A COMPARATIVE ANALYSIS OF THE THREE-FACTOR · PDF filefinance literature is the Fama-French three factor model. ... factors, but the augmented model that includes size and book to

A Comparative Analysis of the Three-Factor and the Capital Asset Pricing Models... 237

* Department of Banking and Finance, Faculty of Management Sciences, University of Benin, Benin City,Edo State, Nigeria, E-mails: [email protected]; [email protected]; [email protected]

Asian-African Journal of Economics and Econometrics, Vol. 14, No. 2, 2014: 237-257

A COMPARATIVE ANALYSIS OF THE THREE-FACTORAND THE CAPITAL ASSET PRICING MODELS IN

THE NIGERIAN STOCK MARKET

AJAO, M. Gabriel* and IGBINOSA, Sunday*

ABSTRACT

The study seeks to determine the risk factors in asset pricing in the Nigerian Stock Marketthrough a comparative analysis of the three factor model and the Capital Asset Pricing Model.Specifically, it examines the behaviour of stock returns in relation to market beta, firm size(market equity), and book-to-market equity (BE/ME) factors. A sample size of sixty eight stockswas selected from all stocks quoted on the Nigerian Stock Exchange (NSE) from 2003 to 2012.The study tests the Fama and French (1992) three factor model in explaining the variation ofstock returns relative to the Capital Asset Pricing Model (CAPM) on Nigerian Stock Marketdata. The Ordinary Least Square (OLS) multiple regression analysis was employed to regressmonthly excess portfolio returns on excess market returns, firm size and book-to-market-equityratio. The results obtained from the analysis reveal significant relationships between expectedportfolio returns and excess stock market returns, firm size and book-to-market equity factorsrespectively. This indicates that the Fama and French three factor model explains the variationof stock returns better than the single factor CAPM in the Nigerian stock market. The studyrecommends that fund managers, investors and researchers should be cautious in their use ofCAPM as an asset pricing model due to its limitation as a single factor model which does notcapture in totality the risk factors affecting asset pricing and returns in the stock market.

Keywords: Risk factors, Asset pricing, stock returns, CAPM, Three factor model

JEL classification: C22, C53, G12

1. INTRODUCTION

Much of the discourse in modern finance concerns the relationship between expected returnand risk. In the context of rational investors and equity markets, the expected return is mainlyrelated to the underlying risk. Consequently, substantial effort has been made to identify factorsthat capture such risk as well as determine assets prices in the equity markets. In the same vein,the way investors act upon a set of estimates in determining the best investment decisions underdifferent probabilities can determine how aggregate investors behave and how prices aredetermined in the stock market. By constructing general equilibrium models, the relevant measureof risk can be uncovered and the relationship between expected return and risk for any asset canbe determined. The main issues in asset pricing theory are the measurement of expected returnand the calculation of risk that is associated with the return.

238 Ajao, M. Gabriel and Igbinosa, Sunday

Factors capturing assets risk in the market place have been identified on the basis of existingtheories and empirical investigations. The market beta from the Capital Asset Pricing Model(CAPM) of Sharpe, (1964); Lintner (1965); Mossin, (1966) and Black, (1972) is the fundamentalof the identified factors while the CAPM is the first model in asset pricing theory (after themean-variance analysis) of Markowitz (1952). The CAPM is the most widely used modelbecause of its simplicity and underlying assumption that investors respect the mean-variancecriterion in choosing their portfolios. Besides CAPM, other factor pricing models that haveattempted to explain the cross-section of average assets returns include: the Inter-temporalCapital Asset Pricing Model, ICAPM (Merton, 1973), the Arbitrage Pricing Model (APM)(Ross, 1976), and the consumption-based Capital Asset Pricing Model (CCAPM) (Rubinstein,1976; Lucas, 1978; Breeden 1979; Mehra and Prescott, 1985). Miller (1999) states that CAPMnot only expressed new and powerful insights into the nature of risk but also through its empiricalinvestigation contributed to the development of finance.

The well-known conclusion of the CAPM is that the expected excess return on an assetequals the beta of the asset times the expected excess return on the market portfolio, where thebeta is covariance of the asset’s return with the return on the market portfolio divided by thevariance of the market return. However, the validity of the CAPM conclusion has been thesubject of several criticisms, for example, Roll (1977) argues that CAPM cannot be testedbecause the tests involve a joint hypothesis on the model and the choice of the market portfolio.On the other hand, many patterns emerge from empirical studies which are not explained bythe CAPM; such as the case of expected returns and earnings to price ratio that exhibiting apositive relation (Basu, 1977, 1983), small capitalizations having higher expected returns thanbig capitalizations (Banz, 1981), and the positive relationship between the level of debt andstock returns (Bhandari, 1988). There is, therefore, the need to look for other factors that playsignificant role in explaining the behaviour of expected stock returns. Fama and French (1992)find that besides beta, two additional factors – firm size and book-to-market ratio play animportant role in explaining the cross section of expected stock returns. They conclude that thecombination of size and book-to-market equity performs best in cross sectional stock risk-return analysis and when these two factors are accounted for, CAPM beta becomes insignificant.

Since its introduction in 1992, the Fama-French three factor model has been subject ofmuch academic debate and empirical application especially in the developed markets (Hodrickand Zhang, 2001). While the model performs exceptionally well compared to the singlefactor Capital Asset Pricing Model (CAPM), its performance against other multifactor modelsin general is inconclusive (Ruzita, 2006). However, the most well known model in the currentfinance literature is the Fama-French three factor model. Liew and Vassalov (2000) investigatethe extent to which profitability of the size effect and book-to-equity factor effect can belinked to future economic growth and conclude that indeed, the Fama-French (1993, 1995,1996) hypothesis is supported across various markets. It is therefore, important to analysethese relationships in different settings to improve our understanding of the degree to whichthey are generally applicable. To the best of my knowledge, it is pertinent to note that mostof the applications of the Fama-French three factor model for asset pricing has been limitedto the United States (US), Europe and Asian stock markets, while this model has only been


applied to the South-African Market (Piesse and Hearne, 2005) and Mauritius market(Bundoo, 2011) in Africa. While in Nigeria most studies on asset pricing focused mainly onthe application of Capital Asset Pricing Model, more recently, Tafamel (2012) in hiscomparative study of CAPM and APT predictive properties finds that the APT outperformsCAPM in predicting equity returns in the Nigerian Stock Market. In the same vein, Osamwonyiand Asein’s (2012) validates the application of CAPM in analyzing equity risk and return inthe Nigerian Stock Market.

The main purpose of this paper is to investigate the explanatory power of market beta,firm size, and book-to-market ratio (the comparison of the CAPM versus three factor model)on the cross-section of expected stock returns by using sample of firms listed on NSE (NigerianStock Exchange, 2003-2012). This study also attempts to determine the applicability of thethree factor model in the Nigerian stock market in a bid to bridge the gap between theoreticaland empirical studies in Nigeria.

2. THEORETICAL AND EMPIRICAL LITERATURES

Stock markets are important institutions in long term financial intermediation. For several reasons,developed stock markets are important for promoting the efficiency of investments, generatinglower cost of capital for firms, as well as giving investors the opportunity to price and hedgeagainst risk. These benefits of developed stock markets may be lacking in emerging stockmarkets as empirical assessment of the stock markets’ role in enhancing efficient investmentsis linked to measures of risk-return relationship and asset price development (Demirguc-kuntand Levine, 1993). For most investors and stakeholders in the financial system, explainingasset returns has been subject of intense debate as there are no asset pricing models with cleartestable predictions about risk and return. The Capital Asset Pricing Model (CAPM) of Sharpe(1964), Lintner (1965), Mossin (1966), and Black (1972), however, marks the birth of assetpricing theory (Osamwonyi and Asein, 2012). While the CAPM is an extremely elegant anduseful tool, there are concerns about the overall efficacy of the model as several criticisms havecome to the fore of academic research because the model is plagued with several limitations,especially in the area of unrealistic assumptions, the use of single market beta for empiricaltesting and inability to explain the behaviour of expected stock returns effectively (Strattman,1980; Reinganum,1981; Lakonishok and Shapiro,1984; Chan, Hamao and Lakonishok 1991).

Based on the identified weaknesses of CAPM, Fama and French (1992) show that stockrisks are multidimensional; therefore many factors besides market beta play significant role inexplaining the risk-return relationship. Several studies [Banz (1981), Basu (1983), Keim (1983),Cook and Rozeff (1984), Reinganum (1982), Lakonishok and Shapiro (1984), Rosenberg,Reid, and Lanstein (1985), De Bondt and Thaler (1987)] have documented that average returnis related to firm size, book-to-market equity ratio (BE/ME), earnings to price ratio (E/P),cashflow to price ratio (C/P) and past sales growth. However, Fama and French (1992) concludethat the combination of size and book-to-market equity performs best in explaining the crosssectional variation in stock returns and when these two factors are accounted for, CAPM betabecomes insignificant. In this respect, Fama and French (1992, 1993, 1995, and 1996) proposea three factor model. The model states that the expected return on a portfolio in excess of the


risk-free rate is explained by the market risks factor; the size effect factor and the book-to-equity effect factor.

The Fama and French (1992) three factor model has been the subject of much academiccontention and has also been subject to intense econometric investigation in different stockmarkets at different times. While some researchers supported the conclusion of Fama andFrench (1992) others such as Daniel and Titman (1997) do not for several reasons.

Charitou and Constantinidis (2004) empirically examined the Fama and French (1993)three factor model using Japanese data over the period of 1992 to 2001. The findings revealsignificant relationship between the three factors and the expected stock returns in the Japanesemarket. Drew and Veerarachavan (2003) test the Fama and French three factor model in theAsian region (Hong Kong, South Korea, Malaysia and the Philippines) and find that size andvalue effects can be identified in these four markets using a cross section approach and that theFama-French model explains the variation in returns better than the single index model. Shumand Tang (2005) test common risk factors in assessing returns in Asian stock markets, usingsample of assets listed on the Hong Kong, Singapore, and Taiwan stock exchanges. Theirresults confirm those of Fama and French for the US when using contemporaneous marketfactors, but the augmented model that includes size and book to market ratios report nosignificant improvement over the traditional CAPM.

Daniel and Titman (1997) use data from NYSE and form 25 stock portfolios on the basisof size and book to market equity for July 1963 to December 1993, similar to those used byFama and French (1993) and rejected the findings of the Fama-French three factor model.They find that size and book to market ratios are both highly correlated with the averagereturns of common stocks. Daniel, Titman and Wei (2001) continue the Daniel and Titman’s(1997) study by examining monthly data on common stocks listed on the Tokyo Stock Exchange(TSE) from January 1971 to December 1997. They rejected the Fama-French three factormodel in favour of the characteristic model. However, Davis, Fama and French (2000) usingan extended data set from 1929 to 1997 contend that Daniel and Titman’s (1997) results arespecific only to the relatively short data set that they used and consequently came out in favourof the risk explanation.

Furthermore, Lam (2002) using data for 100 firms listed in the Stock Exchange of HongKong (SEHK) from July 1980 to June 1997 reports results that support the three factor model.He asserts that beta is unable to explain the average monthly returns on stocks, but size, book-to-market equity ratios seem able to capture the cross-sectional variation of returns. Halliwell,Heaney and Sawicki (1999) in their study of the Australian Stock Exchange for the period ofJanuary 1981 to June 1991 report a statistically significant size effect but find little evidence ofa statistically significant book-to-market effect and conclude that the role of this factor maynot be as strong as suggested in the literature. Similarly, Faff (2001) uses 24 Australian industryportfolio data covering a period from January 1991 to April 1999, and finds strong support forthe Fama-French three factor model but with a negative significant size effect. Gaunt (2004)extends the Halliwell et al (1999) data set and covers a period from 1993 to 2001, reports astatistically significant size effect and strong evidence of a book-to-market effect and a


significant improvement in the explanatory power of the three factor model over the conventionalCAPM.

Also, Bundoo (2011) in a study of the Stock Exchange of Mauritius for the period January1997 to June 2003 based on a sample of 40 listed companies, reports that the Fama-Frenchthree factor holds for the Mauritius market and that both the size and book-to-market equityeffect are present in the market. Besides, the augmented Fama and French model shows thatthe time-variation in betas is priced, but the size and book-to-market equity effects are stillstatistically significant. Kothari, Shanken and Sloan (1995) re-examine the results presentedby Fama and French (1993) by seeking to determine whether beta explains the cross sectionalvariation in average returns and also whether BE/ME capture the cross sectional variation inaverage returns in the US market from 1947 to 1987. They find that BE/ME is weakly relatedto average stock returns.

Dimson, Nagel and Quigley (2003) test for a value premium effect in the UK market witha new defined data set of accounting information covering the period 1955-2001 to cover thewhole population of stocks ever listed on the London Stock Exchange. They find a strongvalue premium effect for stocks within the small cap and large cap universe. Malin andVeeraraghavan (2004) investigated the three factor model on three major European marketsnamely: England, France and Germany over the period 1992 to 2001. They find evidence of asmall firm effect in France and Germany and a big firm effect in the UK. Their final results,however, contradict value effect as no evidence of a value effect was identified in any of themarkets. Their findings also support the conclusions of Al-Horani, Pope and Stark (2003) thatthe CAPM beta does not appear to have significant explanatory power for the cross-section ofUK stock returns.

Maroney and Protopapadakis (2002) tested the Fama and French three factor model onstock markets of Australia, Canada, Germany, France, Japan, the UK and the US. The sizeeffect and the value premium survive for all the countries examined. They conclude that thesize and the BE/ME effects are international in character, and that using a Stochastic DiscountFactor (SDF) model and a variety of macroeconomic and financial variables, do notdiminish the explanatory power of BE/ME and size. The positive relations of returns withBE/ME and the negative relationship with size remains in the model. Griffin (2002), Griffinand Lemon (2002) on the other hand, using monthly data for 1521 companies in Japan, 1234in the UK, and 631 in Canada from January 1981 to December 1995, suggest that practicalapplications of the Fama-French three factor model are best performed on a country specificbasis.

Based on the empirical review highlighted above, it is obvious that most of the applicationof Fama and French three factor model has been predominantly carried out in the developedmarkets. This study therefore aims to contribute to the extant literature through a comparativeanalysis of the CAPM and the Fama-French three factor model. Specifically, we investigatethe explanatory power of market factor, size effect and book-to-market equity effect on thecross section of expected stock returns of quoted stocks on the Nigerian Stock Exchange (NSE)for the period of January 2003 to December 2012.


3. DATA AND METHODOLOGY

The focus of this study is identifying the risk factors in asset pricing in the Nigerian StockMarket through a comparative analysis of the three factor model and the CAPM. The studyutilizes monthly data covering 2003-2012 sample periods. We consider this period to be longenough to assure the adequacy of data and reliability of results. The year 2003 was taken as thestarting year because monthly treasury bill (proxy for risk free rate) data are not available inNigeria prior to 2003 while 2012 was taken as terminal year, also for reason of data availability.A total of Sixty-Eight (68) stocks were selected out of all the stocks listed on the NSE by meansof judgmental sampling technique as the selected stocks must conform to some criteria such asfrequency of trading, presence in the market, and capitalization.

3.1. Model Specification

3.1.1. The Fama and French Three Factor Model

The Fama and French (1992, 1993) three factor model uses the standard multiple regressionapproach. It is expressed in the form of equation (I) below:

Rp,t

- Rf,t = a

pt + bp (R

m,t – R

ft) + Sp (SMB) + hp (HML) + m

pt(I)

whereR

p,t= Average monthly return of portfolio p

Rft

= Monthly risk free rateR

m,t= Expected monthly market return

SMB = Small minus big (proxy for company size)HML = High minus low (proxy for value premium i.e. BE/ME)bp, sp and hp = Factor sensitivities or loading which are the slope coefficients in the

time series regression�

pt= The intercept of the time series regression

µpt

= The stochastic error term

3.1.2. The Capital Asset Pricing Model (CAPM)

In order to test the CAPM of portfolio in this study, we construct six portfolios and estimate theregression model for each of them by imposing hp=sp=0 in equation (I). Therefore, our portfolioCAPM equation for this study is as follows:

Rp,t

- Rf,t = �

pt + bp (R

m,t – R

ft) + µ

pt(II)

Where: All the variables are fully defined in equation (I)

Equation (II) enables us to effectively compare the performance of CAPM and the threefactor model and to identify the risk factors in asset pricing in the Nigerian stock market.

3.1.3. Portfolio Formation

In constructing our portfolios for this study, we classify our sample of stocks listed on NigerianStock Exchange by SIZE and BE/ME based on Fama and French (1992; 1993) specification.


(a) The Size Classification: This grouped the stocks in two classes: small capitalizationand big capitalization. We define our size as Market Equity which is market pricemultiplied by number of outstanding shares for each of the sample firm. We use thesize (ME) capitalization as the market equity as at the last trading day of December ofeach year in the formation of portfolios for the period January to December of subsequentfiscal year. Having done this, all the sampled stocks were ranked according to the sizecapitalization computed and we then determine the median of NSE stocks in order tosplit the market into two halves. Firms with market equity less than the median valuewere considered as SMALL Equity firms while those with values greater than themedian value were considered as BIG market equity firm.

(b) The Book-to-Market Equity (BE/ME) classification:

We calculate the BE/ME for each of the firm as = BE

ME(III)

Where BE is the Book Equity defined as the book value of common shareholders fundsfor each firm {this includes balance sheet deferred taxes (if available), minus the bookvalue of preferred stock (if available) and outside equity interest}

ME is the Market Equity defined as the market share price at time t multiplied by thenumber of outstanding shares (issued and fully paid) for each firm.

The companies were all ranked by BE/ME ratio and then divided into three groups accordingto the calculated BE/ME ratio following the Fama and French (1993) methodology: First group,30% of all stocks that have highest BE/ME (called High BE/ME); second group, 40% of allstocks that have BE/ME in medium (called medium BE/ME); and the last group, 30% of allstocks with lowest BE/ME (called low group). All stocks with negative BE/ME were excludedfrom the grouping in order to prevent distortion of the results. According to Fama and French(1993), the split of the stocks into different categories (two ME groups and three BE/MEgroups) was arbitrary and there was no reason that tests should be sensitive to this choice.Following this argument and on the basis of the above classification by Size (ME) and Book-to-market equity (BE/ME), we construct six (6) intersecting portfolios, namely: SL, SM, SH,BL, BM and BH. Where SL: consists of all stocks in the small market equity group that arealso in the low BE/ME group; SM: consists of all stocks in the small market equity group thatare also in the medium BE/ME group; SH: consists of all stocks in the small market equitygroup that are also in the high BE/ME group; BL: consists of all stocks in the Big marketequity group that are also in the low BE/ME group; BM: consists of all stocks in the Bigmarket equity group that are also in the medium BE/ME group; and BH: consists of all stocksin the big market equity group that are also in the high BE/ME group.

3.1.4. Portfolio Returns

• The monthly return of each portfolio is the value-weighted monthly returns of the stocksincluded in the portfolio, estimated by equation (IV) below:

�

� ��1

, ,n

pmi

R Wi m Ri m (IV)


Where, Rpm

is the portfolio P return in month m

Ri,m

is the stock i return in month m

Wi,m is the weight of stock i in the portfolio P (this is estimated as the ratio of marketvalue of stock i on the total market value of portfolio P in month m)

n is the number of stocks in portfolio P

• SMB (Small minus Big): This represents the risk factor of rate of return involved with sizeeffect. SMB = (Average returns of small size) minus (Average returns of Big size)

�SMB = 1/3(S/H + S/M + S/L) – 1/3(B/H + B/M + B/L) (V)

HML (High minus Low): This represents the risk factor of return rate involved with ratioof book to market value effect.

HML = ½(S/H + B/H) - ½(S/L + B/L) (VI)

3.1.5. The Stationarity test of Data

The stationarity property of each of the time series variable is investigated through theAugmented-Dickey Fuller (ADF) test for the unit root following Dickey and Fuller (1981). TheADF test consists of estimating the following regression:

� � �� 1 2 1 1 1m

t t i t tY t Y Y (VII)

Where Yt represents time series to be tested �

1 is the intercept term, �

2 is the coefficient of

interest in the unit root test, � is the coefficient of the augmented lagged first difference of Yt-1

torepresent the Pth order autoregressive process, and �

t is the pure white noise error term.

4. DATA ANALYSIS AND RESULTS

4.1. Stationarity Test of the Variables

Table IStationarity Test of the Variables

Variables Unit Root Test Conclusion Remark

Level First Diff

BH -6.184969* -9.036207* I(1) StationaryBM -10.27638* -15.0875* I(1) StationaryBL -8.140077* -8.805397* I(1) StationarySL -8.71544* -9.641976* I(1) StationarySM -9.303993* -13.03099* I(1) StationarySH -8.160194* -17.38463* I(1) StationaryRm -9.151454* -8.70767* I(1) StationaryRf -2.285273 -8.015244* I(1) StationaryHML -10.54145* -10.04298* I(1) StationarySMB -9.564405* -9.832056* I(1) Stationary

NB: * represents 1% level of significance.Source: Author’s Computation, (2014) with E-view 7.0


Table I shows the stationarity test of the variables using the Augmented Dickey Fuller(ADF) test. All the variables are found to be stationary at levels except Rf. Based on the nonstationarity of Rf, all the variables were differenced once to further check their stationaritystatus. At first differencing, the calculated ADF test statistics clearly reject the null hypothesisof unit root when compared with their corresponding critical values, hence the ADF test confirmthe stationarity of each variable at first difference and depict the same order of integration I (1)even at the 1% level for all the variables. Therefore, we conclude that the time series variablesare stationary.

4.2. Fama and French Three Factor Model and Capital Asset Pricing Model

Table II shows the results for the Fama and French three-factor model and the Capital AssetPricing Model (CAPM) for the sampled stocks of the Nigerian Stock Exchange from January2003 to December 2012.

For the three factor model, the ap coefficients (intercepts) of all the six portfolios aredifferent from zero except for the BM portfolio with a coefficient of -0.0876. While the interceptsof portfolios BH and SM are statistically significant at 5%, that of SL is significant at 10%level. However, the intercepts of BM, BL and SH are not significant at any level. This indicatesthe presence of abnormal returns on the NSE during the period under consideration, howeverthe model captures the common variation in stock returns. The market factor coefficients (�p)are positive and close to 1 for all the six portfolios and are all statistically significant (differentfrom zero) even at 1% level. This implies that all the stocks in the six portfolios irrespective ofsize generally move in step with the market. This finding is consistent with Gaunt (2004) whoshows that beta risk tends to be greater for smaller companies and those with lower BE/MEratios.

For the size factor coefficient (Sp), they take positive values in three out of the six portfolios.All small size portfolios have highly significant (at 1% level) and positive coefficients, signalinga direct relationship between the portfolio returns of small firms (with respect to size) and theexcess return of the market. The big size portfolios all have negative coefficients which arestatistically significant at different levels (between 1% and 5%). The BH and BL portfolios aresignificant at 1% while the BM portfolio is significant at 5% level. These negative relationshipsindicate that the returns of big size portfolios are inversely related to that of the excess marketreturns. This finding is consistent with Fama and French (1996) who show that small firmsload positively and big firms load negatively on SMB factor. The Book-to-Market equity (BE/ME) factor coefficients (hp) are all statistically significant and different from zero at 1% levelfor all the portfolios except for the BM portfolio which is statistically significant at 5% level.Besides, BH, BM, SH and SM portfolios have positive factor loading on the HML. In additionto the direct relationship that exist between these portfolios HML coefficients and excess marketreturns, medium to high BE/ME portfolios are however associated with distress due topersistently low earnings on book equity which will eventually result in low stock prices. Onthe other hand BL and SL portfolios have negative factor loadings indicating an inverserelationship with excess market returns, but low BE/ME portfolios are characterized with growthstocks with persistently high earnings on book equity that result in high stock prices. This

246 Ajao, M. Gabriel and Igbinosa, SundayT

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finding is equally consistent with Fama and French (1993, 1996) and Drew and Veeraraghavan(2002) who find that high BE/ME firms load positively and low BE/ME firms load negativelyon HML factor. The robustness of the model is further supported by the values of the adjusted

coefficient of determination ( 2R ) which ranges from 0.58 to 0.80 with an average of 0.71. Soon the average 71% of the variations in portfolio returns on the NSE is captured by the threefactor model during the period under consideration.

For the CAPM, the intercept coefficients (�p) are statistically significant and differentfrom zero at 5% level for three portfolios. These results imply that BL, SM and SL portfoliosare not fully explained by the factors contained in the full period CAPM. The coefficients ofthe intercept of BH, BM and SH portfolios are positive and not significant even at 10%. Themarket factor coefficients (�p) are all positive and significant at 1% level for all the six portfolios.The results indicate that there is direct relationship between stock returns and beta. This findingis consistent with previous studies: Osamwonyi and Asein (2012), Tafamel (2012) in whichthey find the existence of positive risk-return relationship.

In comparing the results of the two models (three factor model and CAPM) above, we

adopt the adjusted 2R criterion, it can be affirmed that the three factor model captures bettercommon variation in stock returns than the CAPM. Indeed for the three factor model, the

adjusted 2R for the six portfolios ranges from 0.58 to 0.80 with an average adjusted 2R of

0.71 while the adjusted 2R for the CAPM in the six portfolios ranges from 0.09 to 0.73 with an

Figure I: Three Factor Model vs CAPM (Adjusted R-squared)

Source: Author’s Computation, 2014


average adjusted R2 of 0.47. Moreover, as can be observed in Figure I below, the individualportfolios to portfolio comparison of the six portfolios for the models further shows that theadjusted R2 in each of the three factor model portfolio is higher than the correspondingadjusted R2 in CAPM portfolio. This result suggests that the three factor model captures thecommon variation in stock returns better than the CAPM model. However, the relevance ofmarket beta cannot be replaced by either size or BE/ME factor as indicated by the positiveand statistically significant values of beta coefficient (�p) in both the three factor and theCAPM regression results. This finding is consistent with Fama and French (1993); Bhatnagarand Ramlogan (2012); Ajili (2002); Charitou and Constantinidis (2004) and Firozjaee andJelodar (2010).

We also checked for the residual autocorrelation using the Durbin-Watson (DW) statistics(Durbin and Watson, 1950, 1951 a, b). The DW statistic test for first order serial autocorrelationusually takes values close to 2. An observation of our six portfolios regression (Table II)indicates that the values of the DW statistic ranges between 2.01 and 2.40 for the three factormodel, while it ranges between 1.59 and 2.24 for the CAPM except for the SM portfolio witha DW statistic value of 1.97 in the three factor model and for the CAPM, portfolios BM, SH,SM and SL with their respective DW statistic of 1.92, 1.68, 1.59 and 1.71 which can all beapproximated to 2. This is a clear evidence of absence of first order autocorrelation in theestimates.

4.3. Findings

In this study, we investigate the risk factors in returns and asset pricing in the Nigerian stockmarket. We empirically study the ability of commonly proposed risk factors (market beta, marketequity (size) and the ratio of the market value of equity to book value of equity (BEME) topredict monthly stock returns and asset prices in the Nigerian stock market. Specifically we testthe Capital Asset Pricing Model and the Three Factor Model of Fama and French (1993) on asample of sixty-eight (68) stocks for a period of one hundred and twenty (120) months fromJanuary 2003 to December 2012. Findings from our empirical analysis can be summarized inthe following points:

• The Capital Asset Pricing Models (CAPM) through the market betas (�) explain thecross section of expected returns of stock quoted on the Nigerian Stock Exchange.This result is similar to those of other studies Brailsford and Josev (1997); Fama andFrench (2004), Osamwonyi and Asein (2012) and Tafamel (2012).

• The Fama and French Three Factor Model holds in the Nigerian capital market and itexplains the variation of expected returns of quoted stocks on the Nigerian Stock Marketbetter than the Capital Asset Pricing Model (CAPM). This finding is consistent withthe findings of Fama and French (1993) in the US stock markets; Ajili (2002) in theFrench market; Shum and Tang (2005) in three Asian emerging markets (Hongkong,Singapore and Taiwan; Firozjaee and Jelodar (2010) in the Tehran Stock Exchange;Bundoo (2011) in Mauritius market; and Bhatnagar and Ramlogan (2012) in the UnitedKingdom.


4.4. Conclusion and Recommendations

On the basis of the empirical findings above, it is very clear that the Fama and French threefactor model provides significant improvement over the conventional one factor CAPM incapturing and explaining the cross section of expected returns on quoted stocks in the Nigerianstock market. We have basically compared the three factor model with the famous asset pricingmodel, the CAPM and our findings overwhelmingly supported the three factor model as abetter asset pricing model which explains the cross section of expected return of quoted stocksin the Nigerian stock market. In other words, market beta, firm size (market equity) and firmbook-to-market equity ratio (BE/ME) are significant factors affecting stock returns in the capitalmarket. Though this finding is consistent with of previous studies conducted in other economies,the results must be interpreted with caution, as they may be sample specific. Besides, the smallnumber of quoted companies in the Nigerian stock market coupled with high volatility of returnsin the sample period may have influenced the findings of this study. Similarly, the small samplesize may make it difficult to form portfolios of well diversified stocks, and this may have alsoinfluenced the robustness of the findings.

Since the findings from our analysis reveal that the cross section of expected returns in theNigerian Stock Market are better captured and described by the Fama and French three factormodel than by the traditional Capital Asset Pricing Model. It is hereby recommended that fundmanagers, investors and researchers should be cautious in their use of CAPM as an assetpricing model due to its limitation as a single factor model which does not capture in totalitythe variations of factors affecting asset pricing and returns.

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Appendix I: OLS estimation of the Fama and French Three Factor Model






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A COMPARATIVE ANALYSIS OF THE THREE-FACTOR · PDF filefinance literature is the Fama-French three factor model. ... factors, but the augmented model that includes size and book to