The momentum effect on estimating the cost of equity capital for property-liability insurersJennifer L. Wang (National Chengchi University)Joseph Tien (Tamkang University) NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Outline(1) Introduction: Motivation and Literature(2) Data Resource and Empirical Model(3) Empirical Results(4) ConclusionsNTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Motivation(1/2) Cost of capital estimation is becoming important for insurers especially after financial crisis in 2008. Moreover, insurers need more equity capital if International Financial Reporting Standards (IFRS) is executed. More applications of financial models are used in pricing, reserving, ALM for insurance companies.NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Motivation(2/2)Fama-French(1997) suggest that the cost of capital varies across industries due to heterogeneity of the risks facing in various sectors of the economy. There is a significant factor for insurance. The supervisor needs the reasonable cost of capital to enact the regulations.Few literature discussed how to estimate costs of capital for insurers with different business line compositions.

NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Literature Process 197019801990S(1964),L(1965),B(1972) -- CAPMRefining Beta EstimationMost Results support CAPMAdding different possible factors to explain returnsFama-French Three Factor ModelPossible reasons to explain Size, B/M and Momentum Global market,Different industriesJegadeesh and Titman(1993) --MomentumNTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Literature(1/2)Cummins and Harrington(1985) suggest that beta of property-liability insurers were unstable and conformed to the CAPM in the 1980s but not in the 1970s.Cummins and Lamm-Tennant(1994) figure an additional factor, leverage, for empirical models. Their results suggest that the long-tail commercial lines of property-liability insurance tend to have higher costs of capital than short-tail lines.

NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Literature(2/2)Lee and Cummins(1998) propose that APT and the Wei(1988) model perform better than the CAPM in forecasting the cost of capital for insurers.Using the Fama-French model, Cummins and Phillips(2005) suggest the cost of capital for insurers are significantly higher than estimation based upon the CAPM.Wang et al. (2008) use Rubinstein-Leland (RL) model to improve the cost of equity estimates of insurance companies due to the highly skewed and heavy-tailed distributions associated with the insurance claims process.

NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Purposes(1) To test whether the momentum factor plays the significant role in estimating the cost of equity capital for PL insurers.(2) Moreover, we further use FIB method to calculate the capital cost for different lines of business. (3) Finally, the sum-beta approach is adopted to adjust the infrequent trading. NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Data and Sample Selection(1/3)To select property/casualty insurance (NAICS code 524126) sample by North American Industry Classification System (NAICS). The stock return of insurance companies were obtained from CRSP.To follow Fama-Frenchs(1992,1997) screening rules (a) To eliminate firms didnt have at least 36 consecutive months of return information during estimation period (b) The beta coefficients greater than 5 in absolute value.

NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Excess return data for market systematic risk , size, financial distress (B/M ratio), and momentum factor were obtained from Kenneth Frenchs website.Consequently, we obtained data on insurance revenue by product lines from the NAIC annual statement CD-ROMs.

Data and Sample Selection(2/3)NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Data and Sample Selection(3/3)Estimate betas Period: 1993-2001We abstracted monthly return data from CRSP and use excess return data for market systematic risk , size, financial distress (B/M ratio), and momentum factor to proceed the regression.Estimate the cost of equity: 1999-2001 NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Estimation Methodology (1/4)-- CAPM Methodthe return on stock I in period tthe risk-free rate in period t(30-day Treasury bill yield)the returm on the market portfolio in period tthe CAPM beta coefficient for firm i overall beta estimate for firm inet premiums weight for firm I in business lines kfull-information beta of type j for business line kNTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Estimation Methodology (2/4)-- FF3F Model the market risk premium for firm size in period t the market risk premium for financial distress in period toverall beta estimate of type j for firm ij=m, s, v full-information beta of type j for business lines k j=m, s, vnet premiums weight for firm I in business lines kNTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Estimation Methodology (3/4)-- Momentum Modelthe momentum factor in the period t overall beta estimate of type j for firm ij=m, s, v, mofull-information beta of type j for business lines k j=m, s, v, mo net premiums weight for firm I in business lines kNTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Estimation Methodology (4/4)-- Sum-Beta ApproachIn order to correct for the bias created by infrequent trading, we utilize the sum-beta approach that has become standard in this type of analysis ( e.g., Scoles and Williams(1977), Dimson(1979)) Adding the lagged value of variable in model: The estimated sum beta coefficient is NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

= estimated beta coefficient in first regression for firm i, = the cost of capital of CAPM for firm i, = the expected return of the risk-free asset, the expected return on the market portfolio,excess return on NYSE/AMEX/Nasdaq stocks from 1926 until June of 2001 To Estimate Cost of Equity (1/2)NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

= the expected excess premium for size factor,

= the expected excess premium for financial factor,= the expected excess premium for momentum factor To Estimate Cost of Equity (2/2)NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Empirical Results of Beta Estimations (1/2)(1) The quartile results do not show that large insurers consistently have smaller beta than small insurers.(2) The sum-beta estimates are constantly than the ordinary beta coefficients because infrequent trading.

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NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

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Empirical Results of Beta Estimations (2/2)(3) The market beta estimated in FF3F is larger than in CAPM.(4) The market beta estimated in momentum model is larger than in FF3F.(5) Generally, the market beta or B/M beta is larger than the size beta, the momentum beta is smallest. NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Empirical ResultsOverall cost of equity (1/2)NTUICF, 10/DEC/2010

Risk freeMarketpremiumSMBHMLMomentumFactorCummins(2005)0.04930.08440.02350.0385 -------- Our Paper0.04810.08110.02790.04140.0923

NTUICF, 10/DEC/2010

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Empirical ResultsOverall cost of equity (2/2)The cost of equity estimated with sum-beta adjustment is larger than without sum-beta method.The cost of equity estimated from FF3F is larger than from CAPM. (CAPM:10.5%, FF3F:16.3%)The cost of equity estimated from momentum model is larger than from FF3F. (Momentum:22.56%)NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Comparing with Cummins and Phillips (2005) Financial distress betas are substantially larger than the parameters in the Fama-French all industry average. (0.02)Financial distress factor is significant in estimating the cost of equity for property-liability insurers.NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Our New FindingsAlthough the momentum beta could be the smallest of all beta estimations, the momentum effect still plays a significant role in estimating cost of equity.The estimations of beta and cost equity are dropped sharply in 2001. NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Empirical Results for different lines of business(1) Long-tail and Short-tail (2) Commercial and Personal(3) Workers Compensation, Automobile Insurance and All Other Property-Liability Insurance NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Results of Long-tail and Short-tailLong-tail other liability , products liability (occurrence, claim made), private passenger auto liability, aircraft, commercial auto liability.Short-tail fire, allied lines, homeowners, multiperil, automobile physical damage, accident and health coverage, fidelity, surety, mortgage guaranty. NTUICF, 10/DEC/2010

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NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Empirical Results of Commercial and Personal (1/2)Personal Line- Homeowner, Framowner, Earthquake, Personal Auto Liability, Personal Auto DamageCommercial Line- All other lines of insurance are considered commercial lines. NTUICF, 10/DEC/2010

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Empirical Results of Commercial and Personal (2/2)

Generally Speaking, equity cost in commercial lines is larger than in personal lines. Shareholders ask more risk compensation for operating the commercial line products. NTUICF, 10/DEC/2010

CAPM FF3F MomtPersonal Line10.6512813.7862014.82667Commercial Line 11.0261117.4460521.68727

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Results of Workers, Auto and All other (1/2)

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CAPM FF3F MomentumAutomobile insurance

11.08254 11.92098 14.96861Workers compensation

9.8404210.40837 15.49364All other P&L lines of insurance

10.73661 19.03513 20.88048

NTUICF, 10/DEC/2010

Results of Workers, Auto and All other (2/2)(1) The equity cost of worker compensation is slightly larger than automobile. But the equity cost of other P&L is largest among these three categories. NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Conclusions (1/2)(1) The cost of equity capital estimation based the FF3F (mometum) method is significantly higher than the estimation based on the CAPM (FF3F).(2) It is important to adjust infrequent trading when estimating betas for PL insurers. NTUICF, 10/DEC/2010

NTUICF, 10/DEC/2010

Conclusions (2/2)(3) The cost of equity capital varies significantly by line of insurance.(4) Financial distress factor is significant in estimating the cost of equity for property-liability insurers.NTUICF, 10/DEC/2010

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NTUICF, 10/DEC/2010

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