The aim of this survey is to compare the explanatory power of two plus pricing theoretical account viz. Capital Asset Pricing Model and Fama and French Three Factor Model. This survey investigates the efficiency and feasibleness of TFM in the FTSE 100 index for the period 2008 to 2010. All non- fiscal companies listed in FTSE 100 index was used and were divided into six portfolios viz. BH, BM, BL, SH, SM, SL. Adding two extra factors related to size premium and value premium into the Capital Asset Pricing Model, can increase the efficiency of TFM in explicating the fluctuation in mean stock returns. It is concluded that The Three factor theoretical account can supply better appraisal in stock returns than traditional individual factor theoretical account. Contentss

An extended sum of research has been conducted in the finance literature on how and what extent investors should value hazardous assets. In general, every investor want higher rate of return for trading in hazardous assets. Measuring the relationship between hazard and return is important to many managerial determinations such as portfolio direction and capital budgeting. Investors who make determination to put in a stock market besides have an purpose to wealth maximization. In order to maximise wealth, they should see all necessary factors that could impact future returns. Estimating those factors, Investor demands dependable pricing theoretical account to mensurate the stock monetary value. Employing Capital Asset Pricing theoretical account ( CAPM ) and/or Multifactor Model is an of import consideration to foretell expected returns and besides assist investors to be after investing expeditiously. Although the CAPM is the most influential surveies in the fiscal direction sector, Multifactor theoretical account can supply better appraisal and consequences than CAPM because the theoretical account supports adding multiple hazard factors to capture the forms in mean returns. Since, there have been a figure of surveies conducted on the theoretical accounts globally ; this study compare CAPM and multiple factor attack for FTSE 100 Index over the sample period from 2008 to 2010 utilizing clip series arrested development analysis.

The construct of modern investing is chiefly based on two thoughts. The first thought was established by Markowitz, who developed the modern portfolio theory connoting that if the market is efficient, the outlooks of higher return is chiefly due to the higher hazard exposure. The Second, the thought of systematic and unsystematic hazard is discussed by Sharpe ( 1964 ) , Lintner ( 1965 ) and Mossini ( 1965 ) who explained the unsystematic hazard which can be diversified by puting in portfolios. In contrast, the systematic hazard, which is associated with full market is non possible to extinguish, hence investor are merely compensated for systematic hazard. This construct is globally known as Capital Asset Pricing theory.

The CAPM premises are to the full based on Modern Portfolio Theory developed by Markowitz, ( 1959 ) . The theory assumes that when investors select efficient portfolios among others, they merely see mean-variance portfolio to maximise their wealth, which leads to maximization of return of a portfolio for any given portfolio hazard over a individual period. CAPM implies that there exists a line drive relationship exists between hazard and return with an intercept of nothing and gradient of which beta is the individual market factor that is used to mensurate the systematic hazard. The theoretical account besides assumes that the market beta can explicate all basicss of systematic hazard.

Over the last 50 twelvemonth, legion research workers have documented grounds against the cogency of CAPM. The chief statement is that the market beta fails to explicate fluctuation in mean returns. As a consequence, this creates chance to analyze basic attack for portfolios to include extra hazard factors that has an explanatory power to foretell stock returns. The scrutiny of basic attack is first developed by Ross ( 1977 ) through Arbitrage Pricing theory. This common attack is besides used by Fama and French ( 1992 ) acclaims that the appraisal of beta intercepts significantly different from nothing when portfolios are formed on size and book to market value. Given that happening, the intercepts are close to nothing for given portfolios when the multifactor theoretical account is employed. Since CAPM is considered to be a individual factor theoretical account and neglect to capture fluctuation in mean stock returns for portfolios, Fama and French ( 1993 ) have introduced an alternate theoretical account to explicate extra returns for these portfolios. The theoretical account includes extra hazard factors viz. SMB ( the mean return of little house minus large houses ) and HML ( the mean return of high book to market houses minus low book to market houses ) long with market beta. Sing to portfolio formation based on house size, little houses are likely to give high returns compared to big houses. Whereas high book to market value houses produce higher return than growing house.

The ground we will compared both TFM and CAPM in FTSE 100 index is that these theoretical accounts are reasonably utile to foretell the portfolio returns than other pricing theoretical account. In peculiar, the Fama and French Three Factor Model are comparatively superior to CAPM is because the inclusion of extra hazard factors in the pricing theoretical account increase its ability to explicate the fluctuation in mean portfolio returns. Another of import fact is that, the cogency of the TFM is proven through legion empirical surveies globally.

The chief aims on this paper are to compare CAPM and Three Factor Model ( TFM ) theoretical account utilizing six portfolios formed on size and book to market equity ratio for FTSE 100 Index over the sample period from 2008 to 2010. The aims are:

Investigate the efficiency and feasibleness of TFM whether it can bring forth better consequences than CAPM. Which model provides better anticipation, it wholly depend on what step is used to prove the theoretical account. The Mean Absolute Value ( MAV ) trial will be conducted by the aid of Microsoft Excel Office Harmonizing to Fama and French ( 2004 ) , the alpha or the intercepts value should be near to zero, if the plus pricing theoretical account to keep either in both theoretical accounts. Empirically, plus pricing theoretical account has risk factor or factors to mensurate the adjusted hazard return relationship. If the theoretical account generates little intercepts value, the theoretical account does a good occupation foretelling the fluctuation in the rate of return.

The adjusted R square value of clip series arrested development will be used to compare the efficiency of both theoretical accounts. If the adjusted R square generates higher figure on norm, it can be presume that the theoretical account has successfully explained the fluctuation in return

Second, measuring the being and dependability of market premium, size and book to market equity under three factor theoretical accounts and how these factors affect the portfolio returns. In order to warrant our consequences, we will be looking at the t-statistics of, and for six portfolios

In visible radiation of above aims, the paper is divided as follows: first portion of the paper, offers an in deepness reappraisal on both CAPM and Multifactor theoretical accounts. The cardinal portion of this paper discusses the background on both theoretical account and most significantly, there are a figure of surveies discussed which suggests that the inclusion of other hazard factors such as size premium, book to market premium, gaining to monetary value premium and purchase ratio in multifactor theoretical account can really extinguish the CAPM anomalousnesss. After discoursing the literature reappraisal from behavioral positions, the following subdivision will sketch the empirical findings in which a elaborate methodological analysis has provided with relevant equations and documents used. Microsoft Excel is used to run the testing. The analysis of the findings is besides outlined subsequently in the survey. In this analysis portion, the chief focal point on whether multifactor theoretical account can supply better returns than CAPM to gauge the expected returns for six portfolios listed in FTSE 100 index.

## 2. Literature reappraisal

## 2.1. The Capital Asset Pricing Model

Modern Portfolio Theory is considered to be a constructive investing attack that helps an investor to sort and command the sum of expected hazard and return. The modern portfolio theory was foremost developed by Markowitz ( 1959 ) . The theory assumes that when investors select efficient portfolios among others, they merely see mean-variance portfolio to maximise their wealth which tends to maximise the return of a portfolio for any given portfolio hazard over a individual period.

The theory besides assumes that if investors are offered two portfolios with same expected returns and have different degree of hazard when puting in a portfolio, all investor will prefer to put in a portfolio which is less hazardous. Consequently, the lone clip investor might desire to merchandise in hazardous portfolios if that portfolios output high expected return. Therefore, if investors want higher returns, they must see hazardous portfolio. Due to different feature of hazard antipathies, rational investors may merchandise in an option portfolio which has better expected return for that degree of hazard, ( Edwin, 1997 ) .

Since, the Modern Portfolio has a theoretical repute ; it has struggled to manage big figure of assets in a portfolio due to troubles in work outing quadratic scheduling. The construct of MPT still being used widely in fiscal direction sectors because the CAPM is theoretically based upon the premise of mean- discrepancy portfolio theory. In order to ease the process of managing big portfolios, Sharpe ( 1964 ) , Lintner ( 1965 ) and Mossini ( 1965 ) introduced individual factor theoretical account which was the ‘Capital Asset Pricing Model ‘ . CAPM was among first fiscal theoretical accounts which offer the footing for gauging the needed rate of return on all hazardous assets in a portfolio. The theoretical account has achieved a acknowledgment in plus pricing theoretical account and finance literature which is reviewed by the work of Black, Jensen and Scholes ( 1972 ) .

The chief anticipation of CAPM theoretical account is that all investor invest in an efficient portfolio which is known as market portfolio. The market portfolio is normally a diversified portfolio because it contains all hazardous assets. Therefore, investors want hazard premium for puting in hazardous portfolios. Sharpe ( 1964 ) , Lintner ( 1965 ) and Mossini ( 1965 ) besides province that the beta is a important step of hazardous assets and how that systematic hazard is related to traverse subdivision of mean returns. The theoretical account besides assumes that the market beta can explicate all basicss of systematic hazard. Investors must be compensated for all systematic hazard associated with puting in hazardous assets, ( Ang & A ; Chen, 2005 ) .

They tested whether the beta and mean return are positively correlated. Since, they constructed all the securities into portfolios to extinguish systematic hazard associated with high expected returns ; this likely to hold increased the truth of the explanatory power of beta and besides predicted the portfolio returns. This seems to hold been a successful attack supplying a solution for statistical jobs caused by measurement mistakes in the appraisal of betas. Given that findings, there is a line drive relationship between portfolio beta and its mean rate of stock returns. The theoretical account besides assumes that a higher market beta can explicate higher expected returns. ( Michailidis, Tsopoglou, & A ; Papanastasiou, 2006 )

The chief deduction of CAPM as discussed by Fama ( 1976 ) and Roll ( 1977 ) is that in an equilibrium market, every investors hold value weighted market portfolios, that is, average discrepancy efficient. It says that

The expected return of stocks are correlated with marker beta and there are no other variable that have an explanatory power,

Second, the premium for beta hazard is positive connoting that the rate of return on market portfolios is in surplus of the rate of return on any assets. ( Fama & A ; French, 2004 )

The CAPM theoretical account besides gives other deductions of hazard and return relationship when tested. Assetss are non linearly related to the market in which the expected return on market is equal to rate of a hazard free plus and the premium for taking hazard is the rate of return on market exceeds the hazard free rates. ( Fama & A ; French, 2004 ) . Another of import deduction of CAPM is driven by the thought of hazard free plus. Including hazardous plus into the calculation, the capital market Line derives which is associated with the new efficient frontiers. The return of a hazard free plus is obtained as the procedure of the hazard free involvement rate and hazard premium of an plus. The hazard premium is considered to be a signifier of mensurating hazard related to the beta and per centum market hazard premium, which is the difference between return on an single plus and less hazardous assets. ( Fama & A ; French, 2004 )

Capital Asset Pricing Model beginning: Fama and French ( 2004 )

## 2.1.2. CAPM Equations

The equation is as follows

E ( ) =+ aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦ ( 1 )

Where,

E ( ) = the return on stock I,

= the rate of return on a riskless plus,

E ( ) = the rate of return on the market portfolio and

, = the systematic hazard of plus I, is the covariance of its return with the market return divided by the discrepancy of the market return

While, all investors in a market have an understanding about articulation distribution of their plus returns and investor prefer to put in a portfolios that has a tangency point known as portfolio M, investor will have hazard premium puting in a hazardous plus. In peculiar, there is a line drive relationship between hazard premium and return on an plus. If the plus returns has a covariance near to zero, the hazard premium on puting in hazardous plus will be minimal. ( Khan, et Al. 2011 ) Furthermore, “ hazard premium on the plus will depend on the ratio of the covariance of the aser ‘s and the portfolio M ‘s returns to the discrepancy of the Portfolio M ‘s returns ” ( Khan, et Al. 2011, p. 529 ) . The equation for betas as follows

( Market Beta ) aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦.2

In 1968, Jense has proposed the CAPM to widen into clip series arrested development analysis. They shows that the return of any plus at clip T is in surplus of the hazard free rate ( ) , is to the full captured by market hazard premium ( market beta times the expected return on market portfolios exceeds the hazard free involvement rate ( – ) . is the residuary mistake footings. ( Fama & A ; French, 2004 ) . The equation for the clip series arrested development of CAPM is give holla:

( ) = + – ) +aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦..3

## 2.1.3. CAPM-Assumptions

CAPM is based on the premise of average discrepancy portfolios. Sharpe, 1964, Lintner, 1965 and Mossini ( 1965 ) have added of import premise to the average discrepancy portfolios. All these below premises is paraphrased from a celebrated article that have written by ( Black F. , 1972 )

The premises as follows:

Investors seem to hold average discrepancy efficient portfolios.

All investor in the security market are considered to be risk averse who chiefly increase their wealth at investing skyline.

All investors have homogenous outlook of expected returns and same degree of hazard associated with investing.

The returns are usually distributed.

There exist less hazardous assets. All Investors in a security market can borrow and impart at this hazard free rate. There is no bound on borrowing and merchandising.

The figure of assets is fixed and the assets are easy tradable.

There are no limitation and revenue enhancements imposed in the market on purchasing or selling the assets. This means, there is no dealing cost associated with trading in a stock.

The security monetary values respond rapidly to alterations in market information.

Two extra premises are included to the work of Markowitz theoretical account to simplify the effectivity of average discrepancy model by Sharpe ( 1964 ) , Lintner ( 1965 ) and Mossini ( 1965 ) . The premises are,

Investors who borrow and lend at hazard free rate are independent than sum of borrowed by investors.

The 2nd premise is that the investors must hold an absolute understanding about the entire plus rate of return from old twelvemonth to current twelvemonth. The chance of puting in hazardous portfolios is same for all investors with the absolute understanding about the entire plus return and adoption and loaning at hazard free rate. Thus, investors invest in a tangency point.

There are few premises which does non see with the modern universe, since it has been first introduce in 1960. Therefore, the cogency of CAPM has been question by many research workers.

## 2.1.4. CAPM Beta

The systematic hazard is associated with full market hazard which is non diversifiable such as fiscal hurt and economic business district. In contrast, the unsystematic hazard is diversifiable by adding stocks in the portfolios. In general, CAPM assumes that market beta is linearly related to the plus ‘s hazard premium. Furthermore, beta is the lone important step of how that systematic hazard is related to traverse subdivision of mean returns. Beta determines how expected returns on stocks are sensitive to the alterations in the market. The investors will be compensated for trading in hazardous plus and the chance cost associated with financess. The chance cost of fund is defined as the return on an plus that has smaller covariance, ( Mankiw & A ; Shapiro, 1986 ) . In general, if a stock has a beta of 1.0, is considered to be mean market hazard associated with that beta. Investors can put in a diversified portfolio of stocks that has the same hazard as the market index. If beta less than 1 implies portfolio hazard is less than market. If the portfolio beta, on the other manus, is greater than one, so it has high hazard than market.

In order to better the explanatory power of market beta, Black et Al, ( 1973 ) avoidedA utilizing single stocks in the appraisal of beta. They used portfolios to regress the cross subdivision mean returns on betas to avoid unneeded mistakes on variables. Estimating beta for diverse scope of portfolios can supply precise consequence than gauging beta for an single stock. However, early empirical consequences found really small statistical grounds to back up the work of Sharpe and Linter version of plus pricingA ( Mankiw & A ; Shapiro, 1986 ) .

Even though the beta and returns are positively correlated, the consequences are excessively level, ( Campbell, 2000 ) . Harmonizing to the CAPM premises, the intercept is risk free involvement rates and the coefficient on beta is expected value on market portfolios minus hazard free involvement rate. One of the most contradictory consequences found from CAPM premises is that the mean hazard free involvement rate which is taken as one month exchequer measure is really less than the intercept. Further job was discovered on the estimated beta which is found to be less than the mean extra return on market. ( Fama & A ; French, 2004 )

## 2.1.5. Empirical Surveies

Since 1970, in order to prove the cogency of CAPM, a huge sum of research has been conducted. Many empirical consequences have been documented in favor of CAPM cogency. On the other manus, the cogency of CAPM has besides been questioned by some other authoritative and recent surveies. Some of these authoritative and recent surveies that show grounds of CAPM theoretical account will be discussed here.

Black, Jensen, & A ; Scholes, ( 1972 ) tested the cogency of CAPM by building portfolios of equities instead than single stock listed on New York Stock Exchange ( NYSE ) over the sample period of 40 old ages from 1926 to 1966. Findingss from their early testing documented a strong line drive relationship between mean monthly returns and beta. They besides provided some interesting consequences demoing that even though the intercept seem to hold been greater than hazard free involvement rate, their findings did non annul the CAPM anticipations. Similarly, Lau, Ramsey, & A ; Quay, ( 1974 ) used informations of 100 non fiscal houses traded on Tokyo Stock market over the period from 1964 to 1969. They found beta and mean returns are positively related on Tokyo Stock Market and beta is superior to any other hazard factors that can foretell the stock returns.

Classical surveies such as Fama & A ; MacBeth, ( 1973 ) find important statistical grounds to back up the work of Sharpe and Linter version of plus pricing theoretical account. Fama & A ; MacBeth ( 1973 ) test the hypothesis of two parametric quantity theoretical account. They found that the statistical relationship between market beta and stock returs are frequently important. In their hypothesis testing, the incline of the beta and stock returns is 2.57 for the smaple period of 1935 to 1967 ( Gibbons, 1982 ) . However this figure lessening later to 1.92 and 1.73 for the sample perido of 1935 to 1945 and 1956 to 1968. They besides suggest two deductions of CAPM as follows:

Portfolio beta is linerly related to mean returns.

Portfolio beta is considered to be the lone hazard placeholder. Other than protfolio beta, non-systematic hazard of a porfolios can non capture mean returns

Although, a figure of empirical surveies are found to be in favor of CAPM, there are some other empirical surveies supplying beliing consequences against CAPM. Jense, ( 1968 ) besides tested capital plus pricing theory to mensurate 115 portfolio director ‘s ability to calculate portion monetary values over the period from 1945 to 1964. Conclusion derived from his probe high spots that, on norm, portfolio directors would non be able to foretell future portion monetary values ( Ferson & A ; Schadt, 1996 ) . Furthermore, Dowen ( 1988 ) find that there are other hazard factors other than beta that has prognostic power to capture the fluctuation in returns. Given the consequences from their survey, they indicate that building larger portfolios of stocks can non give confidence of the variegation of hazards.

There are some other surveies chiefly emphasized on the appraisal of beta. The focussed surveies are as follows, the dependability of beta over different period of clip ( Harvey, 1989 ) , limitation in adoption ( Black, 1972 ) , informations issue related to non-synchronous ( Scholes and Williams, 1977 ) . An of import survey sing to beta appraisals conducted by Levhari and Levy ( 1977 ) that the appraisal of beta is biased, if shorter clip period is used by the analyst. Fama ( 1980,1981 ) found a grounds in favor of macroeconomic variables that the ability of macroeconomic variables increases to capture the mean stock return if the clip period additions. ( Gencay, Selcuk, & A ; Whitcher, 2005 )

Wang ( 1993 ) found the CAPM to be widely used plus pricing theoretical account to foretell the stock returns among fiscal analysis. For this case, investors who want to take investing determination in taking a new undertaking reasonably establish their determination on the CAPM. The ground is that CAPM is being used to cipher the plus retunes. This theoretical account is besides a successful effort to extinguish the unsystematic hazard of an investing undertakings. In peculiar, ciphering the cost of capital is a really of import fundamental in an investing undertaking which is besides estimated by the CAPM to supply information to investors whether they should put in that undertaking

Haung ( 2000 ) examined whether beta Cam explain the differences in mean returns. His testing is rather different than others discussed supra. In this survey, he organized stocks into two different classs. The first class consisted with hazardous stocks and the other class consisted with less hazardous stocks. Their determination provided that low hazard stock ‘s returns is to the full explained by the beta, on the other manus, beta fails to foretell the returns of high hazard security for the sample period from 1986 to 1993. On the footing of their determination, it can be concluded that investors can utilize other pricing theoretical account other than CAPM to set about an investing determination since the truth of CAPM is questionable.

In recent development of plus pricing theoretical account, Fraser and Hamelink ( 2004 ) argue in favor of cogency of CAPM. They used GARCH theoretical account and CAPM together in order to compare both consequences. They used the informations for London Stock Exchange over the period from 1975 to 1976. Their findings are similar to others research discussed above demoing that GARCH theoretical account has explanatory power in foretelling plus returns as compared with CAPM. Likewise, Eatzaz and Attiya ( 2008 ) used CAPM and Two factor theoretical accounts together in their trial of foretelling stock returns. They used the information set of 50 fiscal and no fiscal houses listed on Pakistani stock exchange over the period from 1993 to 2004. Findingss from their trial documented that the CAPM merely provided accurate consequences for short sample period and few stocks. It is besides found that two factor theoretical account which is known as Arbitrage Pricing theory provided better anticipation of plus returns as compared to CAPM. They besides concluded that even though CAPM has been widely used as a fiscal modeling, its cogency has been questioned by many recent surveies that give chance to other alternate theory such as multifactor theoretical account, APT to explicate the fluctuation in mean stock return is being investigated

CAPM theoretical account has been widely used by many research workers over the decennaries. Due to miss of empirical support for the theoretical account, a figure of research worker have proposed conditional version of the CAPM. The traditional CAPM assumes that the betas remain inactive over the period and the beta is used a hazard placeholder for all value weighted portfolio of stocks. Likewise, high beta stocks tend to hold high cost of equity and low beta stocks more likely to give low cost of equity as mentioned by Blume & A ; Friend. , ( 1973 ) . Therefore, the traditional version of CAPM fails in explicating the cross subdivision fluctuation in mean returns. In a celebrated article written by Wang and jagannathan ( 1996 ) assumed that “ the CAPM clasp in conditional Sense ” ( p. 3 ) . In other words, differences in beta and market hazard premium vary over clip. Return on human capital is included in their testing when gauging the return on assets. Therefore, the conditional version of CAPM can capture the CAPM anomalousnesss and besides be able to foretell the cross subdivision fluctuation in mean returns. ( Wang & A ; Jagannathan, 1996 ) . However, in a recent a survey, Lewellen & A ; Nagel, ( 2003 ) have questioned against the conditional CAPM. In general, if the conditional CAPM clasp, the intercept is ever zero or shut to zero. However, the unconditioned pricing mistakes are mostly influenced by clip fluctuation in beta. The unconditioned intercept will significantly different from zero if its beta alterations with market hazard premium. Therefore, conditional CAPM fails to capture pricing anomalousnesss, ( Lewellen & A ; Nagel, 2003 ) .

## 2.1.6. CAPM Restrictions

The CAPM theoretical account has been challenge several times since get downing related to certain premise and restrictions.

Beta appraisal: the appraisal of beta for single stocks is non accurate step when they used the theoretical account to explicate mean returns. Another restriction for the CAPM is that if the portfolios are based on book to market value and gaining to monetary value ratio, the theoretical account generates higher than expected mean stock returns and the returns are non to the full captured by the beta ( Lakonishok, Shleifer, & A ; Vishny, 1994 ) . For illustration, the beta appraisals for low book to market stocks has high beta but outputs low mean returns.

Single factor theoretical account: another possible drawback in early empirical trial of CAPM is that the theoretical account is considered to be a individual period theoretical account in which the market portfolio is an lone factor that can capture expected return. Most of the early empirical trial such as Blume & A ; Friend. , ( 1973 ) and Fama & A ; MacBeth, ( 1973 ) used clip series regresson theoretical account. In their determination, beta is non stationary.

Common fluctuation: Similar beginning of fluctuation was found in the residuary arrested development. As a consequence, the common fluctuations in the remainders create negative prejudice in least square the cross subdivision arrested development of incline. ( Fama & A ; French, 2004 ) .

Unrealistic premises: Another of import drawback is that the theoretical account has unrealistic premises. It is assumed that the investors can borrow and impart at hazard free involvement rate or all the investor have similar outlook in the market. Although all market information rapidly reflects to any alteration, these premises are still unrealistic.

Market placeholder job: The market beta of CAPM is linearly related to mean stock returns that hold in the average discrepancy efficient portfolio. However a strong statement against the cogency of CAPM is that it is non easy to happen market placeholder which is near to the minimal discrepancy frontiers. ( Fama & A ; French, 2004 ) . The efficiency of market portfolios has non been stated by the work of Black, Jensen and Scholes ( 1972 ) . Given their findings, beta and expected returns are non linearly related

International market: The Sharpe and linter version of CAPM merely limited to the US stock market. If planetary assets include in a diversify portfolio, the CAPM beta can non capture the stock return for an international stock market. ( Fama & A ; French, 2004 )

## 2.2. Multifactor Models:

Since a figure of scholers and research worker have provided account for early statistical consequences, weak relation between beta and stock returns increases opprtunity to include muliple variables that can explicate fluctuation in returns.

## Arbitrage Pricing Theory:

Lack of empirical supprort for one factor theoretical account of Sharpe ( 1964 ) , Linter ( 1965 ) and enable alternate plus pricing theoretical accounts to be examined. One of the basic specifications for any alternate pricing theoretical account should be that it can capture anomalousnesss that were observed within CAPM. The multifactor theoretical account that was developed by Ross ( 1977 ) through Arbitrage Pricing Theory ( APT ) was a possible option to individual period theoretical account in foretelling the one-dimensionality of stock returns. Even though, the theoretical construct of CAPM has been widely used in many empirical woks over the last decennaries, it lacks the ability to add extra factors to the theoretical account ( Reinganum, 1981 ) .

APT portions some common and realistic premises with CAPM, if non all. First, it does non necessitate the market portfolios has to be in efficient frontiers. Second, it does non take into history that the security returns are usually distributed. Finally, the theory ignores the quadratic public-service corporation map ( Shanken, 1982 ) .

Ross ( 1979 ) assumed that each stock return in any given portfolio does n’t merely depend on the market placeholder ( beta ) but partially relies on macroeconomic influences. The equation can be written as follows

= + + +aˆ¦aˆ¦.+ + aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦.aˆ¦aˆ¦aˆ¦aˆ¦..4

Where,

= the return on security I, a random variable ;

= the expected degree of return for the stock I if all indices have a value of nothing.

= the ith security ‘s return reactivity to factor K ;

= the idiosyncratic hazard or residuary term, which is independent across securities.

= the value O of the J Thursday index that impacts the returns on the stock

Beginning: Elton et Al ( 2011 )

There are two typical differences between CAPM and APT stated by Ross ( 1977 ) . First, as contrary to individual factor theoretical account, The APT can add multiple factors to foretell expected returns. Second, it portions the same premises of frictionless capital market which means, in an equilibrium market, there is no other manner to gain arbitrage net income. In add-on to that, all the investors have same grade of outlook that the return on any plus is positively related by common factors which is by and large known as beta or burdens ( Shanken, 1982 ) . However, Due to its statistical complexness, APT is largely found in faculty members but seldom usage in pattern.

## Intertemporal Capital Asset Pricng Model

CAPM is considered to be a individual period theoretical account as the position of multi- period behavior is to the full ignored by these two theoretical account. Merton ( 1973 ) has developed Intertemporal Capital Aseet Pricing Model ( ICAPM ) to foretell the nature of market equilibrium. Under the theoretical account, there is infinite figure of investing chance sets that might alter over clip. Since the hazard is associated with unfavorable alterations in future investing set, investors want to fudge the hazard against unsure alterations. In general, if the investing chance set is affected by the bad circumstance which seems to give high returns, it is preferred for investor to keep this assets as a hedge. This would take to an increased equilibrium monetary value for the assets ( Merton, 1980 ) .

## Fama and French three Factor Model

Fama and French extended portion linter version of CAPM to add two extra hazard factors viz. SMB and HML to capture the market monetary values. SMB ( the return of little houses minus large houses ) has explanatory power to capture extra returns associated with puting in stocks with little houses. HML ( the return of High value houses minus low value houses ) has the ability to capture value premium associated with puting in high book to value stocks. It is found that the investor consider separate systematic hazard factors viz. , size, book to market value along with market beta instead than beta merely. In other words, combination of these three factors has an advantage over other pricing theoretical accounts to explicate fluctuation in mean returns. ( Fama & A ; French, 1993 )

In an effort to analyze the cogency of these factors, they followed Black, Scholes and Jensen ( 1972 ) multiple arrested development theoretical account in the trial of adjusted risk-return relationship. It is found that betas, house size and book to market ratio can explicate the difference in mean returns.. The arrested development R squared is besides grounds to be really near to 1 for bulk portfolios. Their findings show that TFM can explicate bulk fluctuation in mean portfolio returns. Therefore, SMB and HML can independently entree the footing of systemetic hazard. Harmonizing to the TFM, little capitalisation houses have higher expected return than those of large cap houses. The theoretical account besides have explained possible grounds for the size consequence. Small houses are more liquite and has less dealing cost associated with trading. The handiness of trading information about little capitalisation houses is really limited therefore the cost in detecting portfolios of little houses is dearly-won than big houses. The grounds of high dealing cost requires investors in little houses to keep undiversified portfolios. Therefore, those who keeping undiversified portfolios, require high compensation for entire hazard ( Lakonishok & A ; Shapiro, 1986 ) .

The relability of beta estimations has besides been questioned since the frequincies of little house ‘s stocks are really low compared to big houses. In add-on, The value consequence explains that high book to market ratios have high mean return than low book to market ratios, ( Fama & A ; French,1992 ) . The three factor expression is written as follows

) – = [ E ( ) – ] + E ( SMB ) +E ( HML ) aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦..5

Whereas

) is the return of a portfolio at clip T,

Rf ( T ) is the hazard free rate,

is a beta coefficient for extra market return

E ( ) is the market Return at clip T,

vitamin E ( T ) is the error term.

SMB is the respect between little stock category and large stock category

HML is the difference between High book to market and low book to market category

Adding new variables in the equation, E and E specify the sensitiveness of stock to extra common variables. Using the same information as mentioned in Fama and French ( 1992 ) , Fama and French ( 1993 ) exhibits that E and E are important step of hazard and positively related to the extra returns. The theoretical account besides exhibits clip series arrested development analysis in which B, s, H are slopes as follows

– Rf= a+ baˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦ . 6

## 2.4.1 Empirical Surveies of Fama and French Three Factor theoretical account

Since CAPM and APT both fail to capture fluctuation in mean stock returns, Fama and French ( 1992 ) have introduced an alternate theoretical account to explicate extra returns. They used the information set of non fiscal houses for major US markets inclduing National Association of Securities Dealers Automated Quotations ( NASDAQ ) , American Stock Excahange ( AMEX ) , New York Stock Exchange ( NYSE ) over the sample period from 1963 to 1990. The trial of joint map of hazard factors such as beta, book to market value, house size consequence, gaining per portion, purchase ratio used to explicate in cross subdivision in equity returns. It is found that the house size and book to market value are variables that can foretell fluctuation in equity returns better than others ( Fama and Gallic 1992 ) . Sing to size consequence, little houses likely to give high returns as compared to big houses. Ongoing argument on the map of book to market consequence as a market placeholder exhibits that investors prefer growing stocks instead than value stocks because growing stock like to hold high norm returns than those of big houses.

A decision derived from Fama and French ( 1992 ) sing to the efficiency of CAPM theoretical account that

If one considers fluctuation in CAPM market Bs that is non related to the size, beta and mean return are weakly related from 1941 to 1990.

The prognostic power of beta in explicating the fluctuation in mean returns is questionable ( Fama and Gallic 1996 ) .

Using clip a clip series arrested development model, Fama and French ( 1993 ) have extended their research to corporate and authorities bond. They besides have taken into history five factors to regress clip series approch. : a market portfolio returns, portfolios form on size and book to market consequence, default and hazard premium. Therefore, two extra hazard factors viz. steadfast size and book to market ratio with market beta has included to the Fama and French Three Factor Model. They fund that TFM can explicate most of the CAPM anomlaies for US stock market. ( Azam & A ; Jasirilyas, 2011 ) .

Fama and French ( 1993 ) show that the expected value exceeds the hazard free involvement rate that is given by its return ‘s sensitiveness to three cretiria:

mean return on a bond portfolio.

The difference between the average returns on little portfolios and the average returns on large portfolios.

The differences between the average returns on high book to marktet equity ( BE/ME ) ratios and average returns on low book to marktet equity ( BE/ME ) ratios.

Broad analysis on the effects of hazard return narrative has been illustrated by Fama and French ( 1995 ) . It is found that following the characteristic of Net incomes, the house size and value factors have similar behavior explicating fluctuation in equity returns ( Gaunt, 2004 ) . They besides illustrate that, incline on HML and BE/ME is being used as a placeholder for hurt in the theoretical account. As a consequence of this, less profitable houses with little net incomes seem to hold high book to market equity and frailty versa. Fama and French ( 1996 ) shows different hazard forms related to house size, past growing of gross revenues, short and long term return, monetary value net incomes, monetary value hard currency flows. Differences in the variables are non successfully captured by the CAPM. They find that Three Factor Model can capture most of the anomalousnesss from CAPM in mean stock returns other than short term returns. Their consequences are besides in line with empirical survey of international Capital Pricing Theory ( ICAPM ) and Arbitrage Pricing theory ( Fama and Gallic 1996 )

Fama and French ( 1998 ) used value and growing stock for 13 international stock markets over the sample period from 1975 to 1995. Their determination is similar to their old consequences, documenting that high book to market stocks have high return than low book to market stock in 12 out of 13 major international stock market. Their determination besides suggests that the fluctuation between average return on international portfolios of high and low book to market equity is 7.28. Similar value premium consequence is besides found when they form portfolios on variables such as net incomes to monetary value ratio, hard currency flow to monetary value ratio and dividend to monetary value. In peculiar, they found being of value premium consequence in the international stock market. Furthermore, the value premium in the international market returns is non to the full explained by the ICAPM. However, two factors APT that include risk factors can successfully foretell value premium in international market returns. Value premium consequence is besides captured in both single state and planetary returns ( Fama and Gallic 1998 ) .

## 2.4.2. Size consequence

During 1980 ‘s, a significant sum of empirical research documented the being of extra factors in the pricing theoretical account like EPS, book to market value that give explanatory power to gaining control mean returns other than market beta of stock. In the context of CAPM cogency, Banz ( 1981 ) acclaimed the statistical importance of keeping portions of little houses to explicate extra returns over the period from 1936 to 1977. He found that big houses have lower mean return than little houses and the returns of little house are non to the full captured by beta entirely. As response to Banz ( 1981 ) , Reinganum, ( 1981a, p. 45 ) found that “ after commanding returns for any E/p Effect, A strong house size consequence still emerged. but, after commanding the returns for any market value consequence. a separate E/p Effect was non found. ” Hence, decision can be drawn from Reinganum ‘s findings that house size consequence invalidated the emperical trial of Basu ( 1977 ) who acclaims that high earning to monetary value ratio stock have high expected returns than low gaining monetary value ratio stock. Roll ( 1981 ) found that although both little and big houses have equal hazard, little houses have high returns than big houses. In peculiar, hazard of little houses is unsuitably precise chiefly due to mistakes associated with autocoreltion in stock returns caused by a little sum of frequence in trading. There are besides other variables such as monetary value to gaining ratios and dividend yeilds than can foretell differences in mean returns.

From the statistical point of position, grounds by Christie & A ; Hertzel, ( 1981 ) show that addition in the hazard of house purchase due to stationary mistake in the measuring of hazard which consequence in lessening of the value of stock. Given their findings, the hazard is likely to be changeless for a figure of old ages to minimise the hazard of purchase houses whose stock value has declined ; hence, the mean returns for the low value stock could be positive ( Schwert, 1983 ) . As a response to ( Banz, 1981 ) , Chan and Chen ( 1991 ) have besides explained why big and little companies tend to hold different return features. They used monthly informations for 19 non- fiscal industries for NYSE in the period from 1956 to 1985. Using multiple arrested development model and correlativity, it is found that little industries likely to bring forth higher returns than big industries due to differences in concern operations and handiness in external finance. Jagadeesh & A ; Narasimha, ( 1992 ) prove the portfolios whether market beta can explicate the size consequence for different stock markets. They found that there is a really weak line drive relationship between beta and house size. In peculiar, they besides found that market beta does non capture the cross subdivision fluctuation in stock returns, ( Tanjea, 2010 ) .

Sing to economic factors, Fama and French ( 1993 ) besides admit that it is hard to happen any economic ground for size consequence ; Chan and Chen ( 1991 ) have explained the economic grounds that affect the return feature of big and little companies. The ground is little houses are more likely to execute severely in past and accordingly, these houses are non efficient plenty to run and probably to hold high debt and hard currency flow job. Due to the fluctuation in productiveness, purchase and most significantly, accessing to external finance is by and large hard for these houses. Therefore, little houses are considered to be hazardous than big houses. In peculiar, market index seems to hold less capableness to capture little house ‘s hazard due to assorted economic grounds ( Chan & A ; Chen, 1991 ) . As a consequence, Since Small cap houses tend to hold high hazard than large cap houses, investors want compensation for the sum of hazard they have taken to put in their company. Furthermore, The Fama and French ( 1993, 1996 ) incorporated assorted hazard factors in a diversified portfolios can assist to capture the differences in returns. The chief challenges against CAPM implied by Fama and French ( 1993 ) is that high mean returns on little capitalisation stocks produce a hazard in returns and it can non be to the full explained by the market beta alone..

A conventional survey by Malin & A ; Veeraraghavan, ( 2004 ) found large house consequence in United Kingdom which contradicts to the logic of TFM. Sing to the cogency of CAPM, it is found in their findings that it is non possible for beta entirely to explicate the difference in mean returns. Therefore, two extra hazard placeholders viz. SML and HML, incorporated by TFM, considered being best option to foretell the fluctuation in equity returns. ( Malin & A ; Veeraraghavan 2004 )

A theoretical account is farther provided by Berk ( 1997 ) . Since there is ever an opposite relationship between size consequence and mean returns, high expected return is besides associated with high price reduction rate ensuing in lower market values. As a consequence, house size can non be used as proxy to gauge other variables such as dividend output. In 2005, Fan and liu, utilizing Berk ‘s premises, they incorporated coincident theoretical account to capture the behavior of size and book to market ratio. They suggested a figure of economic factors such as fiscal hurt, impulse that affect the map of size and book to market value instead than systemic hazard to SML or HML. ( Berk 1997 )

Inspired by Keim ( 1983 ) , this paper paperss the clip series behavior of little house. They acclaims that stock with little house ‘s mean returns is high in January compared to the remainder of the twelvemonth. The happening of size consequence is about 50 per centum in January and about 25 per centum of size consequence happens over the first trading hebdomad in January ( Gaunt, 2004 ) . Brown, Kleidon, & A ; Marsh, ( 1983 ) paperss further seasonal feature of the size consequence. Using informations from 1967 to 1979, it is found that go uping portfolios based on house size have resulted in a positive surplus returns. However, these consequences are non consistent with that peculiar sample period. When they extend their sample period from 1969 to 73, they found stocks of little houses have a negative surplus returns. Hence, the hardiness of the size consequence is non supportive to different sample period.

## 2.4.3. Book to Market Value Effect

Sing to the Value consequence, Fama and French ( 1992, 1993 and 1998 ) found grounds of value premium consequence in their testing. Davis ( 1994 ) extended the work of Fama and French ( 1998 ) back to 1941 to be found supportive grounds in favor of value premium consequence. Later, Davis, Fama, & A ; Gallic, ( 2000 ) found support for the TFM widening the information from 1929 to 1997 for US stock market. They observe that Daniel and Titman used short informations set in their testing and value premium consequence was successfully explained by TFM. They besides found strong grounds of value consequence in US market. ( Davis, Fama, & A ; French, 2000 )

The 2nd ground for the value consequence that it is non considered being an anomalousness. One may state that high hazard is involved in trading in high value stock those consequences in a high mean return. These returns are considered to a compensation for puting in hazardous stock which is observed in Merton ‘s 1973 Intertemporal Capital Asset Pricing Theory, ( Davis, Fama, & A ; French, 2000 ) . Likewise, Fama and French ( 1993, 1996 ) proposed a multifactor theoretical account that uses portfolios formed on the size and book to market value. They found that the add-on of two hazard factors related to size and book to market value can capture fluctuation in mean returns.

The 3rd account for value consequence is that investor ‘s sometimes over react to value house. Contrary to the work of Fama and French ( 1993 ) Lakonishok et Al ( 1994 ) and Haugen ( 1995 ) showed that the value consequence occurs in mean stock returns because investor overvalues low value houses and undervalues the value houses. If the pricing mistakes are corrected, the value houses produce high return and low value houses ( growing house ) output low returns ( Fama & A ; French, 1998 )

The concluding account for value consequence is that the value premium is due to characteristic theoretical account instead than covariance of hazard. As argued by Daniel, Kent, & A ; Titman, ( 1997 ) , it is found that Fama French Three Factor Model has less power proving alternate hypothesis, which it is called the characteristic theoretical account ( Eom & A ; Park, 2011 ) . The TFM specifies that the mean stock returns have direct relationship with the features which are size and B/M factors and their features are risk placeholder for the theoretical account. Daniel, Kent, & A ; Titman, ( 1997 ) , test the theoretical account utilizing US stock market informations over the period from 1973 to 1993. They found that the being of size and book to value stock premium is non chiefly due to the association of these stocks with perspective factors. Their findings are in favor of covariance construction of stock returns that can explicate fluctuation in mean returns. Furthermore, they besides found undependability of CAPM beta explicating fluctuation in mean stock returns ( Daniel, Titman, & A ; Wei, 2001 ) . On the other manus, the being of features theoretical account has besides been proven by the work of Daniel, Titman, & A ; Wei, ( 2001 ) . Similarly, ( Lee, Liu, & A ; Strong, 2007 ) have besides found comparatively strong support for TFM in UK stock market over the periods from 1977-2004.

Sing to the market efficiency, another alternate position emerged in the work of Lakonishok, Shleifer, & A ; Vishny, ( 1994 ) who argued that because market does non move in an efficient manner, value stocks are likely to hold high mean stock returns than growing stocks. They found that rational investors predict future public presentations of a house based on its historical public presentations. In general, value stocks tend to hold hapless historical records related to its public presentation in assorted concern countries and it is besides assumed that this hapless public presentation will be reflecting in the hereafter. Since, houses that have hapless past path record may hold experienced bettering public presentation in future, this positive betterment may take to lift in portion monetary values ensuing in higher return ( Chan, Lakonishok, & A ; Sougiannis, 2001 ) . Harmonizing to their findings, it can be said that the investors are being pessimistic about future returns and would hence, can gain high returns puting in value stocks and selling their growing stocks.

Extra grounds in favor of value premium consequence is besides documented by several research workers. The value Premium is used as a placeholder for a variables related to the economic hurt. Compared with growing stocks, Value stocks are usually associated with fiscal hurt and the liquidness job of any house which can mostly impact the public presentation of value stocks. Fama and French ( 1993 and 1996 ) define that value stocks are high book to market ratio and growing stocks are define as low book to market ratio.

Loughran, ( 1997 ) found that utilizing the book to market ratio, value premium consequence is losing among the big houses in US stock market after 1963. As a response to his empirical survey, Fama and French ( 2006 ) found the value premium effects in US stock markets after widening their survey from 1926 to 1996. They compare the consequences of Value premium with size consequence and besides examine whether value premium is filly explained by CAPM. They came to the decision that there is no difference in the value consequence for both little and big cap houses during the sample period from 1926 to 1963. However, alternatively of utilizing the book to market ratio, Gaining to monetary value ratio over the period from 1962 to 2004 can bring forth comparatively strong value premiums for any steadfast size and really similar consequences of value premium consequence is besides grounds for little and big US houses. Findingss from their early trials found that, the value premium consequence can besides be explained by CAPM for the sample period from 1960 to 1963 and neglect to explicate those of 1963 to 2004. The empirical trial of Ang & A ; Chen, ( 2005 ) is farther suggested by Fama and French ( 2006 ) bespeaking that the beta is debatable. In other word, beta is non co related to size and value growing for the sample period of 1926 to 1963. ( Fama and Gallic 2006 )

## 2.4.4. Monetary value Earning and High Leverage Effect

There are some other empirical surveies that contradicted the premises of Capital Asset Pricing Model. Basu ( 1983 ) explained monetary value gaining consequence on stock returns over the period from 1957 to 1971. He showed that keeping high monetary value net incomes ratio stock can bring forth well higher norm returns than low monetary value gaining ratio stocks. It is besides found that the market beta can non explicate the differences in stock returns. The determination of DeBondt & A ; Thaler, ( 1985 ) was that the stocks with low returns over the past five old ages experienced highest mean stock return over the following five old ages and frailty versa. This is yet another chief unfavorable judgment of CAPM non being able to capture differrences in extra returns. In order to make that, houses with low returns stocks would hold higher market beta to formalize the differences in stock returns. A ulterior survey by Bahandari, ( 1988 ) found that houses with high debt to equity ratio tend to be at hazardous than low purchase houses. An addition in the hazard exposure, high purchase houses should hold high figure of beta coffecient to warrant the differences in returns. Consequently, his findings besides contradicted to the premise of CAPM. Another empirical survey by Rosenberg, Ried, & A ; Lanstein, ( 1985 ) provided grounds against CAPM, they showed that high book to market ratio houses can bring forth higher returns than houses with low book to ratio. Due to the sample period used in their survey being reasonably abruptly, their work did non accomplish as much recognitaion as others emperical surveies discussed above. After carry oning a similer empirical survey in the Japaness stock market, the book to market ratio consequence began to gain acknowledgment as a factor that can explicate the fluctuation in stock returns. ( Lyon & A ; Barber, 1997 ) . Later, Fama and French ( 1994 ) have extended their theoretical account by adding three variables such as gaining to monetary value ratio, hard currency to monetary value ratio and high gross revenues growing to capture fluctuation in returns.

## 2.4.5. Momentum Consequence

Every assept pricing theoretical account has some restriction. TFM anomalousnesss that is documented by several writers is momentun consequence. Jegadeesh & A ; Titman ( 1993 ) highlighted that Firms that have good path record over the last few months tend to hold high stock returns and frailty versa. On the other manus, a behavioural theory identified by DeBondt & A ; Thaler, ( 1985 ) who found that impulse result last for several months. Their consequences besides indicate that the consequence of momenturn plants good for those houses that have hapless recent performace. In other words, houses that perform hapless in recent clip could bring forth high return in future. ( Fama E. , 1998 )

## 2.4.6. Data Mining and Selection Bias

Fama and French ( 1993 ) states that little houses and value houses should bring forth higher returns to counterbalance high systematic hazard that involved in trading in these stocks. The cogency of TFM is questioned by the empirical work of Black and Fischer ( 1993 ) . Given their findings, it is suggested that there is an grounds of a information excavation consequence on the anticipation of expected returns. Fama and French used size, book to market value, leverage ratios as an explanatory variables which was wholly depend on the early empirical surveies. Likelihood to hold a batch of informations mining exercising on the early empirical surveies caused jobs in beta estimations. Black and fisher besides found that the efficiency and dependability of these variables to explicate the form in mean equity returns disappeared when different scope of informations series was used to analyze the theoretical account, ( Black and Fischer 1993 ) .

Another of import statement against the survey of Fama and French ( 1992 ) was from Breen & A ; Robert, ( 1995 ) . They argued that the efficiency of book to market values to capture transverse subdivision fluctuation in mean returns are capable to choice prejudices caused by the manner houses being added to the COMPUSTAT information files. This broad scope of paperss contained past accounting informations that was used by many different writers to organize the variables in explainng the adjusted hazard return relationship. The account of ( Breen & A ; Robert, 1995, p. 2 ) is that “ when COMPUSTAT adds a house to its informations file, it frequently “ back-fills ” informations. That is, if a house is added in 1983, for illustration, COMPUSTAT might make full in informations for the house back to 1978. See the high BE/ME houses that 2are non on the COMPUSTAT file in 1978. These houses have low market value relative to book value and, hence, are likely to be executing ill ” . Likewise, utilizing the information from 1947-1987, Kothari, Shanken, & A ; Sloan, ( 1995 ) found that there is a weak relationship between book to market value and mean stock returns which is less dependable than that of Fama and French ( 1992 ) . The ground for this inconsistent consequence is chiefly due to survivor prejudice and informations snooping. The beginning of informations includes inconsistent record of book to market houses ensuing in subsister prejudice. In contrast to the being of informations spying hypothesis, several empirical surveies found really small grounds to back up the construct of subsister prejudice. For this case, Lakonishok, Shleifer, & A ; Vishny, ( 1994 ) found positive additive relationship between book to market value and mean returns for US stocks.

## Three Factor theoretical account in International Market

The Fama and Gallic TFM are capable to US informations set and hence, their statement is simply based on US markets. Fama and French ( 1998 ) have used several international markets in their testing. However, their informations contained little measure of large houses. Griffin ( 2002 ) shows that the map of Fama and Gallic TFM works good in assorted international markets viz. Japan, UK and Canada. Drew and Veeraraghavan ( 2003 ) found grounds in favor of TFM in four stock markets viz. Hong Kong, Korea, Philippines and Malaysia. They reported that house size, book to market value, gaining to monetary value can capture the differences in mean stock returns in all four states.

In Australia stock market, a figure of writers viz. Halliwell etal ( 1999 ) and Faff ( 2004 ) have found support for TFM. Using the information from 1981 to 1991, Halliwell et Al. ( 1999 ) found hebdomad support for the statistical significance of Size consequence and strong relationship between book to market ratios and mean retunes. As a response to Halliwell et a.l ( 1999 ) , Faff ( 2004 ) used day-to-day informations from industrial sectors over the period from 1991 to 1999. They find negative size consequence in their testing and strong support for the value consequence which is consistent with the consequences of TFM.

The TFM is the most discussed pricing theory in empirical surveies in recent periods which explain the differences in the stock returns. The clip series arrested development discussed above, Mitchell & A ; Stafford, ( 2000 ) explains how frequently the equity monetary value reflects to the new information. The utility of the theoretical account is besides related in mensurating the public presentation of common fund direction. For illustration, Chaehart, ( 1997 ) used Three Factor Model instead than CAPM to gauge the equity ‘s capital cost

## Three Factor Model in UK

Previous empirical surveies found grounds in favor of TFM in the UK Market. It is found that the book to market ratio can foretell the differences in the UK mean stock returns. Using simple arrested development analysis, Strong and Xu ( 1997 ) found that there is a strong relationship among beta, purchase and book to market stock and a negative relationship is associated with market value and book purchase. A new set of accounting information is used by Dimson, Nagel and Quigley ( 2003 ) to the trial the being of Value premium consequence in UK market. During the period of 1955 to 2001, little and big houses have similar value premium consequence in the UK market. Research and Development theoretical account of Fama and French ( 1993 and 1996 ) is used by several writers to prove whether the mean returns are related to the research and development activities in UK markets.

In an effort to supply grounds of little house and value consequence on three major markets such as Germany, France and England, Malin and Veeraraghavan ( 2003 ) tested TFM on these three European markets over the period from 1992 to 2001. They found the grounds of a little house consequence in France and Germany and a large house consequence in the UK. They did non happen any grounds of a value consequence for the market mentioned supra. In the visible radiation of above treatment, a decision can be made based on Malin and Veeraraghavan ‘s findings that the CAPM beta seems to hold been undistinguished in explicating cross subdivision in mean returns. The consequences of UK are consistent with the consequences of Fama and Gallic TFM. However, a beliing consequence of Size consequence is found which is inconsistent with