital

23. Implementation: The CAPM  First stage regression  60 monthly observations are used on the return of firm i, the risk free rate, and return on the market  The market return is represented by a broad market index  A U.S. government bill or bond rate is used to represent r f, with the choice of rate depending upon the time horizon of the firm or project being evaluated

24. Implementation: The Sum Beta Approach  Using the time series regression to estimate beta may produce biased estimates for stocks that trade infrequently  To control for this problem, the sum beta method is used:  The beta coefficient for firm i is then given by

25. Implementation: The FF3F Method  The FF3F method uses the following regression:  A sum-beta regression also can be used:

26. The FF3F Method: Estimating Size and BE/ME Factors  The firm size and financial distress (BE/ME) factors are estimated using procedures developed and extensively tested by Fama-French and other researchers  Generally, involves the formation of portfolios of stocks graded by market capitalization (size) and BE/ME ratios and computing returns for the portfolios  See cited literature and Ken French’s web site (url given in our paper) for details

27. Estimating Expected Risk Premia  CAPM systematic market risk premium is the arithmetic average of the difference between the return on a market index and the return on a risk-free asset.  The usual averaging period is 1926-present, and  The broad market index used here is value-weighted return on all NYSE, AMEX, and Nasdaq stocks  r f is a US government bond or bill rate with the choice of rate depending upon the time horizon of the project being evaluated  Long-term averages of π st and π vt are used to estimate π s and π v

28. Full-Information Industry Beta Model  FIB methodology views the firm as a portfolio of assets, where the assets could represent divisions, lines of business, or projects  The firm’s overall market beta coefficients are weighted averages of the beta coefficients of the separate divisions of lines of business  Weights for beta coefficients  In theory, the weight equals the market value of the division divided by the overall market value of the firm  Because divisions are not traded, divisional sales data are used as proxies for market value weights (as in Kaplan and Peterson 1998)

29. FIB Model: Further Discussion  Decompose the overall market beta coefficient (for the CAPM) or coefficients (for the FF3F model) into separate beta coefficients for each industry in which firms participate.  Decomposition based on cross-sectional regression for a sample of firms  Overall market beta(s) as the dependent variable  Line of business participation weights as independent variables

30. FIB Model: CAPM Regression Model  The CAPM FIB regression is where ω ij = firm i’s sales in line j divided by firm i’s total sales β i = firm i’s overall market beta β fj = full information industry beta for industry j  The β fj (varying by industry but not by firm) measure the impact of each line of business on the overall riskiness and hence the beta coefficient of the firm

31. FIB Model: FF3F Regressions  For the FF3F method there are 3 regressions, one for each risk factor

32. FIB Model: FF3F Regressions  In the size factor equation, the log of ME is included to account for known inverse relationship between the size beta and firm size  In the financial distress equation, the log (BE/ME) is included to account for the known positive relationship between the financial distress beta and BE/ME.  β ki = overall beta estimate of type k for firm i, k = m (market), s (size), and v (BV/MV), β fkj = full-information industry beta of type k, industry j, ω ij = industry-participation weight for firm i in industry j, ν jj = random error term for firm i, equation j.

33. Cost of Capital Illustration: Data and Sample  Stock return data are from the University of Chicago’s Center for Research on Securities Pricing (CRSP) and include returns on all NYSE, AMEX, and Nasdaq stocks  The CRSP data for the period 1992-2000, to estimate costs of capital for the period 1997-2000  Standard 60 month estimation period used in estimating CAPM and FF3F betas  Estimation conducted separately for each year of the sample period

34. Data and Sample: Revenues By Line  Revenues from Compustat and the National Association of Insurance Commissioners (NAIC)  Compustat includes revenue data for firms in various industries based on the North American Industry Classification System (NAICS)  Insurance is included in the finance sector, which has two- digit NAICS code of 52  Insurance sub-categories in NAICS  Property/casualty insurance,  Life insurance, and  Health insurance  Property/casualty insurance further disaggregated by line using data from National Association of Insurance Commissioners

35. Data and Sample: r f and Risk Premia  All of the cost of capital estimates use as r f the average 30 day Treasury-bill rate for the sample period 1997-2000  Same risk-free rate used for all estimates to focus on the impact of the models and the beta coefficients  The expected risk-premia are long-run historical average (1926 to present)  Systematic market risk premium (Ibbotson)  Size premium (Ken French’s estimates)  Financial distress premium (Ken French’s estimates)

36. Insurers in Sample: Revenues By Industry DescriptionOther Insurer P/L Insurer P/L Insurance $71,639.2630.2% $134,218.7075.6% Health Insurance 4,050.541.7% 9,283.925.2% Life Insurance 93,430.5939.4% 16,664.259.4% Finance Excl Ins 26,456.1411.1% 5,518.243.1% Non-Finance41,846.7617.6%11.867.406.7% Number of firms 102 146

37. CAPM Cost of Capital: PC Insurers Market Cap Quartile No. PC InsurersAverage β Average Sum β Cost of Capital Small210.6460.89312.5% 2210.8611.14414.6% 3210.7090.80911.8% Big220.8200.93212.8% Total850.7600.94412.03% Note: Estimates for 1997. Assumes risk free rate = 4.93% and market risk premium = 7.88%.

38. FF3F Costs of Capital: PC Insurers Sum β m Sum β s Sum β v Cost of Capital 1.1890.7661.08620.9% 1.2050.7850.83420.1% 0.9780.0930.60815.7% 1.080-0.2200.35514.9% 1.1120.3490.71617.9% Note: Estimates for 1997. Assumes risk free rate = 4.93% and market risk premium = 7.88%. FF3F cost of capital significantly higher than CAPM.

39. FF3F Costs of Capital: Discussion  Insurer response to market risk factors  Insurer stocks about average in their sensitivity to market systematic risk and firm size  Insurer stocks much more sensitive than average to financial distress factor (BE/ME) – a regulated industry where buyers care about financial stability  FF3F cost of capital significantly larger than CAPM  Primarily attributable to financial distress factor  Somewhat higher due to size and higher FF3F systematic market risk betas

40. FF3F By Line: Personal vs. Commercial Annual Average Panel Estimate Personal Lines versus Commercial Lines Cost of Equity Capital (Equally Weighted) Personal Lines21.7% Commercial Lines18.1%18.2% Cost of Equity Capital (Market Value Weighted) Personal Lines18.8%17.6% Commercial Lines21.0%20.5%

41. Discussion: Personal vs. Commercial Lines  Cost of capital estimates  Equally weighted: Personal > commercial  Value weighted: Personal < commercial  Explanation: Value weighted results primarily reflect large insurers – commercial business of large insurers is likely to be higher risk than that written by smaller insurers

42. FF3F By Line: Auto vs. Workers’ Comp Annual Average Panel Estimate Automobile Insurance versue Workers Compensation Cost of Equity Capital (Equally Weighted) Automobile Insurance20.4%20.7% Workers' Compensation17.9%18.0% Cost of Equity Capital (Market Value Weighted) Automobile Insurance18.7%17.5% Workers' Compensation15.0%

43. Cost of Capital: Overall Conclusions  FF3F costs of capital are significantly higher than for CAPM – using the CAPM may lead to serious pricing errors  Cost of capital varies significantly by  Firm size  BE/ME ratio  Line of business

44. Cost of Capital: Overall Conclusions II  Important to use the sum-beta adjustment to allow for infrequent trading  Value-weighted estimates differ signficantly from equally weighted estimates  Therefore, using average cost of capital estimates in rate regulation will result in significant pricing errors for most insurers

45. FF3F FII Betas: Auto and Workers’ Comp 1997199819992000AvgPanel BetaAuto0.7951.0161.0221.2811.0290.971 WC0.9050.9270.8070.5420.7950.864 Other1.1631.1741.2601.4771.2691.227 SMBAuto-0.470-0.464-0.261-0.258-0.363-0.438 WC-0.6060.5610.4710.4960.2310.071 Other-0.359-0.1680.050-0.116-0.148-0.142 HMLAuto0.1350.7271.3211.4400.9060.685 WC0.1480.7610.124-0.1510.2200.137 Other0.2760.6740.8911.0100.7130.708 Cost of CapAuto11.7%16.2%19.5%22.1%17.3%15.7% WC12.3%18.0%13.9%10.6%13.7%13.5% Other15.5%17.9%20.1%21.9%18.8%18.5%

46. The FF3F Method: Estimating Size and BV/MV Factors II  Stocks are divided into 6 portfolios by size and BVMV ratios  (1) HMC and HBMV  (2) HMC and MBMV  (3) HMC and LBMV  (4) LMC and HBMV  (5) LMC and MBMV  (6) LMC and LBMV

47. The FF3F Method: Estimating Size and BV/MV Factors II  Stocks are divided into 6 portfolios by size and BVMV ratios  (1) HMC and HBMV  (2) HMC and MBMV  (3) HMC and LBMV  (4) LMC and HBMV  (5) LMC and MBMV  (6) LMC and LBMV  Market value-weighted average returns are obtained for each portfolio

48. The FF3F Method: Estimating Size and BV/MV Factors II  Size premium π s is obtained as the average return on the three “small” stock portfolios (portfolios (4), (5), and (6)) minus the average return on the three “large” stock portfolios ((1), (2), and (3))  The financial risk premium π v is obtained as the difference between the average return on the two “high” market-to-book portfolios ((1) and (4)) minus the average return on the two “low” market- to-book portfolios ((3) and (6)).

49. Implementation: The DCF Method  The cash flow to market value ratio (Ci1/Vi) is approximated by the firm’s projected dividend-to- price ratio or earnings-to-price ratio obtained from financial reporting services such as Thomson Financial or Value-Line  The projected growth rate, also in earnings or dividends, usually is based on a average of financial analysts’ forecasts obtained from a source such as the Institutional Brokers Estimation Service (IBES).

50. Estimation Methodology: FIIB Model  Estimating the FIIB equation using ordinary least squares yields equally-weighted average industry specific full- information betas.  However, industry participation weights should represent firm market value by industry, so we use an instrumental variables (IV) approach.  The instrument for each firm is the ratio of its market capitalization (S i ) to the total market capitalization of the firms in the sample multiplied by its industry-participation weight, i.e.:

51. Estimation Methodology: The Pure Play Approach  For comparison with the CAPM and FF3F cost of capital estimates, we also conduct a pure play analysis of property-liability (P/L) insurers  The pure play sample is a sub-sample from our overall sample of publicly traded insurers that consists of all firms that self-report their primary business as P/L insurance (primary NAICS codes of 524126 or 52413)

52. Illustration: Calculating Beta Using FF3F  The FF3F model:  Parameters: β m = 1.11, β s = 0.35, β v = 0.72, r f = 0.0588 (12/2000)  Risk premia (from Kenneth French): E(r m ) – r f = 0.0774, π s = 0.0255, π v = 0.0494  Calculation: E(r i ) = r f + β m [E(rm) – r f ] + β s π s + β v π v

53. Illustration: Calculating Beta Using FF3F  Parameters: β m = 1.11, β s = 0.35, β v = 0.72, r f = 0.0588 (12/2000)  Risk premia: E(r m ) – r f = 0.0774, π s = 0.0255, π v = 0.0494  Calculation: E(r i ) = r f + β m [E(rm) – r f ] + β s π s + β v π v = 0.0588+1.11*0.0774+0.35*0.0255+0.72*0.0494 = 0.0588 + 0.086 + 0.009 + 0.036 =.1898

54. FF3F, FII Sum Betas: P/L Insurance Factor1997199819992000AvgPanel Beta Factor1.0211.1311.1481.3551.1641.125 SMB Factor-0.387-0.211-0.015-0.126-0.185-0.218 HML Factor0.2300.7201.0201.1500.7800.686 Cost of Capital14.1%17.6%19.6%21.6%18.2%17.4%

55. FIIB vs. Pure Play Costs of Capital 1997199819992000Avg Full Information Beta Methodology Estimates CAPM Beta13.3% 12.0%12.3%12.7% CAPM Sum Beta12.6% 11.9%13.5%12.6% FF3F17.1%18.4%19.7%21.7%19.2% FF3F Sum Beta14.1%17.6%19.6%21.6%18.2% Pure Play Estimates CAPM Beta11.9%11.6%10.8%10.5%11.2% CAPM Sum Beta13.3%13.1%11.7%11.6%12.5% FF3F18.0%18.3%17.4%19.7%18.4% FF3F Sum Beta19.1%13.1%18.5%21.2%18.0%