Theoretical Assumptions and Implications of the Capital Asset Pricing Model - Research Paper Example

Finance and Accounting CAPM Contents Contents 2 Theoretical assumptions and implications of the Capital Asset Pricing Model (CAPM) derived from papers by Sharpe and Lintner 3 Implications 3 How valid are the assumptions, to what extent does a breach of the assumptions invalidate the CAPM model 4 Summarization and interpretation of the regression output 5 Empirical Results 5 The background and important features of the Fama French three factor model 6 Important Features 7 SMB Factor 7 HML Factor 8 Multivariate Regression and performance evaluation of the mangers with the Three Factor Model 8 References 10 Bibliography 11 Appendices:- 12 a) Regression Analysis Output of Industry 1 – Shops 12 a.1) Run 1 (Period 1980-2009) – 30 Years 12 a.2) Run 2 (Period 1980-1989) – 10 Years 14 a.3) Run 3 (Period 1990-1999) – 10 Years 17 a.4) Run 4 (Period 2000-2009) – 10 Years 19 a) Regression Analysis Output of Industry 2 – Others 22 a.1) Run 5 (Period 1980-2009) – 30 Years 22 a.2) Run 6 (Period 1980-1989) – 10 Years 25 a.3) Run 7 (Period 1990-1999) – 10 Years 27 a.4) Run 8 (Period 2000-2009) – 10 Years 30 Theoretical assumptions and implications of the Capital Asset Pricing Model (CAPM) derived from papers by Sharpe and Lintner The capital asset pricing model was developed by William Sharp in 1964 and John Lintner in 1965 and it had made the introduction of the theory of asset pricing. The CAPM model is based on the model of portfolio choice which was created by Harry Markowitz in 1959. In this model, an investor chooses a portfolio when t – 1 which produces good return on t. This model assumes that investors do not like to take risk during investment in portfolios and they are concern about only the variance and mean of the return. Thus they tend to choose portfolios which are efficient in both mean and variance terms- Given expected return, investors want to minimize the variance of the return from the portfolios. Given the expected variance, investors want to maximize they expected return of the portfolio. Sharpe and lintner have added two more assumptions to the CAPM model. The first assumption discuss about the term complete agreement which states that if clearing asset prices in the market is at t-1 then investors are ready on distribution of returns from assets t-1 to t. Thus this distribution becomes the true distribution as the return from this distribution help to draw the models on it. The second assumption states that lending and borrowing should be at risk free rate and it should be same for every investor and it does not depend on the amount of lending or borrowing. Implications This model can implied in a perfectly competitive securities market where there are lots of small investors and they are the price takers. It can also be implied in those markets which are frictionless and have no transaction cost and taxation system. It can also be used when investors are bigoted and all of them have same and one holding period of securities. CAPM model can be implied when there is limited amount of investments available for publicly traded assets with limitless lending and borrowing at the risk free rate. But this does not include human capital as publicly traded assets on which investment can be done. All investors should be concerned about mean and variance of the realized return of the portfolio which indicates every investor should follow Markowitz method for portfolio selection. Perfect information should be available for all investors and everyone should have access to the similar information and everyone should analyze it in the same way. It can be implied where all the investors either have same belief amount the distribution of the return from securities or have same utilization of the return from the securities. It indicates that every investor should have similar estimation about the expected return with similar covariance matrix (Timsimin, No Date). How valid are the assumptions, to what extent does a breach of the assumptions invalidate the CAPM model The Capital Asset pricing Model is based o9n some unrealistic assumptions like the assumption in which it has been stated that investors only concern about the variance and mean of portfolio returns of a particular period is extreme because investors are also concern about how the return from their portfolios will cover income of labor and future investment options (Fama, 2004, pp. 37-38). Thus variances in returns from portfolio miss the important aspect of different risk factors. Beta of a market is not the ultimate description of the risk exposure of an asset and we can find difference in expected return which was explained by beta. Apart from this, CAPM does not include restrictions on the short term sales and it also includes various liquidity issues for individually owned assets. It includes non tradable assets like human capital and when given same beta it prefers less correlation in the labor income (Research economics, No Date). Thus we can see that Capital Asset Pricing Model includes many invalid assumptions which are not realistic in the current market scenario because in reality, investors are not only concern about the mean and variance of returns from the portfolios for a specific period but also they are concern about the overall performance of the portfolio. Summarization and interpretation of the regression output The main aim of this research is to examine the validity of the Fama and French three factor model. This study has taken the similar methodology which was developed by Fama and French. The research has been done by based upon the monthly stock returns of 10 industry portfolios for the duration of 30 years which ends at 2010 and I needed to test 2 industries and two runs of the time series model which means one run for each industries that I was allocated. The regression equation of Fama and French three factor model is as follows- In the above equation, Ri is the to9tal return from the portfolio I, Rf is known as the risk free rate of return, Rm is return from market portfolio. The left side of the equation states the excess return from the portfolio for the month t, (Rmt - Rft) is the amount of excess return from the market portfolio for the month t. the second factor of risk is SMB which can be calculated as the difference between return on a portfolio of small shares and return on portfolio of large shares. In case of SMB, small and big means the sixe and volume of the market equity which can be calculated by multiplying number of shares outstanding * price per share. The next risk factor HML shows the difference between portfolio which has high book to market value stocks and the portfolio which ahs low book to market value stocks. According to Ruppert, book value is the net value of the company according to the accounting statement and balance sheet. Empirical Results Values of return from the portfolios and the statistical relationship between them are presented with the regression result. Refer to the Appendix for the regression result. As per the three risk factors, surplus market return (Rm- Rf) and high minus low (HML) are more unstable than SMB. While the HML and excess market return can have mean returns in positive value but the SMB has negative value in mean returns. Higher book to market ratios get poor returns as described by Fama and French but except for the case of B/H portfolio. Fama and French have shown that at the presence of HML and SMB risk factors in the three factor model, the slope of market risk factor which is denoted as b, Rm-Rf is near to 1. Fama and French have pointed out that same slopes show that sensitive market factor does not describe much about the variation that occurs in the average returns from the stocks. On the other side HML is the risk factor which captures the effect of book to market ratio on stocks and average return from the portfolio. This study agrees with the CAPM theory and in this study HML factor has the strong power to explain the high book to market stock portfolios statistically as medium and low book to market stock portfolios are insignificant in slope coefficients at significance level of 1%. Thus Fama and French three factor model explains the variations in the return of the portfolio and market risk factor has stronger effect on the return from the portfolios than the other risk factors. The background and important features of the Fama French three factor model The Fama and French three factor model was developed by Fama and French in 1992 to prove that covariance of market return and portfolio return does not clarify the changes on excess return. They found that the covariance has no power to influence the variations in portfolio returns. Fama and French model was developed to explain the realized returns in a better way than the CAPM model. According to Fama and French, this model is based on three important factors- 1. Excess return from the market portfolio. 2. Difference between the excess return from portfolio of large stocks and excess return from the portfolio of small stocks and this is also known as SMB (small minus big). 3. Difference between the surplus return from the portfolio of low book to market stocks and surplus return from the portfolio of high book to market stocks and this is known as HML (high minus low) (Eraslan, 2013, pp. 11-12). The Fama and French three factor model can be formulate as follows- Beta is used to measure the market risk of an asset and the value of the beta will be different from the value of beta in CAPM model. Rf means the risk free return and Rm is rate of return from the market. Sa indicates the level of risk to size and Ha indicates the level of risk to the value. Important Features SMB Factor SMB means small minus big and it was developed to analyze the extra return that investors have earned by investing in shares of different companies with low market capitalization. This extra return can also be called as “size “premium”. Monthly SMB factor can be calculated by subtracting the average return of the 30% largest stocks from the average return of the 30% smallest stocks in the month. Positive SMB for a month states that small cap shares have given better results than the large cap shares in the month but on the other side, negative SMB for a month states that large cap stocks have given better return than the small cap stocks in the month. HML Factor HML means high minus low and it has been developed to analyze the value premium which is provided to the investors for investing in different companies which have high book to market ratio. HML can be calculated by subtracting the average return of 50% of shares which have lower B/M ratio for the month from the average return of 50% of shares which have higher B/M ratio for the month. Positive HML shows that value stocks have given better result than the growth stocks and negative HML shows that growth stocks have given better result than the value stocks for the month. Multivariate Regression and performance evaluation of the mangers with the Three Factor Model The three factor model has the ability to describe the mutual funds and it can demonstrate the capability of investors to face specific risk factors. The logical part of the model is used to measure the past performance of the fund managers which also helps to determine the value that management has added to the organization. In reality, we need to have different time series of factors and returns to carry out the evaluation process. Firstly we need the amount of monthly returns from those stocks whose beta have been calculated for the time period. Second, we need the amount of return from overall market for that specific period. Third, we need to calculate the factors for HML and SMB for every month. Then we will be able to manipulate the Fama and French three factor model by subtracting the amount of risk free rate from both side of the equation and introducing the concept of excess return (alpha) to get the return from the equation In the above equation, historical data can be used in the form of multivariate regression to calculate the value of alpha. If the alpha has positive value then it shows that the fund manager of the mutual fund is adding value to the mutual fund portfolio and has less exposure to three factors of risk. The multivariate regression has two advantages with the three factor model as compared to the simple CAPM model. Firstly, the three factor model shows more variation in the actual returns as the value of R^2 are more than 0.95. Second, the three factor model has shown that positive value of alpha in CAPM regression is not a result from exposure to SMB or HML factors rather than the actual performance of the managers (Tuck School of Business at Dartmouth, 2003, pp. 8-12). References Tuck School of Business at Dartmouth., 2003. Understanding Risk and Return, the CAPM, and the Fama-French Three-Factor Model. [Pdf]. Available at: http://www.portfoliosolutions.com/pdfs/FF_3_Factor_Tucks.pdf. [Accessed on March 1, 2014]. Eraslan, V., 2013. Fama and French Three-Factor Model: Evidence from Istanbul Stock Exchange. [Pdf]. Available at: http://www.berjournal.com/wp-content/plugins/downloads-manager/upload/BERJ%204(2)13%20Article%202%20pp.11-22.pdf. [Accessed on March 1, 2014]. Research economics., No Date. Capital Asset Pricing Model. [Pdf]. Available at: http://research.economics.unsw.edu.au/jmorley/econ487/CAPM_lecture.pdf. [Accessed on March 1, 2014]. Timsimin., No Date. The Capital Asset Pricing Model. [Pdf]. Available at: http://timsimin.net/Files/Fin406/set4.pdf. [Accessed on March 1, 2014]. Fama, E., and French, K., 2004. The Capital Asset Pricing Model:Theory and Evidence. [Pdf]. Available at: http://www-personal.umich.edu/~kathrynd/JEP.FamaandFrench.pdf. [Accessed on March 1, 2014]. Bibliography Al-Mwalla, M., Karasneh, M., 2011. “Fama and French three factor model: Evidence from emerging market”. European Journal of Economics, Finance and Administrative Sciences. Markowitz, H., 1952. “Portfolio selection”. The Journal of Finance. Fama, E., and French, K., 2004. The Capital Asset Pricing Model:Theory and Evidence. [Pdf]. Available at: http://pubs.aeaweb.org/doi/pdfplus/10.1257/0895330042162430. [Accessed on March 1, 2014]. Fama, Eugene F., 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work.” Journal of Finance. Modigliani, F., et al. 1973. A TEST OF THE CAPITAL ASSET PRICING MODEL ON EUROPEAN STOCK MAPKETS. [Pdf]. Available at: http://dspace.mit.edu/bitstream/handle/1721.1/1871/SWP-0667-14514026.pdf?sequence=1. [Accessed on March 1, 2014]. Appendices:- a) Regression Analysis Output of Industry 1 – Shops a.1) Run 1 (Period 1980-2009) – 30 Years Descriptive Statistics Mean Std. Deviation N Others 1.117750 4.9237891 360 Mkt_Rf .541972 4.5933531 360 SMB .132000 3.1865445 360 HML .363361 3.1889596 360 Rf .4473 .26704 360 Correlations Others Mkt_Rf SMB HML Rf Pearson Correlation Others 1.000 .812 .478 -.136 -.047 Mkt_Rf .812 1.000 .217 -.377 -.045 SMB .478 .217 1.000 -.335 -.091 HML -.136 -.377 -.335 1.000 .045 Rf -.047 -.045 -.091 .045 1.000 Sig. (1-tailed) Others . .000 .000 .005 .186 Mkt_Rf .000 . .000 .000 .196 SMB .000 .000 . .000 .042 HML .005 .000 .000 . .195 Rf .186 .196 .042 .195 . N Others 360 360 360 360 360 Mkt_Rf 360 360 360 360 360 SMB 360 360 360 360 360 HML 360 360 360 360 360 Rf 360 360 360 360 360 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, Mkt_Rf, SMB, HMLa . Enter a. All requested variables entered. b. Dependent Variable: Others Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .914a .836 .834 2.0081153 .836 450.830 4 355 .000 a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 7271.941 4 1817.985 450.830 .000a Residual 1431.547 355 4.033     Total 8703.488 359       a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML b. Dependent Variable: Others Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) .255 .209   1.220 .223 -.156 .666 Mkt_Rf .906 .025 .845 36.163 .000 .857 .955 SMB .623 .036 .403 17.487 .000 .553 .693 HML .491 .037 .318 13.121 .000 .417 .564 Rf .249 .399 .013 .623 .533 -.536 1.033 a. Dependent Variable: Others Coefficient Correlationsa Model Rf Mkt_Rf SMB HML 1 Correlations Rf 1.000 .022 .078 -.008 Mkt_Rf .022 1.000 -.101 .331 SMB .078 -.101 1.000 .279 HML -.008 .331 .279 1.000 Covariances Rf .159 .000 .001 .000 Mkt_Rf .000 .001 .000 .000 SMB .001 .000 .001 .000 HML .000 .000 .000 .001 a. Dependent Variable: Others a.2) Run 2 (Period 1980-1989) – 10 Years Descriptive Statistics Mean Std. Deviation N Shops 1.3334 5.60772 120 Mkt_Rf .7088 4.87913 120 SMB .0074 2.36570 120 HML .4930 2.80267 120 Rf .7126 .23725 120 Correlations Shops Mkt_Rf SMB HML Rf Pearson Correlation Shops 1.000 .851 .609 -.476 -.114 Mkt_Rf .851 1.000 .227 -.560 -.216 SMB .609 .227 1.000 -.254 -.048 HML -.476 -.560 -.254 1.000 .159 Rf -.114 -.216 -.048 .159 1.000 Sig. (1-tailed) Shops . .000 .000 .000 .107 Mkt_Rf .000 . .006 .000 .009 SMB .000 .006 . .003 .303 HML .000 .000 .003 . .041 Rf .107 .009 .303 .041 . N Shops 120 120 120 120 120 Mkt_Rf 120 120 120 120 120 SMB 120 120 120 120 120 HML 120 120 120 120 120 Rf 120 120 120 120 120 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, SMB, HML, Mkt_Rfa . Enter a. All requested variables entered. b. Dependent Variable: Shops Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .956a .915 .912 1.66514 .915 308.659 4 115 .000 a. Predictors: (Constant), Rf, SMB, HML, Mkt_Rf ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 3423.277 4 855.819 308.659 .000a Residual 318.861 115 2.773     Total 3742.137 119       a. Predictors: (Constant), Rf, SMB, HML, Mkt_Rf b. Dependent Variable: Shops Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) -.568 .499   -1.137 .258 -1.557 .421 Mkt_Rf .929 .038 .808 24.161 .000 .853 1.005 SMB 1.064 .067 .449 15.860 .000 .931 1.197 HML .160 .067 .080 2.394 .018 .028 .292 Rf 1.623 .660 .069 2.460 .015 .316 2.929 a. Dependent Variable: Shops Coefficient Correlationsa Model Rf SMB HML Mkt_Rf 1 Correlations Rf 1.000 -.009 -.048 .155 SMB -.009 1.000 .158 -.106 HML -.048 .158 1.000 .519 Mkt_Rf .155 -.106 .519 1.000 Covariances Rf .435 .000 -.002 .004 SMB .000 .005 .001 .000 HML -.002 .001 .004 .001 Mkt_Rf .004 .000 .001 .001 a. Dependent Variable: Shops a.3) Run 3 (Period 1990-1999) – 10 Years Descriptive Statistics Mean Std. Deviation N Shops .9145 5.28260 120 Mkt_Rf 1.0637 3.99142 120 SMB -.0864 2.93630 120 HML -.1182 2.77552 120 Rf .4016 .11071 120 Correlations Shops Mkt_Rf SMB HML Rf Pearson Correlation Shops 1.000 .708 .644 -.346 -.167 Mkt_Rf .708 1.000 .184 -.497 -.037 SMB .644 .184 1.000 -.309 -.132 HML -.346 -.497 -.309 1.000 -.206 Rf -.167 -.037 -.132 -.206 1.000 Sig. (1-tailed) Shops . .000 .000 .000 .034 Mkt_Rf .000 . .022 .000 .343 SMB .000 .022 . .000 .075 HML .000 .000 .000 . .012 Rf .034 .343 .075 .012 . N Shops 120 120 120 120 120 Mkt_Rf 120 120 120 120 120 SMB 120 120 120 120 120 HML 120 120 120 120 120 Rf 120 120 120 120 120 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, Mkt_Rf, SMB, HMLa . Enter a. All requested variables entered. b. Dependent Variable: Shops Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .892a .796 .789 2.42612 .796 112.295 4 115 .000 a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 2643.904 4 660.976 112.295 .000a Residual 676.899 115 5.886     Total 3320.802 119       a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML b. Dependent Variable: Shops Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) .716 .891   .803 .423 -1.049 2.480 Mkt_Rf .904 .065 .683 13.879 .000 .775 1.033 SMB 1.015 .081 .564 12.454 .000 .853 1.176 HML .307 .100 .161 3.057 .003 .108 .505 Rf -1.590 2.128 -.033 -.747 .456 -5.804 2.624 a. Dependent Variable: Shops Coefficient Correlationsa Model Rf Mkt_Rf SMB HML 1 Correlations Rf 1.000 .161 .208 .304 Mkt_Rf .161 1.000 -.002 .492 SMB .208 -.002 1.000 .301 HML .304 .492 .301 1.000 Covariances Rf 4.526 .022 .036 .065 Mkt_Rf .022 .004 .000 .003 SMB .036 .000 .007 .002 HML .065 .003 .002 .010 a. Dependent Variable: Shops a.4) Run 4 (Period 2000-2009) – 10 Years Descriptive Statistics Mean Std. Deviation N Shops 1.0373 7.35877 120 Mkt_Rf -.1465 4.80972 120 SMB .4750 4.02890 120 HML .7153 3.83995 120 Rf .2277 .15767 120 Correlations Shops Mkt_Rf SMB HML Rf Pearson Correlation Shops 1.000 .791 .446 -.010 -.137 Mkt_Rf .791 1.000 .267 -.164 -.098 SMB .446 .267 1.000 -.407 -.103 HML -.010 -.164 -.407 1.000 .157 Rf -.137 -.098 -.103 .157 1.000 Sig. (1-tailed) Shops . .000 .000 .455 .068 Mkt_Rf .000 . .002 .037 .144 SMB .000 .002 . .000 .131 HML .455 .037 .000 . .043 Rf .068 .144 .131 .043 . N Shops 120 120 120 120 120 Mkt_Rf 120 120 120 120 120 SMB 120 120 120 120 120 HML 120 120 120 120 120 Rf 120 120 120 120 120 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, Mkt_Rf, HML, SMBa . Enter a. All requested variables entered. b. Dependent Variable: Shops Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .862a .743 .734 3.79594 .743 83.054 4 115 .000 a. Predictors: (Constant), Rf, Mkt_Rf, HML, SMB ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 4786.971 4 1196.743 83.054 .000a Residual 1657.057 115 14.409     Total 6444.028 119       a. Predictors: (Constant), Rf, Mkt_Rf, HML, SMB b. Dependent Variable: Shops Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) 1.286 .618   2.080 .040 .061 2.510 Mkt_Rf 1.123 .075 .734 14.890 .000 .973 1.272 SMB .638 .097 .349 6.578 .000 .446 .830 HML .504 .100 .263 5.030 .000 .305 .702 Rf -3.284 2.242 -.070 -1.465 .146 -7.725 1.156 a. Dependent Variable: Shops Coefficient Correlationsa Model Rf Mkt_Rf HML SMB 1 Correlations Rf 1.000 .066 -.123 .028 Mkt_Rf .066 1.000 .054 -.220 HML -.123 .054 1.000 .375 SMB .028 -.220 .375 1.000 Covariances Rf 5.026 .011 -.028 .006 Mkt_Rf .011 .006 .000 -.002 HML -.028 .000 .010 .004 SMB .006 -.002 .004 .009 a. Dependent Variable: Shops a) Regression Analysis Output of Industry 2 – Others a.1) Run 5 (Period 1980-2009) – 30 Years Descriptive Statistics Mean Std. Deviation N Others 1.1178 4.92379 360 Mkt_Rf .5420 4.59335 360 SMB .1320 3.18654 360 HML .3634 3.18896 360 Rf .4473 .26704 360 Correlations Others Mkt_Rf SMB HML Rf Pearson Correlation Others 1.000 .812 .478 -.136 -.047 Mkt_Rf .812 1.000 .217 -.377 -.045 SMB .478 .217 1.000 -.335 -.091 HML -.136 -.377 -.335 1.000 .045 Rf -.047 -.045 -.091 .045 1.000 Sig. (1-tailed) Others . .000 .000 .005 .186 Mkt_Rf .000 . .000 .000 .196 SMB .000 .000 . .000 .042 HML .005 .000 .000 . .195 Rf .186 .196 .042 .195 . N Others 360 360 360 360 360 Mkt_Rf 360 360 360 360 360 SMB 360 360 360 360 360 HML 360 360 360 360 360 Rf 360 360 360 360 360 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, Mkt_Rf, SMB, HMLa . Enter a. All requested variables entered. b. Dependent Variable: Others Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .914a .836 .834 2.00812 .836 450.830 4 355 .000 a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 7271.941 4 1817.985 450.830 .000a Residual 1431.547 355 4.033     Total 8703.488 359       a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML b. Dependent Variable: Others Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) .255 .209   1.220 .223 -.156 .666 Mkt_Rf .906 .025 .845 36.163 .000 .857 .955 SMB .623 .036 .403 17.487 .000 .553 .693 HML .491 .037 .318 13.121 .000 .417 .564 Rf .249 .399 .013 .623 .533 -.536 1.033 a. Dependent Variable: Others Coefficient Correlationsa Model Rf Mkt_Rf SMB HML 1 Correlations Rf 1.000 .022 .078 -.008 Mkt_Rf .022 1.000 -.101 .331 SMB .078 -.101 1.000 .279 HML -.008 .331 .279 1.000 Covariances Rf .159 .000 .001 .000 Mkt_Rf .000 .001 .000 .000 SMB .001 .000 .001 .000 HML .000 .000 .000 .001 a. Dependent Variable: Others a.2) Run 6 (Period 1980-1989) – 10 Years Descriptive Statistics Mean Std. Deviation N Others 1.3395 5.23023 120 Mkt_Rf .7088 4.87913 120 SMB .0074 2.36570 120 HML .4930 2.80267 120 Rf .7126 .23725 120 Correlations Others Mkt_Rf SMB HML Rf Pearson Correlation Others 1.000 .881 .569 -.473 -.146 Mkt_Rf .881 1.000 .227 -.560 -.216 SMB .569 .227 1.000 -.254 -.048 HML -.473 -.560 -.254 1.000 .159 Rf -.146 -.216 -.048 .159 1.000 Sig. (1-tailed) Others . .000 .000 .000 .055 Mkt_Rf .000 . .006 .000 .009 SMB .000 .006 . .003 .303 HML .000 .000 .003 . .041 Rf .055 .009 .303 .041 . N Others 120 120 120 120 120 Mkt_Rf 120 120 120 120 120 SMB 120 120 120 120 120 HML 120 120 120 120 120 Rf 120 120 120 120 120 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, SMB, HML, Mkt_Rfa . Enter a. All requested variables entered. b. Dependent Variable: Others Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .964a .929 .927 1.41428 .929 378.123 4 115 .000 a. Predictors: (Constant), Rf, SMB, HML, Mkt_Rf ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 3025.258 4 756.315 378.123 .000a Residual 230.021 115 2.000     Total 3255.279 119       a. Predictors: (Constant), Rf, SMB, HML, Mkt_Rf b. Dependent Variable: Others Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) -.058 .424   -.137 .891 -.898 .782 Mkt_Rf .918 .033 .856 28.099 .000 .853 .982 SMB .891 .057 .403 15.630 .000 .778 1.004 HML .190 .057 .102 3.362 .001 .078 .303 Rf .908 .560 .041 1.620 .108 -.202 2.017 a. Dependent Variable: Others Coefficient Correlationsa Model Rf SMB HML Mkt_Rf 1 Correlations Rf 1.000 -.009 -.048 .155 SMB -.009 1.000 .158 -.106 HML -.048 .158 1.000 .519 Mkt_Rf .155 -.106 .519 1.000 Covariances Rf .314 .000 -.002 .003 SMB .000 .003 .001 .000 HML -.002 .001 .003 .001 Mkt_Rf .003 .000 .001 .001 a. Dependent Variable: Others a.3) Run 7 (Period 1990-1999) – 10 Years Descriptive Statistics Mean Std. Deviation N Others 1.3273 4.43848 120 Mkt_Rf 1.0637 3.99142 120 SMB -.0864 2.93630 120 HML -.1182 2.77552 120 Rf .4016 .11071 120 Correlations Others Mkt_Rf SMB HML Rf Pearson Correlation Others 1.000 .701 .554 -.107 -.214 Mkt_Rf .701 1.000 .184 -.497 -.037 SMB .554 .184 1.000 -.309 -.132 HML -.107 -.497 -.309 1.000 -.206 Rf -.214 -.037 -.132 -.206 1.000 Sig. (1-tailed) Others . .000 .000 .122 .010 Mkt_Rf .000 . .022 .000 .343 SMB .000 .022 . .000 .075 HML .122 .000 .000 . .012 Rf .010 .343 .075 .012 . N Others 120 120 120 120 120 Mkt_Rf 120 120 120 120 120 SMB 120 120 120 120 120 HML 120 120 120 120 120 Rf 120 120 120 120 120 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, Mkt_Rf, SMB, HMLa . Enter a. All requested variables entered. b. Dependent Variable: Others Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .916a .840 .834 1.80619 .840 150.900 4 115 .000 a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1969.144 4 492.286 150.900 .000a Residual 375.169 115 3.262     Total 2344.313 119       a. Predictors: (Constant), Rf, Mkt_Rf, SMB, HML b. Dependent Variable: Others Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) .697 .663   1.051 .295 -.617 2.011 Mkt_Rf .930 .048 .837 19.190 .000 .834 1.026 SMB .824 .061 .545 13.588 .000 .704 .944 HML .760 .075 .475 10.176 .000 .612 .908 Rf -.494 1.584 -.012 -.312 .756 -3.632 2.643 a. Dependent Variable: Others Coefficient Correlationsa Model Rf Mkt_Rf SMB HML 1 Correlations Rf 1.000 .161 .208 .304 Mkt_Rf .161 1.000 -.002 .492 SMB .208 -.002 1.000 .301 HML .304 .492 .301 1.000 Covariances Rf 2.509 .012 .020 .036 Mkt_Rf .012 .002 .000 .002 SMB .020 .000 .004 .001 HML .036 .002 .001 .006 a. Dependent Variable: Others a.4) Run 8 (Period 2000-2009) – 10 Years Descriptive Statistics Mean Std. Deviation N Others .6864 5.07953 120 Mkt_Rf -.1465 4.80972 120 SMB .4750 4.02890 120 HML .7153 3.83995 120 Rf .2277 .15767 120 Correlations Others Mkt_Rf SMB HML Rf Pearson Correlation Others 1.000 .821 .421 .105 -.057 Mkt_Rf .821 1.000 .267 -.164 -.098 SMB .421 .267 1.000 -.407 -.103 HML .105 -.164 -.407 1.000 .157 Rf -.057 -.098 -.103 .157 1.000 Sig. (1-tailed) Others . .000 .000 .126 .269 Mkt_Rf .000 . .002 .037 .144 SMB .000 .002 . .000 .131 HML .126 .037 .000 . .043 Rf .269 .144 .131 .043 . N Others 120 120 120 120 120 Mkt_Rf 120 120 120 120 120 SMB 120 120 120 120 120 HML 120 120 120 120 120 Rf 120 120 120 120 120 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Rf, Mkt_Rf, HML, SMBa . Enter a. All requested variables entered. b. Dependent Variable: Others Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .916a .840 .834 2.06783 .840 150.767 4 115 .000 a. Predictors: (Constant), Rf, Mkt_Rf, HML, SMB ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 2578.669 4 644.667 150.767 .000a Residual 491.729 115 4.276     Total 3070.399 119       a. Predictors: (Constant), Rf, Mkt_Rf, HML, SMB b. Dependent Variable: Others Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) .244 .337   .724 .471 -.423 .911 Mkt_Rf .830 .041 .786 20.205 .000 .748 .911 SMB .462 .053 .366 8.743 .000 .357 .567 HML .507 .055 .383 9.296 .000 .399 .615 Rf -.079 1.221 -.002 -.065 .949 -2.498 2.340 a. Dependent Variable: Others Coefficient Correlationsa Model Rf Mkt_Rf HML SMB 1 Correlations Rf 1.000 .066 -.123 .028 Mkt_Rf .066 1.000 .054 -.220 HML -.123 .054 1.000 .375 SMB .028 -.220 .375 1.000 Covariances Rf 1.491 .003 -.008 .002 Mkt_Rf .003 .002 .000 .000 HML -.008 .000 .003 .001 SMB .002 .000 .001 .003 a. Dependent Variable: Others Read More