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

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

Motivation(1/2) Cost of capital estimation is becoming important for insurers especially after financial crisis in Cost of capital estimation is becoming important for insurers especially after financial crisis in Moreover, insurers need more equity capital if International Financial Reporting Standards (IFRS) is executed. 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. More applications of financial models are used in pricing, reserving, ALM for insurance companies. 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. 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. 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. Few literature discussed how to estimate costs of capital for insurers with different business line compositions. NTUICF, 10/DEC/2010

Literature Process S(1964),L(1965), B(1972) -- CAPM Refining Beta Estimation Most Results support CAPM Adding different possible factors to explain returns Fama-French Three Factor Model Possible reasons to explain Size, B/M and Momentum Global market, Different industries Jegadeesh and Titman(1993) -- Momentum 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 1980 ’ s but not in the 1970 ’ s. Cummins and Harrington(1985) suggest that beta of property-liability insurers were unstable and conformed to the CAPM in the 1980 ’ s but not in the 1970 ’ s. 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. 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

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. 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. 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. 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

Purposes (1) To test whether the momentum factor plays the significant role in estimating the cost of equity capital for PL insurers. (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. (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. (3) Finally, the sum-beta approach is adopted to adjust the infrequent trading. NTUICF, 10/DEC/2010

Data and Sample Selection(1/3) To select property/casualty insurance (NAICS code ) sample by North American Industry Classification System (NAICS). To select property/casualty insurance (NAICS code ) sample by North American Industry Classification System (NAICS). The stock return of insurance companies were obtained from CRSP. The stock return of insurance companies were obtained from CRSP. To follow Fama-French’s(1992,1997) screening rules To follow Fama-French’s(1992,1997) screening rules (a) To eliminate firms didn’t have at least 36 consecutive months of return information during estimation period (a) To eliminate firms didn’t have at least 36 consecutive months of return information during estimation period (b) The beta coefficients greater than 5 in absolute value. (b) The beta coefficients greater than 5 in absolute value. NTUICF, 10/DEC/2010

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

Data and Sample Selection(3/3) Estimate betas Period: Estimate betas Period: We 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. We 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: Estimate the cost of equity: NTUICF, 10/DEC/2010

Estimation Methodology (1/4) -- CAPM Method ： the return on stock I in period t ： the risk-free rate in period t(30-day Treasury bill yield) ： the returm on the market portfolio in period t ： the CAPM beta coefficient for firm i ： overall beta estimate for firm i ： net premiums weight for firm I in business lines k ： full-information beta of type j for business line k 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 t ： overall beta estimate of type j for firm i ， j=m, s, v ： full-information beta of type j for business lines k ， j=m, s, v ： net premiums weight for firm I in business lines k NTUICF, 10/DEC/2010

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

Estimation Methodology (4/4) -- Sum-Beta Approach In 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

= 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

= 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

Empirical Results of Beta Estimations (1/2) 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. than the ordinary beta coefficients because infrequent trading. NTUICF, 10/DEC/2010

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

Empirical Results Overall cost of equity (1/2) Empirical Results Overall cost of equity (1/2) Risk freeMarket premium SMBHMLMomentum Factor Cummins (2005) Our Paper NTUICF, 10/DEC/2010

Empirical Results Overall 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 with sum-beta adjustment is larger than without sum-beta method. The cost of equity estimated from FF3F is larger than from CAPM. The cost of equity estimated from FF3F is larger than from CAPM. (CAPM:10.5%, FF3F:16.3%) (CAPM:10.5%, FF3F:16.3%) The cost of equity estimated from momentum model is larger than from FF3F. (Momentum:22.56%) The cost of equity estimated from momentum model is larger than from FF3F. (Momentum:22.56%) 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 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. Financial distress factor is significant in estimating the cost of equity for property- liability insurers. NTUICF, 10/DEC/2010

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

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

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

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

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. Generally Speaking, equity cost in commercial lines is larger than in personal lines. Shareholders ask more risk compensation for operating the commercial line products. CAPM CAPM FF3F FF3F Momt Momt Personal Line Commercial Line NTUICF, 10/DEC/2010

Results of Workers ’, Auto and All other (1/2) CAPM FF3F Momentum Automobile insurance Workers ’ compensation All other P&L lines of insurance 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. (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

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). (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. (2) It is important to adjust infrequent trading when estimating betas for PL insurers. NTUICF, 10/DEC/2010

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