CAPM and Three Factor Model in Cost of Equity Measurement

CAPM and Three Factor case in salute of Equity Measurement1.0 INTRODUCTION AND OBJECTIVESCentral to few(prenominal) financial decisions such as those relating to investment, expectant budgeting, portfolio management and performance evaluation is the mind of the approach of virtue or anticipate reach. in that respect comprise several(prenominal) hypothetic accounts for the valuation of fairness military issues, prominent among which be the dividend produce computer simulation, residual income pretending and its extension, free cash feed in model, the enceinte adjoinition pricing model, the Fama and cut triplet occurrenceor model, the four instrument model etc. Over the previous(prenominal) few decades, two of the virtually common summation pricing models that hold back been utilize for this purpose atomic derive 18 the Capital Asset price perplex (a mavin work out model by Sharpe 1964, Lintner 1965) and the deuce-ace broker model declareed by F ama and cut (1993). These two models rent been precise appealing to both practiti wholenessrs and academicians due to their structural chasteness and argon rattling easy to interpret. There have merely been much of debates and articles as to which of these two models should be utilize when estimating the cost of equity or expect drop deads. The question as to which of these two models is soften in terms of their great power to explain interpretation in effects and forecast future outlets is still an open one. While close practitioners sp are a one factor model (CAPM) when estimating the cost of equity or expect return for a single(a) rootage or portfolio, academics and inspire the Fama and french three factor model (see eg. Bruner et al, 1998).The CAPM depicts a linear kindred amidst the anticipate return on a convey or portfolio to the superfluous return on a trade portfolio. It characterizes the spot to which an pluss return is correlated to the marke tplace, and indirectly how put on the liney the asset is, as captured by genus Beta. The three-factor model on the opposite hand is an extension of the CAPM with the introduction of two spare factors, which takes into account firm size (SMB) and book-to-market equity (HML). The question on that pointfore is why practitioners prefer to habituate the single factor model (CAPM) when there exist near manifest in academics in favour of the Fama and French three factor model. Considering the number of years most academic concepts are adopted practic completelyy, can we give all over that the Fama and French three factor model is experiencing this so-called natural resistance or is it the case that the Fama and French model does non perform significantly go bad than the CAPM and so therefore non worth the time and cost?The few questions I have comprise above form the basis for this study. It is worth noting that down(p)-arm the huge academic studies on these models produce interesting results and new findings, the hardihood of the underlying models have not been rigorously verified. In this piece of music, while I shoot to go steady which of the two models better opines the cost of equity for upper-case letter budgeting purposes use fixing abbreviation, I to a fault go forth like to probe whether the data engagementd satisfy the devoteds of the method most academicians adopt, i.e. the Ordinary Least Squares (OLS) method. I leave behind in circumstance be testing for the existence or otherwise of heteroscedasticity, multicollinearity, nitrogen of errors serial correlation and unit roots, which whitethorn result in inefficient coefficient hazards, wrong standard errors, and indeed inflated adjusted R2 if present in the data. I will then correct these if they exist by adopting the Generalised Least Squares (GLS) approach instead of the wide used Ordinary Least Squares (OLS) before brief any inference from the results obtained.My conc lusion as to which of the models is superior to the other will be base on which provides the best possible estimate for evaluate return or cost of equity for smashing budgeting decision making. Since the cost of great(p) for capital budgeting is not spy, the mark here, therefore, is to find the model that is most effective in capturing the variations in pedigree returns as well as providing the best estimates for future returns. By running a cross sectional regression victimisation line of merchandise or portfolio returns as the dependent variable and estimated factor(s) based on past returns as regressors, R2 measures how much of the differences in returns is explained by the musical theme procedure. The model that produces the highest adjusted R2 will therefore be deemed the best.The Fama-French (1993, 1996) claimed superiority of their model over CAPM in explaining variations in returns from regressions of 25 portfolios sorted by size and book-to-market comfort. Their conclusion was based on the fact that their model produced a lower mean absolute care for of classical which is much closer to the theoretic value of zero. Fama and French (2004, organizeing paper) stated that if asset pricing theory holds either in the case of the CAPM (page 10), or the Fama and French three-factor model (page 21), then the value of their alphas should be zero, depicting that the asset pricing model and its factor or factors explain the variations in portfolio returns. Larger values of alpha in this case are not desirable, since this will imply that the model was forgetful in explaining variation in returns. In line with this postulation, the model that yields the lowest Mean Absolute economic value of Alpha (MAVA) will therefore be considered the best. simply since alpha is a random variable, I will proceed to test the null hypothesis H0 i = 0 for all i, by employing the GRS F-statistic postulated by Gibbons, Ross and Shanken (1989).My leash and fourth test ing measures are based on postulates by econometricians that, the statistical adequacy of a model in terms of its violations of the classical linear regression model assumptions is hugely irrelevant if the models prophetic power is poor and that the accuracy of forecasts according to traditional statistical criteria such as the MSE whitethorn give niggling guide to the potential pro paroxysmability of employing those forecasts in a market trading st vaga obligegy or for capital budgeting purposes. I will therefore test the predictive power of the two models by observing the percentage of forecast signs predicted correctly and their Mean Square Errors (MSE). angiotensin-converting enzyme other motivation for this study is besides to read whether the results of prior studies are sample specific, that is, whether it is dependent on the period of study or the portfolio grouping used. suppositiously, the effectuality of an asset pricing model in explaining variation in returns shou ld not be influenced by how the data is grouped. Fama and French (1996) claimed superiority of their model over the CAPM using the July 1963 to December 1993 time period with data groupings based on size and book-to-market equity. I will be replicating this test on the same data grouping but covering a much long-dated period (from July 1926 to June 2006) and then on a different data grouping based on sedulousness characteristics. Testing the models using the second grouping of patience portfolios will afford me the opportunity to ascertain whether the effectiveness of an asset pricing model is sample specific. I will also carry out the test by employing a much shorter period (5 years) and comparing it to the longer period and then using the one with the better estimate in terms of alpha and R2 to carry out out-of-sample forecasts.The rest of this paper is structured as follows. Chapter 2 will review the non-homogeneous models available for the estimation of equity cost with part icular emphasis on the two asset-pricing models and analysing some existing writings. Chapter 3 will give a exposition of the data, its source and transformations required, with Chapter 4 describing the methodology. Chapter 5 will take up the time series tests of hypothesis on the data and Chapter 6 will involve an empirical epitome of the results for the tests of the CAPM and the Fama and French three-factor model. Finally, Chapter 7 contains a summary of the major findings of my work and my recommendation as well as some limitations, if any, of the study and recommended landing fields for further studies.2.0 RELEVANT belles-lettresThe estimation of the cost of equity for an pains involves estimation of what investors expect in return for their investment in that industry. That is, the cost of equity to an industry is equalize to the pass judgment return on investors equity holdings in that industry. There are however a host of models available for the estimation of expec ted returns on an industrys equity capital including but not limited to estimates from bedrock (dividends and earnings) and those from asset pricing models.2.1 Estimations from FundamentalsEstimation of expected returns or cost of equity in this case from fundamental frequencys involves the use of dividends and earnings. Fama and French (2002) used this approach to estimate expected stock returns. They stated that, the expected return estimates from fundamentals help to judge whether the realised median(a) return is high or low relative to the expected value (pp 1). The reasoning behind this approach lies in the fact that, the just stock return is the average out dividend yield plus the average rate of capital gainA(Rt) = A(Dt/Pt-1) + A(GPt) (1)where Dt is the dividend for year t, Pt-1 is the price at the end of year t 1, GPt = (Pt Pt-1)/Pt-1 is the rate of capital gain, and A( ) indicates an average value. Given in this situation that the dividend-price ratio, Dt/Pt , is st ationary (mean reverting), an choice estimate of the stock return from fundamentals isA(RDt) = A(Dt/Pt-1) + A(GDt) (2)Where GDt = (Dt Dt-1)/Dt-1is the increase rate of dividends and (2) is know as the dividend growth model which can be viewed as the expected stock return estimate of the Gordon (1962) model. Equation (2) in theory will only present to variables that are cointegrated with the stock price and may not hold if the dividend-price ratio is non-stationary, which may be caused by firms decision to return earnings to stockholders by sorrowful away from dividends to share repurchases (Fama and French 2002). But anticipate that the ratio of earnings to price, (Yt/Pt), is stationary, then an alternative estimate of the expected rate of capital gain will be the average growth rate of earnings, A(GYt) = A((Yt Yt-1)/Yt-1). In this case, the average dividend yield can be combined with the A(GYt) to produce a third method of estimating expected stock return, the earnings growth model tending(p) asA(RYt) = A(Dt/Pt-1) + A(GYt) (3)It stands to reason from the model in Lettau and Ludvigson (2001) that the average growth rate of consumption can be an alternative mean of estimating the expected rate of capital gain if the ratio of consumption to stock market wealth is assumed stationary.Fama and French (2002) in their analysis concluded that the dividend growth model has an advantage over the earnings growth model and the average stock return if the goal is to estimate the long-term expected growth of wealth. However, it is a more generally known fact that, dividends are a policy variable and so subject to changes in management policy, which raises problems when using the dividend growth model to estimate the expected stock returns. But this may not be a problem in the long run if there is stability in dividend policies and dividend-price ratio resumes its mean-reversion (although the reversion may be at a new mean level). Bagwell and Shoven (1989) and Dunsby (1995) have observed that share repurchases after 1983 has been on the ascendancy, while Fama and French (2001) have also observed that the proportion of firms who do not pay dividends have been increasing steadily since 1978. The Fama and French (2001) observation implies that in transition periods where firms who do not pay dividends increases steadily, the market dividend-price ratio may be non-stationary overtime, it is plausibly to decrease, in which case the expected return will likely be underestimated when the dividend growth model is used.The earnings growth model, although not superior to the dividend growth model (Fama and French (2002)), is not usurped by possible changes in dividend policies over time. The earnings growth model however may also be affected by non-stationarity in earnings-price ratio since it ability to accurately estimate average expected return is based on the assumption that there are permanent shifts in the expected value of the earnings-price rati o.2.2 Estimations from Asset-Pricing ModelsOne of the most fundamental concepts in the area of asset-pricing is that of venture versus reward. The pioneering work that communicate the encounter and reward trade-off was done by Sharpe (1964)-Lintner (1965), in their introduction of the Capital Asset Pricing Model (CAPM). The Capital Asset Pricing Model postulates that the cross-section(prenominal)al variation in expected stock or portfolio returns is captured only by the market important. However, evidence from past literature (Fama and French (1992), Carhart (1997), Strong and Xu (1997), Jagannathan and Wang (1996), Lettau and Ludvigson (2001), and others) stipulates that the cross-section of stock returns is not fully captured by the one factor market important. Past and present literature including studies by Banz (1981), Rosenberg et al (1985), Basu (1983) and Lakonishok et al (1994) have realized that, in gain to the market beta, average returns on stocks are influenced by size, book-to-market equity, earnings/price and past sales growth respectively. Past studies have also let oned that stock returns tend to display short-term momentum (Jegadeesh and Titman (1993)) and long-term reversals (DeBondt and Thaler (1985)).Growing enquiry in this area by scholars to address these anomalies has led to the development of alternative models that better explain variations in stock returns. This led to the categorisation of asset pricing models into three (1) multifactor models that add some factors to the market return, such as the Fama and French three factor model (2) the arbitrage pricing theory postulated by Ross (1977) and (3) the nonparametric models that intemperately criticized the linearity of the CAPM and therefore added moments, as evidenced in the work of Harvey and Siddique (2000) and Dittmar (2002). From this categorization, most of the asset-pricing models can be draw as special cases of the four-factor model proposed by Carhart (1997). The four-factor model is given asE(Ri) Rf = i + E(RM) Rf bi + si E(SMB) + hi E(HML) + wiE(WML) + i (4)where SMB, HML and WML are proxies for size, book-to-market equity and momentum respectively. There exist other variants of these models such as the three-moment CAPM and the four-moment CAPM (Dittmar, 2002) which add skewness and kurtosis to investor preferences, however the focus of this paper is to compare and test the effectiveness of the CAPM and the Fama and French three-factor model, the two premier asset-pricing models widely ac acquaintanced among both practitioners and academicians.2.3 Theoretical Background CAPM and Fama French Three-Factor ModelThere exist quite a substantial amount of studies in the field of finance relating to these two prominent asset pricing models. The Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) has been the set-back most widely recognized theoretical explanation for the estimation of expected stock returns or cost of eq uity in this case. It is a single factor model that is widely used by Financial Economists and in industry. The CAPM being the counterbalance theoretical asset pricing model to address the risk and return concept and due to its simplicity and ease of interpretation, was quickly embraced when it was front introduced. The models attractiveness also lies in the fact that, it addressed difficult problems related to asset pricing using readily available time series data. The CAPM is based on the idea of the relationship that exists between the risk of an asset and the expected return with beta being the sole risk pricing factor. The Sharpe-Lintner CAPM equation which describes individual asset return is given asE(Ri) = Rf + E(RM) Rf iM i = 1,,N (5)where E(Ri) is the expected return on any asset i, Rf is the risk-free interest rate, E(RM) is the expected return on the value-weighted market portfolio, and iM is the assets market beta which measures the sensitivity of the assets return to variations in the market returns and it is equivalent to Cov(Ri, RM)/Var(RM).The equation for the time series regression can be write asE(Ri) Rf = i + E(RM) Rf iM + i i = 1,,N (6)showing that the unneeded return on portfolio i is dependent on excess market return with i as the error term. The excess market return is also referred to as the market premium.The model is based on several cay assumptions, portraying a simplified world where (1) there are no taxes or transaction be or problems with indivisibilities of assets (2) all investors have identical investment horizons (3) all investors have identical opinions about expected returns, volatilities and correlations of available investments (4) all assets have limited liability (5) there exist sufficiently rotund number of investors with comparable wealth levels so that each investor believes that he/she can purchase and sell any amount of an asset as he or she deems fit in the market (6) the capital market is in equilib rium and (7) Trading in assets takes place continually over time. The merits of these assumptions have been hold forthed extensively in literature.It is ostensible that most of these assumptions are the standard assumptions of a entire market which does not exist in reality. It is a known fact that, in reality, indivisibilities and transaction costs do exist and one of the reasons assigned to the assumption of continual trading models is to implicitly give recognition to these costs. It is imperative to note however that, trading intervals are stochastic and of non-constant length and so making it off to assume no trading cost. As mentioned earlier, the assumptions made the model very elementary to estimate (given a proxy for the market factor) and interpret, thus making it very attractive and this explains why it was easily embraced. The CAPM stipulates that, investors are only rewarded for the systematic or non-diversifiable risk (represented by beta) they persist in holding a portfolio of assets. Notwithstanding the models simplicity in estimation and interpretation, it has been criticized heavily over the past few decades.Due to its many unrealistic assumptions and simple nature, academicians almost immediately began testing the implications of the CAPM. Studies by Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) gave the first strong empirical support to the use of the model for determining the cost of capital. Black et al. (1972) in combining all the NYSE stocks into portfolio and using data between the periods of 1931 to 1965 set in motion that the data are consistent with the predictions of the Capital Asset Pricing Model (CAPM). Using return data for NYSE stocks for the period between 1926 to 1968, Fama and MacBeth (1973) in examining whether other stock characteristics such as beta squared and idiosyncratic volatility of returns in addition to their betas would help in explaining the cross section of stock returns better base tha t knowledge of beta was sufficient.There have however been several academic challenges to the validity of the model in relation to its practical application. Banz (1981) revealed the first major challenge to the model when he provided empirical evidence to show that stocks of smaller firms earned better returns than predicted by the CAPM. Banzs finding was not deemed economically important by most academicians in the light that, it is unreasonable to expect an abstract model such as the CAPM to hold exactly and that the proportion of small firms to occur market capital is insignificant (under 5%). Other early empirical works by Blume and whizz (1973), Basu (1977), Reinganum (1981), Gibbons (1982), Stambaugh (1982) and shanken (1985) could not offer any significant evidence in support of the CAPM.In their paper, Fama and French (2004) noted that in regressing a cross section of average portfolio returns on portfolio beta estimates, the CAPM would predict an intercept which is equal to the risk free rate (Rf) and a beta coefficient equal to the market risk premium (E(Rm) Rf). However, Black, Jensen and Scholes (1972), Blume and confederate (1973), Fama and MacBeth (1973) and Fama and French (1992) after running series of cross-sectional regressions found that the average risk-free rate, which is proxied by the one month T-bill, was always less that the realised intercept. surmisal stipulates that, the three main components of the model (the risk free, beta and the market risk premium) must be forward-looking estimates. That is they must be estimates of their true future values. experimental studies and survey results however show substantial disagreements as to how these components can be estimated. While most empirical researches use the one month T-bill rate as a proxy to the risk-free rate, interviews depicts that practitioners prefer to use either the 90-day T-bill or a 10-year T-bond (normally characterised by a flat yield curve). Survey results have revealed that practitioners have a strong preference for long-term bond yields with over 70% of financial advisors and corporations using Treasury-bond yields with maturities of ten 10 or more years. However, many corporations reveal that they match the tenor of the investment to the term of the risk free rate.Finance theory postulates that the estimated beta should be forward looking, so as to reflect investors doubtfulness about future cash flows to equity. Practitioners are forced to use various kinds of proxies since forward-looking betas are unobservable. It is therefore a common practice to use beta estimates derived from diachronic data which are normally retrieved from Bloomberg, regular Poors and Value Line. However, the lack of consensus as to which of these three to use results in different betas for the same company. These differences in beta estimates could result in significantly different expected future returns or cost of equity for the company in question ther eby yielding foreign financial decisions especially in capital budgeting. In the work of Bruner et al. (1998), they found significant differences in beta estimates for a small sample of stocks, with Bloomberg providing a fancy of 1.03 while Value Line beta was 1.24. The use of historical data however requires that one makes some practical compromises, each of which can adversely affect the quality of the results. Forinstance, the statistically reliability of the estimate may improve greatly by employing longer time series periods but this may include nurture that are stale or irrelevant. Empirical research over the years has shown that the precision of the beta estimates using the CAPM is greatly improved when working with well diversify portfolios compared to individual securities.In relation to the equity risk premium, finance theory postulates that, the market premium should be equal to the difference between investors expected returns on the market portfolio and the risk-free rate. Most practitioners have to bonk with the problem of how to measure the market risk premium. Survey results have revealed that the equity market premium prompted the superior diversity of responses among survey respondents. Since future expected returns are unobservable, most of the survey participants extrapolated historical returns in the future on the assumption that future expectations are heavily influenced by past experience. The survey participants however differed in their estimation of the average historical equity returns as well as their choice of proxy for the unhazardous asset. Some respondents preferred the geometric average historical equity returns to the arithmetic one while some also prefer the T-bonds to the T-bill as a proxy for the riskless asset.Despite the numerous academic literatures which discuss how the CAPM should be implemented, there is no consensus in relation to the time frame and the data frequency that should be used for estimation. Barthold y Peare (2005) in their paper concluded that, for estimation of beta, five years of monthly data is the appropriate time period and data frequency. They also found that an equal weighted office, as opposed to the usually recommended value-weighted index provides a better estimate. Their findings also revealed that it does not really matter whether dividends are included in the index or not or whether new(a) returns or excess returns are used in the regression equation.The CAPM has over the years been said to have failed greatly in explaining accurate expected returns and this some researchers have attributed to its many unrealistic assumptions. One other major assumption of the CAPM is that there exists complete knowledge of the true market portfolios composition or index to be used. This assumed index is to consist of all the assets in the world. However since only a small fraction of all assets in the world are traded on stock exchanges, it is impossible to construct such an i ndex leading to the use of proxies such as the SP500, resulting in ambiguities in tests.The greatest challenge to the CAPM divagation that of Banz (1981) came from Fama and French (1992). Using similar procedures as Fama and MacBeth (1973) and ten size classes and ten beta classes, Fama and French (1992) found that the cross section of average returns on stocks for the periods spanning mid-sixties to 1990 for US stocks is not fully explained by the CAPM beta and that stock risks are multidimensional. Their regression analysis suggest that company size and book-to-market equity ratio do perform better than beta in capturing cross-sectional variation in the cost of equity capital across firms. Their work was however preceded by Stattman (1980) who was the first to document a positive relation between book-to-market ratios and US stock returns. The findings of Fama and French could however not be dismissed as being economically insignificant as in the case of Banz.Fama and French ther efore in 1993 identified a model with three common risk factors in the stock return- an overall market factor, factors related to firm size (SMB) and those related to book-to-market equity (HML), as an alternative to the CAPM. The SMB factor is computed as the average return on three small portfolios (small cap portfolios) less the average return on three big portfolios (large cap portfolios). The HML factor on the other hand is computed as the average return on two value portfolios less the average return on two growth portfolios. The growth portfolio represents stocks with low Book Equity to food market Equity ratio (BE/ME) while the value portfolios represent stocks with high BE/ME ratio. Their three-factor model equation is described as followsE(Ri) Rf = i + E(RM) Rf bi + si E(SMB) + hi E(HML) + i (7)Where E(RM) Rf, , E(SMB) and E(HML) are the factor risk premiums and bi , si and hi are the factor sensitivities. It is however believed that the introduction of these two addi tional factors was motivated by the works of Stattman (1980) and Banz (1981).The effectiveness of these two models in capturing variations in stock returns may be judged by the intercept (alpha) in equations (6) and (7) above. Theory postulates that if these models hold, then the value of the intercept or alpha must equal zero for all assets or portfolio of assets. Fama and French (1997) tested the ability of both the CAPM and their own three-factor model in estimating industry costs of equity. Their test considered 48 industries in which they found that their model outperform the CAPM across all the industries considered. They however could not conclude that their model was better since their estimates of industry cost of equities were observed to be imprecise. Another disturbing outcome of their study is that both models displayed very large standard errors in the order of 3.0% per annum across all industries.Connor and Senghal (2001) tested the effectiveness of these two models in predicting portfolio returns in indias stock market. They tested the models using 6 portfolio groupings formed from the intersection of two size and three book-to-market equity by examining and testing their intercepts. Connor and Senghal in this paper examined the values of the intercepts and their corresponding t-statistics and then tested the intercepts simultaneously by using the GRS statistic first introduced by Gibbons, Ross and Shanken (1989). Based on the evidence provided by the intercepts and the GRS tests, Connor and Senghal concluded generally that the three-factor model of Fama and French was superior to the CAPM.There have been other several empirical papers ever since, to ascertain which of these models is better in the estimation of expected return or cost of equity, most producing contrasting results. Howard Qi (2004) concluded in his work that on the sum total level, the two models behave fairly well in their predictive power but the CAPM appeared to be modera tely better. Bartholdy and Peare (2002) in their work came to the conclusion that both models performed sick with the CAPM being the poorest.3.0 DATA SOURCESTCAPM and Three Factor Model in Cost of Equity MeasurementCAPM and Three Factor Model in Cost of Equity Measurement1.0 INTRODUCTION AND OBJECTIVESCentral to many financial decisions such as those relating to investment, capital budgeting, portfolio management and performance evaluation is the estimation of the cost of equity or expected return. There exist several models for the valuation of equity returns, prominent among which are the dividend growth model, residual income model and its extension, free cash flow model, the capital asset pricing model, the Fama and French three factor model, the four factor model etc. Over the past few decades, two of the most common asset pricing models that have been used for this purpose are the Capital Asset Pricing Model (a single factor model by Sharpe 1964, Lintner 1965) and the three f actor model suggested by Fama and French (1993). These two models have been very appealing to both practitioners and academicians due to their structural simplicity and are very easy to interpret. There have however been lots of debates and articles as to which of these two models should be used when estimating the cost of equity or expected returns. The question as to which of these two models is better in terms of their ability to explain variation in returns and forecast future returns is still an open one. While most practitioners favour a one factor model (CAPM) when estimating the cost of equity or expected return for a single stock or portfolio, academics however recommend the Fama and French three factor model (see eg. Bruner et al, 1998).The CAPM depicts a linear relationship between the expected return on a stock or portfolio to the excess return on a market portfolio. It characterizes the degree to which an assets return is correlated to the market, and indirectly how ris ky the asset is, as captured by beta. The three-factor model on the other hand is an extension of the CAPM with the introduction of two additional factors, which takes into account firm size (SMB) and book-to-market equity (HML). The question therefore is why practitioners prefer to use the single factor model (CAPM) when there exist some evidence in academics in favour of the Fama and French three factor model. Considering the number of years most academic concepts are adopted practically, can we conclude that the Fama and French three factor model is experiencing this so-called natural resistance or is it the case that the Fama and French model does not perform significantly better than the CAPM and so therefore not worth the time and cost?The few questions I have posed above form the basis for this study. It is worth noting that while the huge academic studies on these models produce interesting results and new findings, the validity of the underlying models have not been rigorou sly verified. In this paper, while I aim to ascertain which of the two models better estimates the cost of equity for capital budgeting purposes using regression analysis, I also will like to test whether the data used satisfy the assumptions of the method most academicians adopt, i.e. the Ordinary Least Squares (OLS) method. I will in particular be testing for the existence or otherwise of heteroscedasticity, multicollinearity, normality of errors serial correlation and unit roots, which may result in inefficient coefficient estimates, wrong standard errors, and hence inflated adjusted R2 if present in the data. I will then correct these if they exist by adopting the Generalised Least Squares (GLS) approach instead of the widely used Ordinary Least Squares (OLS) before drawing any inference from the results obtained.My conclusion as to which of the models is superior to the other will be based on which provides the best possible estimate for expected return or cost of equity for ca pital budgeting decision making. Since the cost of capital for capital budgeting is not observed, the objective here, therefore, is to find the model that is most effective in capturing the variations in stock returns as well as providing the best estimates for future returns. By running a cross sectional regression using stock or portfolio returns as the dependent variable and estimated factor(s) based on past returns as regressors, R2 measures how much of the differences in returns is explained by the estimation procedure. The model that produces the highest adjusted R2 will therefore be deemed the best.The Fama-French (1993, 1996) claimed superiority of their model over CAPM in explaining variations in returns from regressions of 25 portfolios sorted by size and book-to-market value. Their conclusion was based on the fact that their model produced a lower mean absolute value of alpha which is much closer to the theoretical value of zero. Fama and French (2004, working paper) stat ed that if asset pricing theory holds either in the case of the CAPM (page 10), or the Fama and French three-factor model (page 21), then the value of their alphas should be zero, depicting that the asset pricing model and its factor or factors explain the variations in portfolio returns. Larger values of alpha in this case are not desirable, since this will imply that the model was poor in explaining variation in returns. In line with this postulation, the model that yields the lowest Mean Absolute Value of Alpha (MAVA) will therefore be considered the best. But since alpha is a random variable, I will proceed to test the null hypothesis H0 i = 0 for all i, by employing the GRS F-statistic postulated by Gibbons, Ross and Shanken (1989).My third and fourth testing measures are based on postulates by econometricians that, the statistical adequacy of a model in terms of its violations of the classical linear regression model assumptions is hugely irrelevant if the models predictive po wer is poor and that the accuracy of forecasts according to traditional statistical criteria such as the MSE may give little guide to the potential profitability of employing those forecasts in a market trading strategy or for capital budgeting purposes. I will therefore test the predictive power of the two models by observing the percentage of forecast signs predicted correctly and their Mean Square Errors (MSE).One other motivation for this study is also to ascertain whether the results of prior studies are sample specific, that is, whether it is dependent on the period of study or the portfolio grouping used. Theoretically, the effectiveness of an asset pricing model in explaining variation in returns should not be influenced by how the data is grouped. Fama and French (1996) claimed superiority of their model over the CAPM using the July 1963 to December 1993 time period with data groupings based on size and book-to-market equity. I will be replicating this test on the same data grouping but covering a much longer period (from July 1926 to June 2006) and then on a different data grouping based on industry characteristics. Testing the models using the second grouping of industry portfolios will afford me the opportunity to ascertain whether the effectiveness of an asset pricing model is sample specific. I will also carry out the test by employing a much shorter period (5 years) and comparing it to the longer period and then using the one with the better estimate in terms of alpha and R2 to carry out out-of-sample forecasts.The rest of this paper is structured as follows. Chapter 2 will review the various models available for the estimation of equity cost with particular emphasis on the two asset-pricing models and analysing some existing literature. Chapter 3 will give a description of the data, its source and transformations required, with Chapter 4 describing the methodology. Chapter 5 will involve the time series tests of hypothesis on the data and Chapt er 6 will involve an empirical analysis of the results for the tests of the CAPM and the Fama and French three-factor model. Finally, Chapter 7 contains a summary of the major findings of my work and my recommendation as well as some limitations, if any, of the study and recommended areas for further studies.2.0 RELEVANT LITERATUREThe estimation of the cost of equity for an industry involves estimation of what investors expect in return for their investment in that industry. That is, the cost of equity to an industry is equal to the expected return on investors equity holdings in that industry. There are however a host of models available for the estimation of expected returns on an industrys equity capital including but not limited to estimates from fundamentals (dividends and earnings) and those from asset pricing models.2.1 Estimations from FundamentalsEstimation of expected returns or cost of equity in this case from fundamentals involves the use of dividends and earnings. Fama and French (2002) used this approach to estimate expected stock returns. They stated that, the expected return estimates from fundamentals help to judge whether the realised average return is high or low relative to the expected value (pp 1). The reasoning behind this approach lies in the fact that, the average stock return is the average dividend yield plus the average rate of capital gainA(Rt) = A(Dt/Pt-1) + A(GPt) (1)where Dt is the dividend for year t, Pt-1 is the price at the end of year t 1, GPt = (Pt Pt-1)/Pt-1 is the rate of capital gain, and A( ) indicates an average value. Given in this situation that the dividend-price ratio, Dt/Pt , is stationary (mean reverting), an alternative estimate of the stock return from fundamentals isA(RDt) = A(Dt/Pt-1) + A(GDt) (2)Where GDt = (Dt Dt-1)/Dt-1is the growth rate of dividends and (2) is known as the dividend growth model which can be viewed as the expected stock return estimate of the Gordon (1962) model. Equation (2) in theory will only apply to variables that are cointegrated with the stock price and may not hold if the dividend-price ratio is non-stationary, which may be caused by firms decision to return earnings to stockholders by moving away from dividends to share repurchases (Fama and French 2002). But assuming that the ratio of earnings to price, (Yt/Pt), is stationary, then an alternative estimate of the expected rate of capital gain will be the average growth rate of earnings, A(GYt) = A((Yt Yt-1)/Yt-1). In this case, the average dividend yield can be combined with the A(GYt) to produce a third method of estimating expected stock return, the earnings growth model given asA(RYt) = A(Dt/Pt-1) + A(GYt) (3)It stands to reason from the model in Lettau and Ludvigson (2001) that the average growth rate of consumption can be an alternative mean of estimating the expected rate of capital gain if the ratio of consumption to stock market wealth is assumed stationary.Fama and French (2002) in their analys is concluded that the dividend growth model has an advantage over the earnings growth model and the average stock return if the goal is to estimate the long-term expected growth of wealth. However, it is a more generally known fact that, dividends are a policy variable and so subject to changes in management policy, which raises problems when using the dividend growth model to estimate the expected stock returns. But this may not be a problem in the long run if there is stability in dividend policies and dividend-price ratio resumes its mean-reversion (although the reversion may be at a new mean level). Bagwell and Shoven (1989) and Dunsby (1995) have observed that share repurchases after 1983 has been on the ascendancy, while Fama and French (2001) have also observed that the proportion of firms who do not pay dividends have been increasing steadily since 1978. The Fama and French (2001) observation implies that in transition periods where firms who do not pay dividends increases s teadily, the market dividend-price ratio may be non-stationary overtime, it is likely to decrease, in which case the expected return will likely be underestimated when the dividend growth model is used.The earnings growth model, although not superior to the dividend growth model (Fama and French (2002)), is not affected by possible changes in dividend policies over time. The earnings growth model however may also be affected by non-stationarity in earnings-price ratio since it ability to accurately estimate average expected return is based on the assumption that there are permanent shifts in the expected value of the earnings-price ratio.2.2 Estimations from Asset-Pricing ModelsOne of the most fundamental concepts in the area of asset-pricing is that of risk versus reward. The pioneering work that addressed the risk and reward trade-off was done by Sharpe (1964)-Lintner (1965), in their introduction of the Capital Asset Pricing Model (CAPM). The Capital Asset Pricing Model postulate s that the cross-sectional variation in expected stock or portfolio returns is captured only by the market beta. However, evidence from past literature (Fama and French (1992), Carhart (1997), Strong and Xu (1997), Jagannathan and Wang (1996), Lettau and Ludvigson (2001), and others) stipulates that the cross-section of stock returns is not fully captured by the one factor market beta. Past and present literature including studies by Banz (1981), Rosenberg et al (1985), Basu (1983) and Lakonishok et al (1994) have established that, in addition to the market beta, average returns on stocks are influenced by size, book-to-market equity, earnings/price and past sales growth respectively. Past studies have also revealed that stock returns tend to display short-term momentum (Jegadeesh and Titman (1993)) and long-term reversals (DeBondt and Thaler (1985)).Growing research in this area by scholars to address these anomalies has led to the development of alternative models that better expl ain variations in stock returns. This led to the categorisation of asset pricing models into three (1) multifactor models that add some factors to the market return, such as the Fama and French three factor model (2) the arbitrage pricing theory postulated by Ross (1977) and (3) the nonparametric models that heavily criticized the linearity of the CAPM and therefore added moments, as evidenced in the work of Harvey and Siddique (2000) and Dittmar (2002). From this categorization, most of the asset-pricing models can be described as special cases of the four-factor model proposed by Carhart (1997). The four-factor model is given asE(Ri) Rf = i + E(RM) Rf bi + si E(SMB) + hi E(HML) + wiE(WML) + i (4)where SMB, HML and WML are proxies for size, book-to-market equity and momentum respectively. There exist other variants of these models such as the three-moment CAPM and the four-moment CAPM (Dittmar, 2002) which add skewness and kurtosis to investor preferences, however the focus of t his paper is to compare and test the effectiveness of the CAPM and the Fama and French three-factor model, the two premier asset-pricing models widely acknowledged among both practitioners and academicians.2.3 Theoretical Background CAPM and Fama French Three-Factor ModelThere exist quite a substantial amount of studies in the field of finance relating to these two prominent asset pricing models. The Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) has been the first most widely recognized theoretical explanation for the estimation of expected stock returns or cost of equity in this case. It is a single factor model that is widely used by Financial Economists and in industry. The CAPM being the first theoretical asset pricing model to address the risk and return concept and due to its simplicity and ease of interpretation, was quickly embraced when it was first introduced. The models attractiveness also lies in the fact that, it addressed difficult problems re lated to asset pricing using readily available time series data. The CAPM is based on the idea of the relationship that exists between the risk of an asset and the expected return with beta being the sole risk pricing factor. The Sharpe-Lintner CAPM equation which describes individual asset return is given asE(Ri) = Rf + E(RM) Rf iM i = 1,,N (5)where E(Ri) is the expected return on any asset i, Rf is the risk-free interest rate, E(RM) is the expected return on the value-weighted market portfolio, and iM is the assets market beta which measures the sensitivity of the assets return to variations in the market returns and it is equivalent to Cov(Ri, RM)/Var(RM).The equation for the time series regression can be written asE(Ri) Rf = i + E(RM) Rf iM + i i = 1,,N (6)showing that the excess return on portfolio i is dependent on excess market return with i as the error term. The excess market return is also referred to as the market premium.The model is based on several key assumptio ns, portraying a simplified world where (1) there are no taxes or transaction costs or problems with indivisibilities of assets (2) all investors have identical investment horizons (3) all investors have identical opinions about expected returns, volatilities and correlations of available investments (4) all assets have limited liability (5) there exist sufficiently large number of investors with comparable wealth levels so that each investor believes that he/she can purchase and sell any amount of an asset as he or she deems fit in the market (6) the capital market is in equilibrium and (7) Trading in assets takes place continually over time. The merits of these assumptions have been discussed extensively in literature.It is evident that most of these assumptions are the standard assumptions of a perfect market which does not exist in reality. It is a known fact that, in reality, indivisibilities and transaction costs do exist and one of the reasons assigned to the assumption of co ntinual trading models is to implicitly give recognition to these costs. It is imperative to note however that, trading intervals are stochastic and of non-constant length and so making it unsatisfactory to assume no trading cost. As mentioned earlier, the assumptions made the model very simple to estimate (given a proxy for the market factor) and interpret, thus making it very attractive and this explains why it was easily embraced. The CAPM stipulates that, investors are only rewarded for the systematic or non-diversifiable risk (represented by beta) they bear in holding a portfolio of assets. Notwithstanding the models simplicity in estimation and interpretation, it has been criticized heavily over the past few decades.Due to its many unrealistic assumptions and simple nature, academicians almost immediately began testing the implications of the CAPM. Studies by Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) gave the first strong empirical support to the use of the model for determining the cost of capital. Black et al. (1972) in combining all the NYSE stocks into portfolio and using data between the periods of 1931 to 1965 found that the data are consistent with the predictions of the Capital Asset Pricing Model (CAPM). Using return data for NYSE stocks for the period between 1926 to 1968, Fama and MacBeth (1973) in examining whether other stock characteristics such as beta squared and idiosyncratic volatility of returns in addition to their betas would help in explaining the cross section of stock returns better found that knowledge of beta was sufficient.There have however been several academic challenges to the validity of the model in relation to its practical application. Banz (1981) revealed the first major challenge to the model when he provided empirical evidence to show that stocks of smaller firms earned better returns than predicted by the CAPM. Banzs finding was not deemed economically important by most academicians in the light t hat, it is unreasonable to expect an abstract model such as the CAPM to hold exactly and that the proportion of small firms to total market capital is insignificant (under 5%). Other early empirical works by Blume and friend (1973), Basu (1977), Reinganum (1981), Gibbons (1982), Stambaugh (1982) and shanken (1985) could not offer any significant evidence in support of the CAPM.In their paper, Fama and French (2004) noted that in regressing a cross section of average portfolio returns on portfolio beta estimates, the CAPM would predict an intercept which is equal to the risk free rate (Rf) and a beta coefficient equal to the market risk premium (E(Rm) Rf). However, Black, Jensen and Scholes (1972), Blume and Friend (1973), Fama and MacBeth (1973) and Fama and French (1992) after running series of cross-sectional regressions found that the average risk-free rate, which is proxied by the one month T-bill, was always less that the realised intercept. Theory stipulates that, the three m ain components of the model (the risk free, beta and the market risk premium) must be forward-looking estimates. That is they must be estimates of their true future values. Empirical studies and survey results however show substantial disagreements as to how these components can be estimated. While most empirical researches use the one month T-bill rate as a proxy to the risk-free rate, interviews depicts that practitioners prefer to use either the 90-day T-bill or a 10-year T-bond (normally characterised by a flat yield curve). Survey results have revealed that practitioners have a strong preference for long-term bond yields with over 70% of financial advisors and corporations using Treasury-bond yields with maturities of ten 10 or more years. However, many corporations reveal that they match the tenor of the investment to the term of the risk free rate.Finance theory postulates that the estimated beta should be forward looking, so as to reflect investors uncertainty about future c ash flows to equity. Practitioners are forced to use various kinds of proxies since forward-looking betas are unobservable. It is therefore a common practice to use beta estimates derived from historical data which are normally retrieved from Bloomberg, Standard Poors and Value Line. However, the lack of consensus as to which of these three to use results in different betas for the same company. These differences in beta estimates could result in significantly different expected future returns or cost of equity for the company in question thereby yielding conflicting financial decisions especially in capital budgeting. In the work of Bruner et al. (1998), they found significant differences in beta estimates for a small sample of stocks, with Bloomberg providing a figure of 1.03 while Value Line beta was 1.24. The use of historical data however requires that one makes some practical compromises, each of which can adversely affect the quality of the results. Forinstance, the statisti cally reliability of the estimate may improve greatly by employing longer time series periods but this may include information that are stale or irrelevant. Empirical research over the years has shown that the precision of the beta estimates using the CAPM is greatly improved when working with well diversified portfolios compared to individual securities.In relation to the equity risk premium, finance theory postulates that, the market premium should be equal to the difference between investors expected returns on the market portfolio and the risk-free rate. Most practitioners have to grapple with the problem of how to measure the market risk premium. Survey results have revealed that the equity market premium prompted the greatest diversity of responses among survey respondents. Since future expected returns are unobservable, most of the survey participants extrapolated historical returns in the future on the assumption that future expectations are heavily influenced by past experi ence. The survey participants however differed in their estimation of the average historical equity returns as well as their choice of proxy for the riskless asset. Some respondents preferred the geometric average historical equity returns to the arithmetic one while some also prefer the T-bonds to the T-bill as a proxy for the riskless asset.Despite the numerous academic literatures which discuss how the CAPM should be implemented, there is no consensus in relation to the time frame and the data frequency that should be used for estimation. Bartholdy Peare (2005) in their paper concluded that, for estimation of beta, five years of monthly data is the appropriate time period and data frequency. They also found that an equal weighted index, as opposed to the commonly recommended value-weighted index provides a better estimate. Their findings also revealed that it does not really matter whether dividends are included in the index or not or whether raw returns or excess returns are us ed in the regression equation.The CAPM has over the years been said to have failed greatly in explaining accurate expected returns and this some researchers have attributed to its many unrealistic assumptions. One other major assumption of the CAPM is that there exists complete knowledge of the true market portfolios composition or index to be used. This assumed index is to consist of all the assets in the world. However since only a small fraction of all assets in the world are traded on stock exchanges, it is impossible to construct such an index leading to the use of proxies such as the SP500, resulting in ambiguities in tests.The greatest challenge to the CAPM aside that of Banz (1981) came from Fama and French (1992). Using similar procedures as Fama and MacBeth (1973) and ten size classes and ten beta classes, Fama and French (1992) found that the cross section of average returns on stocks for the periods spanning 1960s to 1990 for US stocks is not fully explained by the CAPM beta and that stock risks are multidimensional. Their regression analysis suggest that company size and book-to-market equity ratio do perform better than beta in capturing cross-sectional variation in the cost of equity capital across firms. Their work was however preceded by Stattman (1980) who was the first to document a positive relation between book-to-market ratios and US stock returns. The findings of Fama and French could however not be dismissed as being economically insignificant as in the case of Banz.Fama and French therefore in 1993 identified a model with three common risk factors in the stock return- an overall market factor, factors related to firm size (SMB) and those related to book-to-market equity (HML), as an alternative to the CAPM. The SMB factor is computed as the average return on three small portfolios (small cap portfolios) less the average return on three big portfolios (large cap portfolios). The HML factor on the other hand is computed as the average re turn on two value portfolios less the average return on two growth portfolios. The growth portfolio represents stocks with low Book Equity to Market Equity ratio (BE/ME) while the value portfolios represent stocks with high BE/ME ratio. Their three-factor model equation is described as followsE(Ri) Rf = i + E(RM) Rf bi + si E(SMB) + hi E(HML) + i (7)Where E(RM) Rf, , E(SMB) and E(HML) are the factor risk premiums and bi , si and hi are the factor sensitivities. It is however believed that the introduction of these two additional factors was motivated by the works of Stattman (1980) and Banz (1981).The effectiveness of these two models in capturing variations in stock returns may be judged by the intercept (alpha) in equations (6) and (7) above. Theory postulates that if these models hold, then the value of the intercept or alpha must equal zero for all assets or portfolio of assets. Fama and French (1997) tested the ability of both the CAPM and their own three-factor model in es timating industry costs of equity. Their test considered 48 industries in which they found that their model outperformed the CAPM across all the industries considered. They however could not conclude that their model was better since their estimates of industry cost of equities were observed to be imprecise. Another disturbing outcome of their study is that both models displayed very large standard errors in the order of 3.0% per annum across all industries.Connor and Senghal (2001) tested the effectiveness of these two models in predicting portfolio returns in indias stock market. They tested the models using 6 portfolio groupings formed from the intersection of two size and three book-to-market equity by examining and testing their intercepts. Connor and Senghal in this paper examined the values of the intercepts and their corresponding t-statistics and then tested the intercepts simultaneously by using the GRS statistic first introduced by Gibbons, Ross and Shanken (1989). Based on the evidence provided by the intercepts and the GRS tests, Connor and Senghal concluded generally that the three-factor model of Fama and French was superior to the CAPM.There have been other several empirical papers ever since, to ascertain which of these models is better in the estimation of expected return or cost of equity, most producing contrasting results. Howard Qi (2004) concluded in his work that on the aggregate level, the two models behave fairly well in their predictive power but the CAPM appeared to be slightly better. Bartholdy and Peare (2002) in their work came to the conclusion that both models performed poorly with the CAPM being the poorest.3.0 DATA SOURCEST