MUHAMMAD AZAM Student of MS-Finance Institute of Management Sciences, Peshawar.

Transcription

1 An Empirical Comparison of CAPM and Fama-French Model: A case study of KSE MUHAMMAD AZAM Student of MS-Finance Institute of Management Sciences, Peshawar. JASIR ILYAS Student of MS-Finance Institute of Management Sciences, Peshawar. Abstract The main aim of this paper is to compare the predictive power of two assets valuation models; CAPM and Fama-French three factor and five factor models. This research tests the effectiveness of three asset-pricing models by using five economic variables of fifty firms listed in Karachi stock exchange for the period January 2003 to December The CAPM relates the expected return on a portfolio or stock to a single factor or the excess return on a market portfolio. The three-factor model expands on the CAPM with the introduction of two additional factors i.e. size premium and book to market equity premiums. The five factor model is addition to Fama and French three-factor model with additional variable of Price to earning premium and leverage premium. Results of the study showed that there is little difference in the performance of three asset valuation models. CAPM and Fama-French five factor model indicated four intercepts as significant whereas Fama-French three factor model indicated five intercepts as significant. However Fama-French five-factor model has more explanatory power than other two. The study concluded that these three models can be used as proxy for risk but Fama-French five-factor has slight edge over others. Keywords: Empirical Comparison ; CAPM ; Fama-French Model: KSE COPY RIGHT 2011 Institute of Interdisciplinary Business Research 415

2 INTRODUCTION Extensive part of the research labors in finance has been made to answer the query that How an investor should value a risky securities. It is generally a view that investor demands higher expected rate of return for investment in riskier projects or securities. Estimation of expected return and risk associated with investment in risky securities is indispensable to many financial decisions such as those relating to portfolio management, capital budgeting, and performance evaluation. Prevailing modern investment theories are embedded largely on two initial concepts. The first, due to the work of Harry Markowitz, is that in an efficient financial market, higher risk exposure leads to higher return expectations. The second concept established by William F. Sharpe, is that since the risks (unsystematic risk) associated with individual securities have a tendency to offset each other in diversified portfolios, the relevant factor is systematic risk. Hence investor is a paid off for exposure to greater "systematic" risk (risk that cannot be diversified away). This concept is known as the Capital Asset Pricing Model (CAPM) presented by William F. Sharpe. In recognition of their formative work both economists, Harry Markowitz and William F. Sharpe, received Nobel Prizes. Sharpe's CAPM characterize that stock returns and market beta has linear combination and investor is just compensated for systematic risk, not for unsystematic risk as it can be eliminated through appropriate diversification. Beta, a measure of systematic risk, is obtained from a regression of securities' returns against the market's returns. The CAPM attributed risk to a single systematic factor which led to academic argument that risk is multidimensional factor. Thus many theories containing diverse factors were presented. Arbitrage pricing theory (1976), first presented by Stephen Ross, established a firm theoretical groundwork for the existence of multiple systematic sources of risk and return, and provided the way for the multi-factor models of today. The CAPM followed the model of portfolio choice developed by Harry Markowitz (1959). In Markowitz's model assumes that investors are risk averse and, when choosing among portfolios, they concern only about the mean and Variance of return from one period investment. Consequently investors choose "mean-variance-efficient" portfolios in the sense that the portfolios minimize the variance of portfolio return given expected return, or maximize expected return given variance. Thus, the Markowitz approach is repeatedly called as "mean variance model." The basic purpose of using CAPM approach is to find the true price of securities based on their combination of risk and return. This model facilitates to calculate the required rate of return (RRR), a rate that an investor requires from his investment, on a security based of its systematic risk. Required rate of return has two components i.e. risk free rate and risk premium on the given security. Risk premium depends on how risky is a security, therefore for riskier securities the risk premium is high and vise versa. The empirical findings against CAPM s zero-intercept hypothesis has naturally led to the empirical examination of multifactor asset pricing models motivated by the arbitrage pricing theory (APT) developed by Ross (1976), the intertemporal capital asset pricing model (ICAPM) developed by Merton (1973) and Fama-French Three factor model (1993). The basic approach has been to introduce additional factor contributing to risk and return on traded portfolios and then retrace the zero-intercept hypothesis. Fama and French (1993) used this approach and documented that the estimates of the CAPM intercepts deviate from zero for portfolios formed on the basis of the ratio of book to market COPY RIGHT 2011 Institute of Interdisciplinary Business Research 416

3 value of equity as well as for portfolios formed based on market capitalization along with usual market premium. On finding that the intercepts for these portfolios with a three-factor model are closer to zero, they concluded that missing risk factors in the CAPM were the source of the deviations. Three factor models say that the expected return on a portfolio in excess of the risk free rate is explained by the sensitivity of its return to three factors. First, the excess return (or market premium) on a wide market portfolio, secondly the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks (SMB) and thirdly the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to- market stocks (HML). If estimation is based on Fama French, then an estimate for the beta for each factor is obtained using a simple regression and these estimates are multiplied by the risk premium for the relevant factor to obtain an estimate of price or value for portfolio. Objectives of the Study: The main objectives of this paper were to compare empirically the CAPM and Fama-French approaches i.e. 1. To investigate the performance of CAPM model 2. To investigate the existence of the size, book-to-market equity and market premium, and its effects on risky security return. 3. To attempt an augmentation of the Fama and French (1993) three-factor model along with the two variables, leverage and E/P risk premiums, by taking into account the time variation of stock returns in betas. In the light of above stated research objective, the research questions to be investigated were, how should the market risk premium be measured and what are the factors that determine the price of risky securities. In order to give answer to these questions, this paper investigated the relation among stock returns, Beta, size, book-to market equity ratio along with two additional factors, leverage and price earning ratio in order to make estimation of market premium more reliable, using data of Pakistani firms of textile sector listed on Karachi stock exchange. LITERATURE REVIEW After Sharpe empirical work, Fama and Macbeth (1973) empirical work support two-parameter model hypothesis of regarding risk averse investor attempting to holding efficient portfolio reflected in New York stock exchange stocks return, thus proving linear relation between expected return and dispersion in return. Work of Blume (1970), Black Jensen and Scholes (1972) and Stambaugh (1982) establish evidence that the relation between beta and average return is a linear, higher beta firm will give higher return and there will be high risk involves. However after the work of Basu (1977) and Banz (1981), a decade later Sharpes theory was presented, empirical evidences turned out to be strongly against CAPM. Basu (1977) exposed that the CAPM underestimates the future returns on high earnings to price stocks for the reason that beta under CAPM does not capture it. After that many researches found others factors like size, book to market value of equity and leverage etc, not being captured by beta in determining stock expected returns. Banz (1981) draw attention to point that Small size firms have higher average returns than large size firms on the basis of systematic risk, indicating the inability of the CAPM to capture returns of small stocks. Bhandari (1988) found high leverage or debt-equity associated with returns but not captured by CAPM. Whereas Stattman (1980) along with Rosenberg, Reid, and Lanstein (1985) suggested stock having high book to market value result in higher average return as compared to stock with low COPY RIGHT 2011 Institute of Interdisciplinary Business Research 417

4 Book to market equity value relative to their respective betas, thus indicating the inability of the CAPM. Another study of New York stock exchange listed stocks by Chan and Chen (1991) again pointed that small firms are firms that are less proficiently handled and their leverage is also high, resulting in underperformance and riskiness. Thus being riskier than large firms, a small firm provides high average return than large firms. After much criticism, for the first time Fama and French 1993 presented three factor asset pricing model after their study in 1992 in which they studied the part of beta, size, Earnings to Price fraction, leverage and book to market value of equity on returns of stocks from 1963 to 1990 in the cross-section over different markets and finding out size and book to market equity fraction has more explanatory value. In 1993 they extended their study on bonds along with stock returns taking in consideration factors for bonds return i.e. a term premium and a default premium, and taking three factors, i.e. market premium, size and book to market equity fraction, to explain returns on stock. The study found these factors significantly capturing much of return on stocks when cross-sectionally studied. Thus Fama and French (1993) put up a three-factor asset pricing model for stocks taking in account premium based on beta factor, size (i.e. difference between returns of small size firms stock portfolio and return of large size firms stock portfolio) and book to market equity (i.e. difference between return of portfolio stocks with low book to market equity and return of portfolio stock with high book to market equity). Jagannathan, Rand Z.Wang (1996) found support for CAPM when they tested the assumption that betas do not remain constant over time using stocks listed NYSE and AMEX during the period 1962 to They sorted all stocks according to their market value and respected betas were calculated and ranked in ascending order. The study findings supported CAPM provided with betas and expected returns vary over time. According to Heston, Rouwenhorst, and Wessels (1995) study of European markets valueweighted portfolios likely to have lesser average returns equally-weighted stock portfolios, whereas also argued that the size effect may not only be limited to domestic market. Cross Sectional study of Common Stock Returns by Gabriel Hawawini and Donald B Kein (1998) also argued prediction of stocks return is affected by many factors like size, ratio of book to market value, EPS, etc which play significant role instead of just beta of common stock. The study of Ashton and Tippett (1998) concluded the mis-specification in estimation of asset can lead dismissal of the CAPM in favor of other factors after studying the performance of beta and other factors in the presence of a mis-specified cumulative wealth process. The test study of CAPM on Dhaka Stock Exchange by Muhammad Mostafizur Rahman and Muhammad Azizul Baten (2006) using sample of 123 stocks and by following the methodology of Fama and French Model found that the despite beta has a positive association with the stock returns, it is not the only cause affecting returns. They emphasis that among many factors like size and EPS ratio, timing factor is also important in affecting the returns of stocks. Howton and Peterson s (1998) examine stock returns in bullish and bearish market and found out that beta in bull market is significantly positively to returns, whereas in bear market it is significantly negatively related to returns except for some models in January even in presence others factors in cross sectional regression. Additional they pointed that Book-to-market equity is an essential factor in bearish market and size is key factor in January in bull market. COPY RIGHT 2011 Institute of Interdisciplinary Business Research 418

5 RESEARCH METHODOLOGY This research study is based on the data set containing 50 firms listed in the KSE for the entire test period that is January 2003 to December The share prices and market index data for the study have been obtained form Karachi stock exchange, and annual reports of the selected companies obtained from their web addresses. However during selection of sample companies, financial firms like banks and insurance companies were not selected on the basis of the fact that, on average, these financial firms have higher leverage as compared to other firms and their inclusion can change the test result significantly. Following CAPM and Fama French approaches, this study defines market beta, size, book to market equity, Price to Earning and leverage variables based on the idea that the returns of individual assets are influenced by the market itself and other broadly influential factors affirmed. The CAPM, Fama French 3-factors, Fama French-5 factors approach by performing crosssectional regression on monthly returns against the variables shown in the following equations: R i R f = + 1 (R m R f ) Whereas; R i R f = + 1 (R m R f ) + 2 (SMB) + 3 (HML) R i R f = + 1 (R m R f ) + 2 (SMB) + 3 (HML) + 4 (HML-PE) + 5 (HML-L) R i = Security returns = (previous price current price)/ previous price or (p 0 p 1 )/ p 0 R m = R f = R i R m Return on M. Port = (Index1-Indexo)/Index o Risk free rate (T-bill rates) R f = the excess return on a individual selected stocks. R f = the excess return on a broad market portfolio. SMB = the difference between the return on a portfolio of small stocks and the return on portfolio of large stocks. HML = the difference between the return on a portfolio of high book to market equity stocks and the return on a portfolio of low book to market equity stocks. HML-PE = the difference between the return on high price to earning ratios firm's stocks and the return on high price to earning ratios firm's stocks. HML-L = the difference between the return on high leverage firm's stocks and the return on lower leverage firm's stocks. In order to find High minus low book to market and small minus large firms, the study arranged the data in ascending order and selected 15 lower and 15 top firm to calculate desired variables. Hypotheses: The study used firm s panel data at the end of December of each year to compute its book-tomarket, leverage, and price earning ratio for the analysis from January 2003 to December The study took monthly stock prices in order to obtained monthly returns for the specified period. This study hypothesizes following statements; a COPY RIGHT 2011 Institute of Interdisciplinary Business Research 419

6 H 0 : There is no relationship between beta and expected rate of return. H 1 : Firms with small Size has low high average return than firms of large size. H 2 : Firms with high book to market equity has high average returns than firms with low book to market equity. H 3 : Firm with high price earning ratio has high average returns than firms with low price earning ratio. H 4 : Firms with high leverage has high average returns than firms with low leverage. To estimate this panel data models this study used ordinary least square regression method. REGRESSION ANALYSIS AND ITS RESULTS Regression Analysis of CAPM After data was arranged, regression model was run in which individual excess security returns was dependent and market excess returns was independent variable of the study. In equation form their relationship in established as following R i R f = + 1 (R m R f ) Whereas results of regression model are summarized as followed. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 59 R i R f = (R m R f ) ANOVA df SS MS F Significance F Regression E-14 Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept X Variable E From above regression results one can interpret that even if there is no market excess returns still there will 1.1% individual security excess return but one can clearly see that the P- value for this parameter is insignificant as its exceeds 10% level. This parameter make obvious that the CAPM model is a good fit. Coefficient of independent variable i.e. market excess returns shows that if there is one percent change in markets excess returns, it would lead to 0.91% change in individual security excess return in same direction. About the precision of this parameter P-value shows that it is highly significant statistically. COPY RIGHT 2011 Institute of Interdisciplinary Business Research 420

7 About overall model, regression model shows that the model has 62% explanatory power i.e. market excess return explain 62% out of total change in individual security excess return which is visible in coefficient of determination or R 2 value. However this explanatory power reduces by only 1% when it is adjusted for degree of freedom. About significance of the regression model statistically as a whole, F-value is which is much greater than 4, using rule of thumb, one can say that model as whole is significant statistically. Regression analysis of Fama-French three factor model Fama-French 3 factor model, excess return on individual stocks is dependent variable where as independent variables are market excess returns, difference between the return on a portfolio of small stocks and large stocks and difference between the return on a portfolio of high and low book to market equity stocks. In equation form; R i R f = + 1 (R m R f ) + 2 (SMB) + 3 (HML) Regression analysis over the data produces following results; R i R f = 1.82E (SMB) (HML) (Rm - Rf)) SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 59 ANOVA Df SS MS F Significance F Regression E-16 Residual Total Coefficients Standard Error T Stat P-value Lower 95% Upper 95% Intercept 1.82E X Var (SML) X Var (HML) E X Var (R i R f ) E Regression results shows that holding other factors equal to zero, still there will 1.82E-05% individual security excess return but once again one can clearly see that the P- value for this parameter is insignificant. Coefficient of SML variable shows that if there is one percent change in SML factor, it would lead to 0.03% change in individual security excess return in opposite direction. About the precision of this parameter, P-value also shows that it is not significant statistically. Coefficient of HML book to equity variable shows that if there is one percent increase in HML, it would lead to 0.12% decrease in individual security excess return. P-value for this parameter shows that it is highly significant statistically. Coefficient of market excess returns variable shows that if there is one percent change in markets excess returns, it would lead to 0.86% COPY RIGHT 2011 Institute of Interdisciplinary Business Research 421

8 change in individual security excess return in same direction. P-value of this parameter also shows that it is highly significant statistically. Regression model shows that overall this three factor model has 74% explanatory power i.e. three factor included in this model explains 74% change out of total change in individual security excess return which is visible in coefficient of determination or R 2 value. When it is adjusted for degree of freedom, this explanatory power reduces by only 1%. About significance of the regression model statistically as a whole, F-value is again much higher than 4, showing that model as whole is significant statistically. Analysis of Fama-French five factor model In this model two more factor i.e high minus price to earning and leverage ratio were added in addition to Fama-French three factor model as shown below; R i R f = + 1 (R m R f ) + 2 (SMB) + 3 (HML) + 4 (HML-PE) + 5 (HML-L) After regression it can be written as R i -R f = (Rm - Rf) (SMB) (HML) (HML-P) (HML-L) Other results are as following; SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 59 ANOVA df SS MS F Significance F Regression E-18 Residual Total Coefficients Standard Error T Stat P-value Lower 95% Upper 95% Intercept ( ) X-1. (Rm Rf) E X-2. SMB X-3.HML X-4.HML-P X-5. HML-L Here intercept estimate value suggests that holding all independent variables equal to zero, still there will negative excess return on individual security of 0.005% however this estimate is insignificant statistically. Respected coefficient of the factors of study shows that 1% change in market excess returns leads to 0.97 % positive change in individual security excess returns, 1% in small minus big firms returns leads to 0.12 % negative change in individual security excess returns, 1% change in high minus large book to market ratio of firm s returns leads to 0.21 % COPY RIGHT 2011 Institute of Interdisciplinary Business Research 422

9 negative change in individual security excess returns, 1% change in high minus high P/E ratios of firms returns leads to % negative change in individual security excess returns and 1% change in high minus high leverage of firms returns leads to 0.31% negative change in individual security excess returns. Except small minus large firm and high minus low price to earning ratio, rest of the factors that included in this model are significant statistically basis on their P-value. This five factor model has explained 82% change out of total change in individual security excess return which is visible in coefficient of determination or R 2 value which reduces by only 2% when it is adjusted for degree of freedom. About significance of the regression model statistically as a whole, based on rule of thumb, showing that model as whole is significant statistically. FINDINGS OF THE STUDY Total 50 Pakistani firms listed on Karachi stock exchange were selected for this study. First the study calculated average monthly returns from stock prices of the selected firms. Through regression study calculated parameters of the models used in this study. The study traced the significance and insignificance of parameters on basis of P-value. Using CAPM approach, out of total 50 regression results, only five company s intercepts were significant. CAPM approach strongly relies on intercept or alpha but here out of 50 companies 46 were insignificant and only four firms intercept was significant. CAPM model of the study explained only 62.6 % variation in risky stock excess returns by the market excess returns and the rest is error. The regression results rejected the hull hypothesis i.e. there is no relationship between beta and expected rate of return, therefore the study accepts alternative hypothesis that there is significant relationship between beta and expected rate of return. Individual company s regression results under CAPM are summarized in table 1 in appendix. In Fama-French approach, the study took two additional independent variables i.e. size premium and book to market equity premium in addition to market excess premium. To calculate these factors, 30 firms were taken on the basis of size risk premium and 30 firms on the basis of book to market equity premium. Results showed five firm s intercepts were significant and the rest were insignificant. As compared to CAPM, Fama and French three factors approach had more explanatory power as its independent variables explained 74% of total variation in dependent variable. Here as well the study accepts alternative hypothesis that there is significant relationship between beta and expected rate of return. The study found size risk premium insignificantly affects the expected return on risky stock, the average return decrease as size increases, whereas the book to market equity ratio significantly affects the expected return negatively when book to market ratio increase. Thus study accepts the null hypothesis for size factor but rejects the hypothesis for book to market equity ratio factor. Under three- factor model, individual company s regression results are summarized in table 2 in appendix. Third model of the study was Fama-French five factors model in which this study took two additional factors in addition to Fama-French three factor which were leverage risk premium and E/P risk premium. Regression results showed four companies intercepts significant and the rest were insignificant. The shows that 82 % variation in stock returns are due to explain variable and rest of the variation is explained by factors that are not included in the model. Based on the explanatory power of the models, five factors model is better as compare to CAPM and Fama French three factors model. In case of five factor model the study once again accepts alternative hypothesis that there is significant relationship between beta and expected rate of return. About size and book to market equity factors the study again accepts and rejects the null hypothesis respectively. Results of price earning ratio factor have insignificantly negative relation with average return on stock. Where as increase in leverage factor results in significantly decrease in the average stock s return. This leads this study to acceptance of null hypothesis regarding price COPY RIGHT 2011 Institute of Interdisciplinary Business Research 423

10 earning ratio factor and rejection of null hypothesis regarding leverage factor. Five-factor model regression results for each company are summarized in table 3 in appendix. CONCLUSION This study empirically examined three different asset-pricing models i.e. CAPM, Fama-French three and five factor models applied to fifty firms listed on Karachi stock exchange from time period 2003 to CAPM model has only one factor i.e. market risk premium whereas Fama- French three-factor model contains a market factor, size premium and book to market equity premium. Fama-French five factor model was also included in this study which contained additional P/E premium and leverage premium factors along with market, size premium and book to market equity premium factors. Although study of Fama and French (1998) provide confirmation for the international adaptation of the model (i.e. when the factors are global), however many studies by practitioners and academics used a domestic account of this model. Likewise, Griffin (2002) shows that the domestic three factor model evidently outperforms the global model for the US, Canada, Japan and the UK. This study also used domestic three factors model which result in better performance of these asset pricing models. Fama-French trace empirically the unexplained elements of Sharp's CAPM, which have a little empirical evidence for implication. But our result shows that CAPM, Fama-French three and five factors model have good explanatory power. The result showed that three models performed well to calculate better companies stock's returns listed on Karachi stock exchange for the entire test period January 2003 to December The study compared these models on the basis of parameter alpha or intercept, if alpha is insignificant the model is said to be correct. The regression results showed that five intercepts for Fama French 3-factor model, four each for CAPM and fama French 5-factor model were significant indicating that three models performed well and explanatory power of these models are reliable. However Fama-French five factors model has a slight edge over other models. Five accounting variables, size premium, book-to-market equity premium, leverage premium, market premium and E/P premium, enable us to capture the average returns on risky stock over the period. CAPM, Fama and French three-factors and five-factors models are correct to serve as proxy for risk. These models can be used as benchmark for portfolio performance valuation by investors and fund managers. Investors and fund managers can evaluate their portfolios by comparing their portfolio returns to the benchmark model with similar size, book-to-market equity characteristics. If their portfolio returns are higher than the benchmark, they will be able to outperform the market. COPY RIGHT 2011 Institute of Interdisciplinary Business Research 424

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