hassan and javed

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African Journal of Business Management Vol. 5(16), pp. 6747-6755, 18 August, 2011Available online at http://www.academicjournals.org/AJBMDOI: 10.5897/AJBM10.817ISSN 1993-8233 2011 Academic Journals

Full Length Research Paper

Size and value premium in Pakistani equity market

Arshad Hassan1* and Muhammad Tariq Javed2

1Muhammad Ali Jinnah University, Islamabad, Pakistan.

2Quaid-e-Azam University Islamabad, Pakistan.

Accepted 28 January, 2011

This study examined the relationship among size premium, value premium and equity returns inPakistani equity market for the period of June 2000 to June 2007 by using Fama and French (1992, 1993)

methodology. This is the first study in Pakistan that explores the relationship among stated variablesby employing a large sample of more than 250 stocks listed at the Karachi Stock Exchange. An analysisof the results reveals that size and book to market ratio are priced by market. Size factor is foundsignificantly positively related to portfolio returns at 95% confidence interval. Book to market factor isalso found significantly positively related to portfolio returns. Traditional CAPM is found valid as marketfactor is significant factor in explaining portfolio returns. However, explanatory power of Fama andFrench three factor model is 15% higher than explanatory power of conventional capital asset pricingmodel (CAPM). These results are in line with empirical results reported by Iqbal (2004) and Nawasish(2008 for the Pakistani market and are also in broad agreement with studies that report the validity ofFama and French the three factor model in emerging markets. As size and value premium exist in equitymarkets so decision makers should consider these factors in making decisions regarding investment,financing and valuation of financial instruments. These results are important, in the sense, that thesecan facilitate investors in efficient resource allocation.

Key words:Fama and French three factor model, Pakistan, size and value premium.

INTRODUCTION

Research in financial economics has historically beenfocused on the behavior of asset returns and especiallythe forces that determine the prices of risky assets. Thereare number of competing theories of asset pricing. Theseinclude the capital asset pricing models (CAPM) ofSharpe (1964), Lintner (1965) and Black (1972), the inter-temporal models of Merton (1973), Rubinstein (1976),and Cox (1985), and the arbitrage pricing theory (APT) ofRoss (1976). The CAPM is the dominant asset pricingmodel in the literature. However some multi-factor assetpricing models have also been discussed in literature.

Increasing role of the equity markets in the economyhas always attracted the researcher to investigate therelationship between pricing mechanism and resource

*Corresponding author. E-mail: [email protected]: 0321-5532408.

allocation. An efficient performance of pricing mechanismof stock market is a driving force for channeling savinginto profitable investment and hence, facilitate in an op-timal allocation of capital. Therefore, pricing mechanismensures a suitable return on investment and exposesviable investment opportunities to the potential investorsThus, in equity market, the pricing function has been considered important and remained a subject of extensiveresearch.

Markowitzs model of portfolio choice (1952, 1959) laysdown the foundations for asset pricing models. Thecapital asset pricing model (CAPM) of Sharpe (1964) andLintner (1965) marks the birth of asset pricing theory. Thecapital asset pricing theory is based on mean varianceanalysis and analyses the process of construction oefficient portfolios. The APT does not deal with the issueof portfolio efficiency but it assumes that equitys returndepend on number of factors. The APT has been empiri-cally studied in several markets. APT of Ross does not


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6748 Afr. J. Bus. Manage.

identify the factors. So number of studies has been con-ducted in various parts of the world to identify the factors.Antoniou (1998) uses the APT to identify the factors thatinfluence asset returns and asset prices in Londonstockexchange. Dhankar and Esq (2005) applies it onIndian stock market, Berry (1988) examines S&P 500 by

using APT. New York stock exchange, Japanese stockmarket and Russian stock markets have also beenexamined by Chen (1986), Azeez and Yonezawa (2003)and Anatolyev (2005) through APT. These studiesgenerally identify three types of factors that are companyspecific factors, macroeconomic factors and statisticalfactors. Fama and French (1992, 1993, 1996, 1998) hascontributed significantly in this area and proposed analternative model for asset pricing based on APT frame-work. The Fama and French three factor model havebeen examined in various markets of the world but onlylittle work has been done in Pakistan. Pakistani equitymarket is of special interest for several reasons. Pakistanis an important emerging market of south Asia and islocated at cross roads of central Asia, Middle East andemerging giants India and china so it is desirable to beable to apply this widely accepted factor approach to thePakistani equity market.

Secondly, Fama and French (1998) and Griffin (2002)report that size and book to market factors are country-specific and application of international factors to indivi-dual countries may lead to inadequate results. Therefore,it is need to time to explore the factors priced byPakistani equity market. Therefore, this study is aimed totest Arbitrage Pricing Theory by using Fama and Frenchthree factor model. Another importance of this study isuse of large sample. It is first study that uses a large

sample of more than 200-275 companies listed atKarachi stock exchange. In previous studies Iqbal (2004)uses a sample of 24 companies whereas Nawazish(2008) uses a sample of approximately 80 companies.Therefore, this study provides a better insight in the assetpricing dynamics of Pakistani securities. It also helps toanswer the issue of data snooping.

LITERATURE REVIEW

Fama and French (1992) studies the joint roles of marketbeta, size, Earnings/Price (E/P) ratio, leverage and book-

to-market equity ratio in the cross-section of averagestock returns for NYSE, Amex and NASDAQ stocks overthe period 1963 to 1990. Results reveal that that beta hasalmost no explanatory power whereas Size, E/P,leverage and book to market equity have significantexplanatory power in explaining the cross-section ofaverage returns. However when beta is included, sizeand book-to-market equity are significant and they seemto absorb the effects of leverage and E/P in explainingthe cross-section average stock returns. FF (1992)therefore, argues that if stocks are priced rationally, risks

must be multidimensional. Fama and French (1993)extend its study to both stocks and bonds by using atime-series regression approach.

Monthly returns on stocks and bonds are regressed onfive factors: returns on a market portfolio, a portfolio fosize and a portfolio for the book-to-market equity effect, a

term premium and a default premium. For stocks, the firsthree factors returns on a market portfolio, a portfolio forsize and a portfolio for the book-to-market equity effectare found to be significant and for bonds term premiumand default premium are significant. As a result, Famaand French (1993) construct a three-factor asset pricingmodel for stocks that includes the market factor and twoadditional risk factors related to size and book to marketequity. Study reports that extended model captures muchof the cross section of average returns. The model saysthat the expected return on a portfolio in excess of therisk free rate is explained by the sensitivity of its return tothree factors: (i) the excess return on a broad markeportfolio, (ii) the difference between the return on aportfolio of small stocks and the return on a portfolio oflarge stocks (SMB) and (iii) the difference between thereturn on a portfolio of high-book-to-market stocks andthe return on a portfolio of low-book-tomarket stocks(HML). Fama and French three-factor model appears tobe an extension of the CAPM. The size effect providesthat firms with small market capitalization exhibit returnsthat on average significantly exceed those of large firmsThe book-to-market equity effect shows that averagereturns are greater the higher the book value to market-value ratio (BE/ME) and vice versa. It is also referred toas the value premium. Fama and French (1995) analysesthe characteristics of firms with high book-to-market and

those with low book-to-market equity. They find that firmswith high BE/ME tend to be persistently distressed andthose with low BE/ME are associated with sustainedprofitability. Study reports that the high returns of highBE/ME stocks are can be attributed to holding of lessprofitable and riskier stocks. Study further reveals thatHML in the three factor model is a proxy for relativedistress. Weak firms with persistently low earnings tendto have high BE/ME and positive slopes on HML; strongfirms with high earnings have low BE/ME and negativeslopes on HML. Dennis, Perfect, Snow, and Wiles (1995)provide support to Fama and Frenchs results andconfirm prior findings that for any given size category

average annual portfolio returns increase as the BE/MEincreases and, for any given BE/ME category, averagereturns decrease as size increases. The BE/ME effect isfound significant for different holding periods and atrading strategy based on BE/ME and size could havebeen profitable. The implication of their study is thatinvestors can significantly outperform the market if theyselect small-size-high-BE/ME securities for their portfoliosduring the period. Fama and French (1998) provideadditional valuable out-of-sample evidence by testing theFF three factor models in thirteen different markets ove


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the period 1975 - 1995. Study reports that 12 of the 13markets record a premium of at least 7.68% per annumto value stocks. Seven markets show statistically signi-ficant BM/ME betas. However, Daniel and Titman (1997)do not agree with Fama and French (1992, 1993, 1996).Daniel and Titman (1997) investigate the impact of factor

loadings on stock returns for the period 1973 1993 andreport that expected returns are not a function of loadingson the Fama and French risk factors. They argue that it isthe covariance between high book-to-market ratio stocksthat leads to similar properties rather than a common riskfactor. . Kothari (1995) MacKinlay (1995) and Loughran(1997) see the matter in from a different perspective.Kothari (1995) and MacKinlay (1995) argue that a sub-stantial part of the premium is due to survivor bias anddata snooping. The data source for book equity containsa disproportionate number of high-BE/ME firms that sur-vive distress so the average return for high-BE/ME firmsis overstated. The data snooping hypothesis posits thatresearchers desire to search for variables that arerelated to average return, may lead to identification ofanomalies that are present only in the sample used toidentify them. However, number of studies consider it aweak argument and dismiss the survivorship-bias and thedata snooping hypothesis. Halliwel et al. (1999) tests theFama and French (1993) model in Australian equitymarket and reports the presence of some premia onsmall sized and high book-to-market ratio stocks. How-ever, study reports that explanatory power of Fama andFrench three factor model is not significantly higher thattraditional CAPM. Halliwel et al. (1999) do not find anyevidence for the decrease in size sensitivity, given atransition from low to high book-to-market ratio stocks.

This behavior is found inconsistent with Fama andFrench (1993) that reports the presence of a tendencyfor size sensitivity to fall when moving from lower tohigher book-to-market portfolios. Connor and Sehgal(2001) tests the model for India and finds that power ofmarket, size and book-to-market factors to explain thecross-sectional mean returns is higher than CAPM basedon single the market factor. Faff (2001) uses Australiandata over the period 1991 to 1999 to examine the powerof the Fama French three-factor model and finds strongsupport for the Fama and French three factor model. Studyprovides evidence about existence of significant negativerelationship which is in contravention to expected

positive, premium for small size stocks. Faff (2001)concludes that his results appear to be consistent withother recent evidence of a reversal of the size effectDrew and Veera raghavan (2003) compare the explana-tory power of a CAPM with FF three-factor model forsouth east Asian markets and report the presence ofsize and value premiums in these markets. This studyalso provides evidence that Fama and French threefactor model can better explain the variations in return forthese markets. Drew and Veera raghavan (2003) arguethat premiums are compensation for risk that is notcaptured by single factor capital asset pricing model

Hassan and Javed 6749

(CAPM). Gaunt (2004) performs out of sample test inAustralian equity market for the period 1991 to 2000 andfinds that beta risk tends to be greater for smallecompanies and those with lower BM ratios.

This study also provides evidence of the BM/ME effecincreasing monotonically from the lowest to the highes

book-to-market equity portfolios. There is a monotonicincrease in loading on the SMB factor as well, whenmoving from the largest to the smallest portfolios. Theresults also confirm that explanatory power of three factomodel is much higher than CAPM. In Pakistani equitymarket Javid and Ahmad (2008) report that explanatorypower of standard CAPM is not adequate and conditionaCAPM has better explanatory power. Attiya (2009) againtest CAPM in KSE by using daily and monthly prices ostocks listed for the period 1993 - 2004 and report thatCAPM does not explain equity returns. Mirza and saima(2008) use daily data of 81 companies to test the validityof Fama and French three Factor model in Pakistanequity market and provide evidence about existence osize and book to market effect. They also report arepriced and FF model explains the portfolio returns. Thestudy also confirms the robustness of the model by usinga reduced model.

The aforementioned review indicates that asset pricingmechanism in Pakistani equity markets has not beeninvestigated in detail. Only few studies are available andthese too are restricted to conditional and unconditionaCAPM or and Fama and French three factor modelThese studies are based on very limited sample so it isneed of time to investigate this important market of southAsia with a large set of sample that captures the currendynamics of equity market. This study is an effort to fil

that gap in empirical literature.

METHODOLOGY

The study uses monthly closing prices of all stocks listed at KSE forthe period 6/2000 - 6/2007 which satisfies the following criteria;

1. Sample consists of stocks from non financial sector2. Stocks with negative book value of equity are excluded fromsample3. Only those stocks are included which have evidence ofreasonable liquidity that is stock which have an evidence of tradingin at least 8 months during a year.Accounting data has been collected from various bulletins o

balance sheet analysis published by state bank of Pakistan. Stockprices and turnover has been obtained form websites of businessrecorder and Karachi stock exchange which are reliable sources oinformation.

On the basis of aforementioned criteria, Appendix is finallyselected.

CAPM uses a single factor to compare a portfolio with the marketas a whole. Fama and French observe that certain classes oassets perform better than others. So, in order to capture the effecof size and market to book ratio, they added two factors sizepremium and value premium to CAPM. In order to capture thesefactors, portfolio approach proposed by Fama and French (1993has been adopted. The procedure of formation of portfolio is


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Table 1.Descriptive statistics size-B/M ratio sorted portfolios.

Variable S/H S/M S/L B/H B/M B/L

Mean 0.0155 0.0133 0.0115 0.0181 0.0128 0.0108

Median 0.0055 0.0111 0.0051 0.0221 0.0056 0.0086

Std Dev 0.0791 0.0650 0.0641 0.0760 0.0646 0.0585

Kurtosis -0.0633 -0.4852 0.1481 -0.3314 -0.3386 -0.2658Skewness 0.5952 0.2877 -0.1213 -0.0822 0.0817 -0.0754

Minimum -0.1183 -0.1111 -0.1637 -0.1450 -0.1363 -0.1351

Maximum 0.2163 0.1670 0.1503 0.2060 0.1820 0.1566

explained as follows:

Portfolio formation

1. For size sorted portfolios, market capitalization of each stock iscalculated at the end of June for year t-1 and then stocks arearranged on descending order. Now median is calculated and

sample is divided in two portfolios. First portfolio comprises ofstocks that have market capitalization less than median. Thisportfolio is called Small. Other portfolio comprises of stocks thathave market capitalization more than median. This portfolio isnamed as Big.2. Size sorted portfolios are further subdivided into three portfolioson the basis of book to market ratio. The first portfolio contains 30%stocks with lowest book to market ratio, second portfolio containsnext 40% stocks on the basis of book to market ratio, third portfoliocomprises of 30% stocks with highest book to market ratio. Whensmall is further subdivided three portfolios on the basis of book tomarket ratio, it forms three portfolios namely S/L, S/M, S/H. WhenBig is further subdivided in three portfolios on the basis of book tomarket ratio, it forms three portfolios namely B/L, B/M, B/H.

Variable construction

To isolate the factor premiums from each other, the two factors areconstructed as zero-investment portfolios from six sub portfolios asunder:

SMB = 1/3 * [ ( S/H B/H) + (S/M B/M) + (S/L B/L)]

HML =1/2 * [ ( S/H S/L) + (B/H B/L)]

MKT = (Rmt- Rft )

Where,Rm= ln (It/ It-1)

Rmis market return for month t and It and It-1are closing values ofKSE- 100 Index for month t and t-1 respectively. Rft is risk freerate. Monthly T bill rate has been used as proxy for risk free rate.

Model specification and regression estimation method

The algebraic relationship among variables is thus presented:

Rit- Rft = + 1MKTt+ 2SMBt +3HMLt+ e it

Where,

Rit = Return of portfolio ifor period t and Rft = Risk Free Rate.

This formula captures the following dimensions:

1. The zero risk return2. The market premium3. Size premium4. Value premium5. The impact of management (Alpha)6. Random error

RESULTS

Fama and French three factor model considers SMB andHML along with market premium to explain the portfolioreturns. Statistical properties of portfolios sorted on Size-BMR are reported in Table 1

Table 1 indicates that B/H and S/H portfolios are highrisk and high returns portfolios. However, B/H is foundefficient as it offers higher returns at lower level of risk. Insmall as well as big stocks segments high book to markestocks out performed low book to market stocks. B/L

offers the lowest return which is in line with empiricawork on the subject that big companies earn lower rate oreturn and stocks with low book to market ratio undeperform in comparison to stocks with high book to markereturn (Stattman, 1980).

It is also evident that S/M performs better than B/M andS/L perform better than B/L which is consistent with sizeeffect reported in various equity markets of the worldSimilarly, this additional return appears to be an outcomeof higher risk associated with small size portfolios.

The standard deviation of different portfolios supporthe risk based explanation of higher returns. So thesefinding of this study are in line with fama and French

(1992, 1993, 1996). Statistical properties of the variablesconstructed for Fama and French three factor model arereported in Table 2

Table 2 indicates that average market premium andvalue premium are positive whereas size premium isnegative. Market premium is found more volatile in com-parison to size premium and value premium. It is worthmentioning that market premium is on higher side incomparison to size and value effect, it may be a result ofoutstanding performance of Pakistani equity markeduring 2000 to 2007.

Positive average HML indicates that value stocks out


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Table 2. Descriptive statistics: Fama and French three factors.

Variable MKT SMB HML

Mean 0.0208 -0.0004 0.0056

Median 0.0179 -0.0008 0.0075

Std Dev 0.0811 0.0343 0.0330

Kurtosis 0.1083 -0.1087 0.4932Skewness 0.1239 -0.0568 -0.0348

Minimum -0.1630 -0.0959 -0.0917

Maximum 0.2335 0.0754 0.0912

Table 3. Fama and French three factor model.

Dependent variable Intercept MKT SMB HML Adj. R2

F Statistic F sig.

P -0.004 0.580

0.55 100.75 0.00T statistics -0.749 10.037

P value 0.456 0.000

P -0.0070 0.6524 0.5725 0.3838

0.73 75.17 0.00t statistics -1.8661 11.7836 3.8915 2.7172

P value 0.0657 0.0000 0.0002 0.0081

S 0.0030 0.4861

0.34 44.03 0.00t statistics 0.4984 6.6353

P value 0.6196 0.0000

S -0.0076 0.6523 1.0682 0.4013

0.74 80.88 0.00t statistics -1.9551 11.3590 7.0006 2.7390

P value 0.0541 0.0000 0.0000 0.0076

B 0.0010 0.6564

0.70 196.24 0.00t statistics 0.2478 14.0087

P value 0.8049 0.0000

B -0.0064 0.6525 0.0767 0.3663

0.74 80.64 0.00t statistics -1.7276 11.9461 0.5288 2.6287

P value 0.0879 0.0000 0.5984 0.0103

S/H -0.0003 0.4990

0.25 28.31 0.00t statistics -0.0426 5.3204

P value 0.9661 0.0000

S/H -0.0078 0.6291 1.1327 0.95180.81 116.21 0.00t statistics -1.9625 10.6684 7.2297 6.3263

P value 0.0532 0.0000 0.0000 0.0000

S/M -0.0020 0.4782

0.34 43.65 0.00t statistics -0.3344 6.6064

P value 0.7389 0.0000

S/M -0.0067 0.6413 1.0688 0.3246

0.72 7.2E+01 1.1E-22t statistics -1.7044 10.9875 6.8917 2.1794

P value 0.0922 0.0000 0.0000 0.0322


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Table 3.Contd.

S/L -0.0042 0.4989

0.38 52.23 0.00t statistics -0.7383 7.2270

P value 0.4625 0.0000

S/L -0.0069 0.7025 1.0907 -0.19350.60 41.98 0.00t statistics -1.4761 10.1713 5.9438 -1.0983

P value 0.1438 0.0000 0.0000 0.2754

B/H -0.0027 0.7392

0.61 128.65 0.00t statistics -0.5001 11.3423

P value 0.6184 0.0000

B/H -0.0063 0.7135 0.1567 0.7516

0.73 76.40 0.00t statistics -1.3957 10.7025 0.8847 4.4189

P value 0.1667 0.0000 0.3789 0.0000

B/M -0.0064 0.6611

0.67 169.45 0.00t statistics -1.5038 13.0172

P value 0.1365 0.0000

B/M -0.0079 0.6194 -0.0631 0.4343

0.70 66.42 0.00t statistics -1.9645 10.3732 -0.3977 2.8505

P value 0.0529 0.0000 0.6919 0.0056

B/L -0.0070 0.5982

0.66 165.95 0.00t statistics -1.8179 12.8821

P value 0.0727 0.0000

B/L -0.0072 0.6400 0.1986 -0.1031

0.66 55.68 0.00t statistics -1.8527 11.1024 1.2968 -0.7010P value 0.0676 0.0000 0.1984 0.4853

performed growth stocks. Negative SMB indicates thataverage of big stocks is higher than small stocks. Corre-lation among explanatory variables is also calculated toexplore the possibility of multicolinearity problem and isfound within permissible limit. Now explanatory power ofCAPM and three factor models has been explored andresults of multivariate regression analysis performed tocapture the relationship among portfolio return and

market premium, size premium and value premium arereported in Table 3.

It is worth mentioning that value premium is positiveand significant for all portfolios except S/L and B/L. Itmeans HML does not explain low B/M stocks. Therefore,this factor can not be ignored in making economicdecisions. It must be noticed that incorporation of twoadditional factors leads to increase in Adj. R

2of the

model. Similarly, size premium is found significantlypositively related to small portfolio returns. Similarly, sizepremium is observed as insignificant for portfolios B, BL,

B/M, and B/H. It means SMB is not significantly influencereturns of big stocks. Therefore, behavior of size is noconsistent but it is priced in many stylized portfoliosMarket premium is found significantly positively related toportfolio returns and this is consistent with conventionacapital asset pricing model. Therefore, it can be said thatmarket factor can significantly explain equity returns but iis not capable to explain returns fully. So size and value

premium captures the returns which are not explained bymarket factor. A comparison of two models is reported inTable 4.

Conventional CAPM is found valid in Pakistani equitymarket in general. It is evident that three factor modesubstantially explains the portfolio returns and it explanatory power ranges from 63 - 82%. It is significantlyhigher than explanatory power of conventional capitaasset pricing model which explains 24 - 66% of the totavariation in various portfolios. Therefore, it can be con-cluded that market prices size and book to market ratio


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Table 4. Comparative statement of Adj. R2

Dependent variable CAPM 3FM-FF

P 0.55 0.73

S 0.35 0.74

B 0.71 0.74

S/H 0.25 0.81S/M 0.34 0.72

S/L 0.38 0.60

B/H 0.61 0.73

B/M 0.67 0.70

B/L 0.66 0.66

and investors can use these factors in designing thereinvestment strategies. Specially, for the small sizeportfolios relationship is quite strong.

Conclusion

This study investigates the asset pricing mechanism inPakistani equity market for the period June 1998 to June2007 by using monthly equity prices. To explore the jointeffect of size premium and value premium, Fama andFrench three factor model has been tested. Valuepremium is found positive and significant for all portfoliosexcept low book to market stocks. Therefore, it can beconcluded that book to market effect is present inPakistani equity market. High book to market stocks outperform low book to market stocks. Size premium is

found significantly positively related to small portfolioreturns but it is found insignificant for portfolios of bigstocks. However, inconsistency is observed withreference size effect. Average returns of size sortedportfolios indicate small portfolios are high risk and highreturn portfolios but average of SMB factor reportsopposite result. It may be result of abnormal behavior ofmarket during 2005 to 2006. The findings of the studyfurther reveal that Fama and French three factor modelsubstantially explains the portfolio returns and it expla-natory power ranges from 63 - 82% for various portfolios.It is significantly higher than explanatory power of con-ventional capital asset pricing model that explains 24 -66% of the total variation in various portfolios. There-fore,decision makers should carefully account for thesefactors in there decisions regarding investment, financingand valuation.

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APPENDIX

Years 2000-2001 2001-2002 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007

Number of stocks 193 218 271 274 272 274 274

hassan and javed

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