This study explores the impact of market premium, size premium, value premium and information efficiency premium on average equity returns of Pakistani equity market from June 2002 to June 2012 for 152 stocks using the methodology proposed by Fama and French (1992, 1993). Result indicates that market premium, size premium, value premium and information efficiency premium are priced by the market. These premiums significantly explain equity returns in single factor, three factor and four factor model. Capital asset pricing model (CAPM) is valid for explaining average equity returns but multifactor model captures additional information. Therefore, it can be concluded that size premium, value premium and information efficiency premium are considered as systematic risk and priced by the market. As Size premium. Value premium and information efficiency premium exists in Pakistani equity market investors and portfolio managers should consider these premiums along with market premium for selecting and valuation of their portfolios.

JEL Classification: G110, G120, G150

Keywords: Size Premium, Value Premium, Information Efficiency Premium, CAPM

1. INTRODUCTION

Precision of information in stock prices is an important characteristic of information environment, which reduces the uncertainty about firm value [Lambert and Verrecchia (2015)]. High quality disclosure has more precision of information in stock prices and decease cost of equity [Francis, et al. (2005)]. Botosan, et al. (2004) examine the quality of public and private information, using analyst forecasts and report negative association between precision of public information in analyst's forecasts and cost of equity. The study also suggests that precision of private information in analysts' forecasts are positively associated with cost of equity and both private and public information offset the effect of each other. However, Lambert, Leuz, and Verrecchia (2012) suggest that prevision of public and private information is an increasing function and it is negatively associated with the cost of equity.

Public information is not fully captured by market and the residual movements in stock price variations are captured by private information [Roll (1988)]. The study further suggests that more firm specific information tend to have low R square or Stock price synchronicity (SPS). SPS is defined as the tendency of stock market prices to move in the same direction in a given period of time. Farooq and Ahmed (2014) argue that SPS is an increasing function of governance environment of a firm and better governance mechanism reveal higher SPS and poor governance mechanism exhibit lower SPS. Leuz, et al. (2003) argue that monitoring of managerial discretion is difficult for those firms have inadequate governance mechanism and managers of these firms do not disclose true information. Poor disclosure increases the information asymmetries for the investors. Prior literature suggests that investors show more reaction towards negative news for poor governance mechanism firms than higher governance mechanism firms [Douch, Farooq, and Bouaddi (2015)]. So, investors react more severely to the negative shocks in those firms having higher information asymmetries than firms have better governance mechanisms [Mitton (2002)].

Bae, Lim, and Wei (2006) suggest that firms with poor governance environment hide bad information or release bad information slowly. As a result of such behavior, returns of these firms are positively skewed. Whereas, Douch, Farooq, and Bouaddi (2015) argue that even in an inefficient market, investors are able to see such behaviours and will penalise such firms. So, there is more probability of negative tails in these firms with low governance environment. Results of this study report that low SPS is associated with poor governance and have higher probability of dominant negative tails.

Kelly (2007) reports that high SPS firms attract institutional investors and institutional investors are holding long term positions for stocks, they do not overreact to negative news. Institutional investors have positive relationship with corporate governance mechanism, because they prefer to invest in firms with better governance mechanisms, because of lower monitoring costs [Chung and Zhang (2011)]. Therefore, the returns of those firms will be higher with high SPS than low SPS firms. As, Roll (1977) argues that market risk premium proxy of difference between market return and risk free rate is not capture true and complete market information and leads CAPM being invalid. Empirical literature identifies various anomalies which include size, BTM ratio, leverage, momentum, dividend yield etc. So, SPS based premium may also help to capture the variations in portfolio returns as a proxy of information efficiency using asset pricing models as an additional factor.

This study makes a substantial contribution to the existing literature by providing the evidence about information environment quality in general and Pakistani equity market particular. Because, Pakistani market is an emerging market during last decade phenomenal growth is observed, but at the same time market saw number of ups and downs. It is generally considered as high risk and high return market. The market also attracted foreign investment during last decade. But, it is also criticised that foreign investment is a source of volatility in market. In developed markets like, US, UK, Japan etc., any information is quickly incorporated in the security prices and markets are considered more efficient.

In case of an emerging market like Pakistani stock market the situation may be different due to different political, social and economic conditions of the country as compare to developed countries. The empirical literature states that an established and emergent stock market is an indication of economic growth. When social, economic or political condition of any country changes, it affect the performance of stock market. In this context, Pakistan faces these types of changes in recent past and it is also observed that these changes have linked with fluctuation of Pakistani stock market. The findings of this are helpful to add the role of information environment quality in explaining the equity market returns along with price adjustment dynamics of Pakistani equity market.

The rest of the paper is organised as follows: Section 2 provides a brief overview of empirical work done and covers the literature on the subject. Section 3 provides data description and deals with methodological issues which discuss the econometric model Section 4 reports and analyses the results, and Section 5 concludes the study.

2. LITERATURE REVIEW

Corporate managers are always interested in information issues. Along with corporate managers, individual as well as institutional investors also give a suitable weightage to company specific information while selecting the portfolios of stocks or bonds. Information efficiency has presented a lot of discussion in financial economics, which is expected to affect an immediate increase or decrease in the stock prices. Asset pricing theory implies that expected returns on market securities have a positive linear relationship with market beta and market beta explains future expected returns. So, stocks with high return should have higher beta. Conversely, empirically evidences have provided by different studies and fail to find the variations in stock returns by following market beta alone.

CAPM is one of the most important and debatable topic of modern finance. CAPM is the central idea of finance based on "The portfolio theory of Markowitz (1952)". The portfolio theory is based upon the portfolio selection by investors on the basis of expected return and risk. CAPM is based on the idea that principle if there is high expected risk investors demand additional risk. It is an economic model for valuing different securities and stock that are traded in equity market, different derivatives and assets that are associated with some kind of risk and expected return attached with it.

The problem arises that what should be done for calculating the expected return and risk, Sharpe (1964) developed a model, as an extension of Markowitz's portfolio theory to introduce the concept of systematic and specific risk. Some parallel work has also been done by Treynor (1961), Lintner (1965), Mossin (1966) and Black (1972), and CAPM come in to existence. It is also named as SLB model that is Sharpe (1964), Lintner (1965) and Black (1972) model and SLM model Sharpe (1964), Lintner (1965) and Mossin (1966) model. For the work have been done on CAPM, Sharpe shared the 1990 Nobel Prize in Economics with Markowitz and Miller.

The traditional CAPM has long been debated by the researchers in a context to portfolio risk and returns that tries to find out the relationship between risk and return in a rational equilibrium market. It assumes that variance is sufficient tool to measure the risk and it might be acceptable if returns were normally distributed. But often returns are not normally distributed [Galagedera (2004)]. In other words, CAPM states that expected returns of stocks are positively related to market betas and these betas are the only risk factor to explain the cross-sectional variation of expected returns. CAPM does not help to identify and understand the ground factors and included their affect in the risk and return relationship. This model assumes that investors have the same opinion for the given beta and its return of any asset.

The idea behind CAPM is that investors need to be compensated in two ways. One is the time value of money and the second one is risk. Risk free rate is given for time value of money and is used as a compensation for the investors putting the money for that time period. The other portion of this formula represents the market risk premium. CAPM assumes that variance is sufficient tool to measure the risk. It might be acceptable if returns were normally distributed and CAPM does not explain the variation in stock returns. Jensen, Black and Scholes (1972) examine that those stocks have low beta that may offer higher returns than the model would predict.

Roll (1977) argues that using stock index as a proxy for the true market portfolio can lead to CAPM being invalid. Since the true and complete market index is not available such tests will be biased. Moreover, CAPM is used as a forecasting model that is the reason that it should be tested fairly and correctly to predict investor expectations regarding risk and return. This criticism led to the development of alternative models. Arbitrage pricing theory (APT) is one of such models that discuss the probability of more than one factor. The APT is an extension of the CAPM but in much more general concept. Both compute a linear relation between assets' expected returns and their covariance with other random variables. In CAPM, the covariance is with the market portfolio's return and in APT impact of as covariance with other factors is also considered. APT does not identify factors for a particular stock of industry/market. So the real challenge for the investor is to identify three things. First, each of the factors affecting a particular stock, second expected returns for each of these factors and the third one is the sensitivity of the stock to each of these factors.

APT is a valuation model developed by Ross (1976). The APT has the power to reduce CAPM weaknesses. CAPM argues that security rate of return is linearly related to a single common factor, the rate of return on the market portfolio. The APT assumes that each stock's or asset's return to the investor is influenced by several independent factors. This theory has the potential to predict a relationship between the returns of a portfolio and the returns of a single security through a linear combination of many independent macro-economic variables. APT covers a lot of factors which may occur for calculating the return of stock or assets. These can be divided into different groups, i.e. Macroeconomic factors, Company specific factors and behavioural factors.

Early work in this area including Jensen, Black and Scholes (1972), Fama and MacBeth (1973) and Blume and Friend (1973) support the standard and zero beta model of CAPM. A lot of criticism on single market premium model CAPM questions the asset pricing theory. Lately, anomalies are reported, Basu (1977) discuss earning price ratio and report that firms with low earning price ratio have yielded higher returns and firms with higher earning price ratio have produced lower returns than justified by beta. The famous study of Banz (1981) finds that size (market capitalisation) effect increase the explanatory power of model and helps to better explain cross section returns with market beta. This study reports that portfolio returns of small size stock are high with their given beta estimates as compare to large size stocks. Stattman (1980) and Rosenberg, Reid and Lanstein (1985) investigate book to market (BTM) ratio and find that it is positively related with US stocks. BTM ratio takes significant part to explain cross-section portfolio returns [Chan, Hamao, and Lakonishok (1991)]. Bhandari (1988) also examines the relationship of leverage and average stock returns. This study suggested that there exists a positive relationship between leverage and portfolio returns.

Chen, et al. (1986) have identified different macro-economic factors include Changes in inflation, Changes in GNP, Changes in investor confidence due to changes in default premium in corporate bonds, changes shift in the yield curve. Recently, Fama and French (1992, 1993, 1995, 1996 and 2015) have reported that calculation of simple beta is an insensible approach to forecast stock returns. They have examined that the portfolios formed on the basis of high BTM ratio, high earning price ratio, small size and high leverage earn higher returns. Therefore, it can be concluded that size, earning to price ratio, BTM and leverage can capture the cross-sectional differences in return better than market p. All these firm specific variables incorporate information to the market and contribute towards explaining the equity market returns.

Rich literature exists that identifies number of factors that influence equity returns. The significance of different factors explaining cross-sectional returns have contradicted the presence of single market factor CAPM based on mean variance theory. Numerous studies reject the single factor model and state that market risk premium is not capture fiill relevant information [Officer (1973) and Breeden and Douglas (1979)]. Fama and French (1992) investigate the relationship among Size, BTM, E/P and market beta in the equity market returns for NYSE, AMEX and NASDAQ from 1963 to 1990. This study uses portfolio betas to predict the stated variables by using second pass regression of Fama and Macbeth (1973). Results indicate that all relevant variables have significant power to predict equity returns except beta. Fama and French (1993) extend the previous study by using Jensen, et al. (1972) time series approach both on stocks and bonds. Results reveal from the study report that size and BTM have significant impact on equity returns and bond default premium. Hence, suggests that three factor model consists of market premium should also be used size and BTM to predict future equity returns.

Fama and French (1995) investigate the behaviour of equity returns by using size and BTM by using full and sub period sample regression. Results revealed from this study suggests that returns respond to the BTM ratio, and firms with persistent low earnings tend to have high BTM ratio and positive relationship with HML, whereas firms with persistent high earning have low BTM ratio and negative relationship with HML and BTM portfolios of small stocks are less profit able than big stocks. Chan, et al. (1991) examine size, BTM, earning yield and cash flow yield for monthly equity returns of Tokyo stock exchange for the period of 1971 to 1988. This study has employed Seemingly Unrelated Regression (SUR) model and Fama and MacBeth (1973) methodology. This study finds BTM and cash flow yield are significantly positively related to expected average returns.

Daniel and Titman (1997) contradict the findings of Fama and French (1992, 1993, 1996) by using data from 1973 to 1993. This study reports that average equity returns are not function of loading factor of Fama and French. Davis, et al. (2000) have extended the Daniel and Titman (1997) work and contradicts to their findings. In this study expected returns and factor loadings are examined after controlling size and BTM. In their study the argument of Daniel and Titman against Fama and French is rejected on the basis of low power of prediction due to short period sample of 20 years. Kothari, Shanken and Sloan (1995) argue that betas are estimated for short intervals and are biased due to using monthly returns rather than using annual returns for trading frictions and nonsynchronous trading. They find a significant relation between beta and cross-sectional returns. Even in late 1920's and early 1930's the period of great economic instability and markets are found inefficient, the smaller firms are more influenced the returns than the larger firm.

Kothari and Shanken (1997) explore the relationship among BTM ratio, dividend yield and US equity market returns by employing Bayesian bootstrap procedure from 1926 to 1991. Results indicate that BTM ratio has a strong relationship for the sample period, but dividend yield and equity returns are found related for the period of 1941 to 1991 only. Chui and Wei (1998) have first time tested the multifactor model for Asian region including Hong Kong, Korea, Malaysia, Taiwan and Thailand from 1977 to 1993. A weaker relationship is found between portfolio returns and market betas, but finds BTM ratio and size significantly explained the stock returns variations. This study has also indicated that BTM ratio has insignificant relationship with stock returns in January.

Gaunt (2004) investigates multifactor model using size and BTM ratio for Australian equity market for the period of 1991 to 2000. Results reveal from this study suggests that size and BTM ratio is significantly related with stock returns. Results of this study are aligned with Fama and French (1993). In addition, this study provides the evidence that BTM ratio has more effect than size. Fan and Liu (2005) examine the relationship of size and BTM to explain the future expected returns of US equity market for the period of 1965 to 1998 by using second pass regression. The study reports that size and the BTM ratio contain distinct and significant components of financial distress, growth options, the momentum effect, liquidity, and firm characteristics.

Peterkort and Nielsen (2005) use BTM ratio as a proxy of risk for the equity market of US by developing similar model to Fama and French (1992) for the period of 1978 to 1995. This study finds inverse relationship between BTM ratio and portfolio returns of the firms with negative book value. Whereas no relationship has reported between BTM ratio with equity returns after controlling size. They suggest that BTM ratio increases due to market leverage and vice versa. Javid and Ahmad (2008) investigate that existence of CAPM with macroeconomic variables in Pakistani equity market for the period of 1993 to 2004. This study suggests that CAPM has no adequate explanatory power for equity returns. Mirza and Shahid (2008) has tested Fama and French model by using size and BTM ratio for 81 companies listed at Pakistani equity market. This study suggests that size and value premium is priced and confirm the presence of Fama and French model validity for Pakistani equity market.

Hassan and Javed (2011) also examine the multifactor model of Fama and French (1992) for the period of 2000 to 2007 by using size and value premium for Pakistani equity market. Both size and BTM ratio are found positively related to equity market returns. This study provides evidence that BTM ratio effect is less for lowest BTM ratio portfolios and higher for high BTM ratio portfolios. Results also provide insight about size factor loading is less for largest size portfolio and high for smallest portfolios returns. This study confirms that CAPM has low predictive power than multifactor model.

The CAPM can be used in several purposes. For example, Portfolio evaluation, Making Financing decisions, Valuation of stocks, Value of Companies, Capital budgeting, CAPM gives the rate to discount expected cash flows, Mergers and acquisition etc. with the passage of time certain issues have been identified, which are not discussed by CAPM. For example, CAPM assumes that asset returns are jointly normally distributed for random variables. But often returns are not normally distributed. The abovementioned discussion has indicated that asset pricing mechanism has a long debate. Only few studies on CAPM and Fama and French three factor model have been conducted in Pakistan. However, information efficiency factor R square is not explored. This study is an effort to explain role of information efficiency in explaining returns in Pakistani market.

3. DATA AND METHODOLOGY

3.1. Data Description

In this study for testing multifactor asset pricing model weekly and monthly closing prices for 152 stocks listed at KSE for the period of 2002 to 2012 are employed with the following criteria:

(1) The sample consists of 152 stocks from non-financial sector.

(2) Stocks included companies that are the part of KSE-100 index over the sample period.

(3) Six-month treasury bill rates are used as a proxy of risk free rate.

(4) Market value index of KSE-100 index is used for market return.

(5) For calculating BTM ratio and size data for book value and number of outstanding shares have been collected from the financial statements of the companies and for market value is taken from different websites.

(6) R square is calculated from 52 weeks' stock returns at the end of June for every year t-1 by using market model.

Accounting data collected from Balance Sheet Analysis published by State Bank of Pakistan, stock prices data obtained from business recorder.

3.2. Methodology

3.2.1. Portfolio Formation

The following criterion is used for portfolio construction.

(1) In order to capture size effect, size sorted portfolios have been constructed. Market capitalisation is calculated by multiplying market price per share with number of outstanding share for individual stock at the end of June for every year t-1 and then stocks are organised small to big. After finding the median that data is divided into two equal portfolios. First portfolio consists of stocks having low market capitalisation called "Small". The other portfolio consists of large market capitalisation called "Big".

(2) In second step BTM ratio is calculated by dividing book price per share with market price per share at the end of June for every year t-1 and then the size sorted portfolios are further divided into two portfolios on the basis of BTM ratio. The first portfolio contains High BTM ratio stocks and the second portfolio contains Low BTM ratio stocks. When "Small" is further subdivided into two portfolios on the basis of BTM ratio, it forms two portfolios namely S/H and S/L. When "Big" is further subdivided into two portfolios on the basis of BTM ratio, it forms two portfolios B/H and B/L.

(3) In third step R square is calculated by using market model for 52 weeks' stock returns at the end of June for every year t-1 and then the BTM ratio sorted portfolios are further divided into two portfolios on the basis of R square. The first portfolio contains High R square stocks and the second portfolio contains Low R square stocks. When "S/H" is further subdivided into two portfolios on the basis of R square, it forms two portfolios namely S/H/HR and S/H/LR. When "S/L" is further subdivided into two portfolios on the basis of R square, it forms two portfolios namely S/L/HR and S/L/LR. When "B/H" is further subdivided into two portfolios on the basis of R square, it forms two portfolios namely B/H/HR and B/H/LR. When "B/L" is further subdivided into two portfolios on the basis of R square, it forms two portfolios namely B/L/HR and B/L/LR.

3.2.2. Variable Construction for Information Premium

To separate the factor premiums from each other, the three factors are construed as follows:

SMB = 1/4 x (S/H/HR - B/H/HR) + (S/H/LR - B/H/LR) +(S/L/HR - B/L/HR) + (S/H/LR - B/H/LR) ... (1)

HML = 1/4 x (S/H/HR - S/L/HR) + (S/H/LR - S/L/LR) +(B/H/HR - B/L/HR) + (B/H/LR - B/L/LR) ... (2)

IEP = 1/4 x (S/H/HR - S/H/LR) + (S/L/HR - S/L/LR) +(B/H/HR - B/H/LR) + (B/L/HR - B/L/LR) ... (3)

MKT = (Rmktt - Rft) ... (4)

Where,

[Rmkt.sub.t] = Ln ([MP.sub.t] / [MP.sub.t-1])

MKT is market premium. [Rmkt.sub.t] is market return for the month "i" and "[MP.sub.t]" and "[MP.sub.t-1]" are the month end values of KSE 100 index for the months of "f and "M". [Rf.sub.t] is 6 months t bill rate used as a proxy of risk free rate.

3.2.3. Model Specification for Information Premium

This study employs a three factor model to capture the role of market premium, BTM ratio and information efficiency premium in determining the equity returns. This methodology is in line with famous three factor model proposed by Fama and French (1993).

The algebraic representation of models is as under.

The first equation is:

.sub.t] - [R.sub.ft] = [alpha] + [[beta].sub.1] (Market premium) + error term ... (5)

[R.sub.t] - [R.sub.ft] = [[alpha].sub.i] + [[beta].sub.1] [MKT.sub.t] + [e.sub.t] ... (6)

Where,

[R.sub.t] = Return of portfolio for period "t"

[R.sub.ft] = Risk Free Rate.

MKT = [Rmkt.sub.t] - [Rfr.sub.t]

The second equation is:

[R.sub.t] - [R.sub.ft] = [alpha] + [[beta].sub.1] (Market premium) + [[beta].sub.2] (Size premium) + [[beta].sub.3] (Value premium) + error term... (7)

[R.sub.t] - [R.sub.ft] = [[alpha].sub.i] + [[beta].sub.1] [MKT.sub.t] + [[beta].sub.2] [SMB.sub.t] + [[beta].sub.3] [HML.sub.t] + [e.sub.t] ... (8)

Where,

[R.sub.t] =Return of portfolio for period "t"

[R.sub.ft] = Risk Free Rate.

MKT = [Rmkt.sub.t] - [Rfr.sub.t]

S MB - [S.sub.Return of small size stocks t] - [B.sub.Return of big size stocks, t]

HML - [H.sub.Return of high BTM ratio stocks, t] - [L.sub.Return of low BTM ratio stocks, t]

The third equation is:

[R.sub.t] - [R.sub.ft] = [alpha] + [[beta].sub.1] (Market premium) + [[beta].sub.2] (Size premium) + [[beta].sub.3] (Value premium) + [[beta].sub.4] (information efficiency premium) + error term ... ... (9)

[R.sub.t] - [R.sub.ft] = [[alpha].sub.i] + [[beta].sub.1] [MKT.sub.t] + [[beta].sub.2] [SMB.sub.t] + [[beta].sub.3] [HML.sub.t] + [[beta].sub.4][IEP.sub.t] + [e.sub.t] ... (10)

Where,

[R.sub.t] = Return of portfolio for period "t"

[R.sub.ft] =Risk Free Rate.

MKT= [Rmkt.sub.t] - [R.sub.ft]

SMB = [S.sub.Return of small size stocks t] - [B.sub.Return of big size stocks, t]

HML = [H.sub.Return of high BTM ratio stocks,t] - [L.sub.Return of low BTM ratio stocks t]

IFP = [H.sub.Return of high R square stocks,t] - [L.sub.Return of low R square stocks t]

The Fourth equation is:

[R.sub.t] - [R.sub.ft] = [[beta].sub.0] + [[lambda].sub.1] Beta of (Market premium) + [[lambda].sub.2] Beta of (Size premium) + [[lambda].sub.3] Beta of (Valuepremium) + error term ... ... ... (11)

[R.sub.t] - [R.sub.ft] = [a.sub.i] + [[lambda].sub.1][[beta].sub.1i][MKT.sub.i] + [[lambda].sub.2] [[beta].sub.2i] [SMB.sub.i] + [[lambda].sub.3] [[beta].sub.3i] [HML.sub.t] + [e.sub.t] ... (12)

Where,

[R.sub.t] =Return of portfolio for period "t"

[R.sub.ft] = Risk Free Rate.

[[beta].sub.1i] MKT = beta of ([Rmkt.sub.t] - [Rf.sub.i])

[[beta].sub.2i]SMB = beta of ([S.sub.Return of small size stocks, t] - [B.sub.Return of big size stocks, t])

[[beta].sub.3i] HML = beta of ([H.sub.Return of high BTM ratio stocks, t] - [L.sub.Return of low BTM ratio stocks, t])

The Fifth equation is:

[R.sub.t] - [R.sub.ft] = [[beta].sub.0] + [[lambda].sub.1]Beta of (Market premium) + [[lambda].sub.2]Beta of (Size premium) + [[lambda].sub.3]Beta of (Value premium) + [[lambda].sub.4]Beta of (information efficiency premium) + error term ... (13)

[R.sub.t] - [R.sub.fi] = [a.sub.i] + [[lambda].sub.1] [[beta].sub.1i] [MKT.sub.i] + [[lambda].sub.2] [[beta].sub.2i] [SMB.sub.i] + [[lambda].sub.3] [[beta].sub.3i] [HML.sub.i] + [[lambda].sub.2][[beta].sub.2i] [IEP.sub.i] + [e.sub.t] (14)

Where,

[R.sub.t] = Return of portfolio for period "t"

[R.sub.ft] = Risk Free Rate.

[[beta].sub.1i] MKT = beta of [Rmkt.sub.t] - [Rf.sub.i]

[[beta].sub.2i] SMB = beta of ([S.sub.Return of small size stocks, t] - [B.sub.Return of big size stocks, t])

[[beta].sub.3i] HML = beta of ([H.sub.Return of high BTM ratio stocks, t] - [L.sub.Return of low BTM ratio stocks, t])

[[beta].sub.4i] IEP = beta of ([HR.sub.Retun of high R square stocks, t] - [LR.sub.Return of low R square stocks, t])

4. RESULTS AND DISCUSSION

This Section reports the results of single factor CAPM based on market premium, three factor model based on market premium, size premium and value premium and four factor model based on market premium, size premium, value premium and information efficiency premium for sample period from 2002 to 2012. Descriptive statistics are presented in Table 1 for monthly returns of portfolios constructed on the basis of size, BTM ratio and R square for 152 stocks for the period of 2002 to 2012.

Results presented in Table 1 indicates that small stocks portfolio provides high return at high risk level as compare to big stocks portfolio (B) provides low return at low risk level that are aligned with the empirical work on size effect [Banz (1981)]. It is also found that BTM ratio results are also in line with the results of Stattman (1980) that stock with small size and high BTM ratio (S/H) earn higher return than stocks with small size and low BTM ratio (S/L). That confirms the hypothesis of value stocks have more returns than growth stocks. After sorting on the basis of BTM ratio, portfolios are further divided on the basis of R square. Results shows that returns of low R square stocks from big size and high BTM ratio (B/H/LR) and returns of low R square stocks from big size and low BTM ratio (B/L/LR) have more returns that those stocks having high R square from big size and high BTM ratio (B/H/HR) and having high R square from big size and low BTM ratio (B/L/HR) Thus low R square stocks are risker stocks and should have to provide more return than these stocks having high R square stock. Reasons of this behaviour might be the ups and down of the KSE during this period. The one declaration of KSE as the most liquid and biggest stock exchange in the world during 2002 and index reached at the ever highest point in 2007 as well as in this period market was crashed in 2008.

Whereas, some portfolios results are contrary, for example (B/H) stocks are riskier and providing less returns and (B/L) are less risky providing high return. Along with these results, returns of small size portfolios that are further sub divided portfolios on the basis of R square are not evident of West (1988) hypothesis. It is observed that small size, high BTM ratio and low R square (S/H/LR) stocks and stocks with small size, low BTM ratio and low R square (S/L/LR) have less returns that those stocks having high R square from small size, high BTM ratio and high R square (S/H/HR) and stocks with small size, low BTM ratio and high R square (S/L/HR).

First pass regression results of CAPM, three factor Fama and French (1992) and four factor model for low R square sorted portfolios from 2002 to 2012 are presented in Table 2.

Table 2 reports the results of single factor CAPM based on market premium, three factor model based on market premium, size premium and value premium and four factor model based on market premium, size premium, value premium and information efficiency premium for low R square portfolios. Results indicate that market premium and size premium is significant and positive for single factor, three factor and four factor model. It is also found that value premium is significant and positive for portfolio with high BTM ratio and significant and negative for portfolio with low BTM ratio. It shows that high BTM ratio stocks earn more return than low BTM ratio stocks.

Whereas, information efficiency premium is found significant and negative for low R square stocks. Results suggest that prevision of public and private information is an increasing function and it is negatively associated with the equity return. These results are consistent with Lambert, et al. (2012). Therefore, SMB, HML and IEP factor cannot be ignored for low R square stocks. The explanatory power of four factor model based on information efficiency premium is higher than single factor model CAPM and three factor Fama and French (1992) model. However, CAPM results shows that market premium is significant and positively related to all portfolios returns and the intercept is found insignificant. It is also observed that CAPM is a valid model for explaining the results of low R square stocks. CAPM does not capture precise information regarding firm specific factors so, its explanatory power is lower which is in line with low SPS. The missing information can be captured by using premium associated with difference of SPS.

First pass regression results of CAPM, three factor Fama and French (1992) and four factor model for high R square sorted portfolios from 2002 to 2012 presented in Table 3.

Table 3 reports the results of single factor CAPM, three factor model and four factor model for high R square portfolios. Results indicate that market premium, size premium and information efficiency premium is significant and positive for in single factor, three factor and four factor model. It is also found that value premium is significant and positive for portfolio having high BTM ratio and significant and negative for portfolio having low BTM ratio. The behaviour of value premium and stock returns is same for low R square portfolios and results of Table 2 and Table 3 are consistent. It shows that high BTM ratio stocks earn more return than low BTM ratio stocks. Size and value premium results are in line with the previous study of Hassan and Javed (2011). Therefore, SMB, HML and IEP factor cannot be ignored for low R square stocks also.

The explanatory power of four factor model based on information efficiency premium is higher than single factor model CAPM and three factor Fama and French (1992) model. However, CAPM results shows that market premium is significant and positively related to all portfolios returns and the intercept is found insignificant. It is also observed that CAPM is still a valid model for explaining the results of low R square stocks. Overall results of first pass regression indicate that traditional CAPM is a valid model for Pakistani equity market. It is also found that size premium, value premium and information efficiency premium have significant effect on overall portfolios. It is evident that three factor and four factor model raise adjusted R square which explains the model better than the single factor CAPM based on market premium. Therefore, it can be concluded that size, value premium and information efficiency premium exists in Pakistani equity market and investor should consider these three factors while devising their investment strategies.

Second pass Fama and Macbeth (1973) regression results of three factor and four factor model for overall portfolio from 2002 to 2012 presented in Table 4.

Table 4 presents the results of cross-sectional Fama and Macbeth (1973) second pass regression. Average portfolio returns are regressed on factor loading estimated for first pass regression (market premium, size premium, value premium and information efficiency premium). Results of three factor and four factor model indicate that market beta and HML beta can explain portfolio returns. Whereas, factor loadings with SMB beta and IEP beta are insignificant indicating that these are not priced during the sample period.

4.2. Discussion

Table 2 and Table 3 report the results of single factor CAPM based on market premium, three factor model based on market premium, size premium and value premium and four factor model market premium, size premium, value premium and information efficiency for high R square and low R square portfolios. Results indicate that market premium, size premium and information efficiency is significant and positive for in single factor, three factor and four factor model. It is also found that value premium is significant and positive for portfolio having high BTM ratio and significant and negative for portfolio having low BTM ratio. It shows that high BTM ratio stocks earn more return than low BTM ratio stocks.

Value premium results are in line with Stattman (1980), Rosenberg, et al. (1985), Fama and French (1993) and Hassan and Javed (2011) that value premium is significant and positive for high BTM ratio portfolios. Whereas, value premium is found significant and negative for low BTM ratio. Peterkort and Nielsen (2005) report that BTM ratio has inverse relationship with stock returns and portfolio returns of the firms with negative book value. Roll (1988) argues that stock prices capture firm as well as market information to drive the stocks in same or opposite direction.

Results of low SPS stocks are consistent with Lambert, et al. (2012), who suggest that prevision of public and private information is an increasing function and it is negatively associated with the cost of equity. High quality disclosure has more precision of information in stock prices and decease cost of equity [Francis, et al. (2005)]. Farooq and Ahmed (2015) argue that SPS is an increasing function of governance environment of a firm and better governance mechanism reveal higher SPS. Findings of high SPS stocks are in line with this argument. Therefore, information premium is present in the market.

The empirical results also documented that Fama and Macbeth (1973) second pass regression found that past betas can explain current returns. It is evident that three factor and four factor model raise adjusted R square which explains the model better than the single factor CAPM based on market premium. Therefore, it can be concluded that information efficiency and value premium exists in and emerging market and investor should consider these two factors while devising their investment strategies.

5. CONCLUSION

This study examine the relationship between beta and stock returns by using CAPM and multifactor models based on value premium and information efficiency premium in Pakistani equity market for the period of 2002 to 2012. This study employs Fama and Machbeth (1973) second pass regression methodology used in famous studies of Fama and French (1992, 1993). This is the first study that investigates the relationship of information efficiency premium by using R square. Small capitalisation stocks earn high return than large capitalisation stocks and high BTM ratio earn higher return than those stocks having low BTM ratio. Further results of R square sorted portfolios show that returns of low R square have more returns that those stocks having high R square.

West (1988) argue that stocks with low market model R square have small size, low analyst coverage, age, institutional holding higher transaction cost and more volatile. Results of single factor CAPM based on market premium, three factor model based on market premium, size premium and value premium and four factor model based on market premium, size premium, value premium and information efficiency premium indicate that MKT, SMB, HML and IEP factor is priced in Pakistani equity market. Regression results indicate that market premium; size premium and information efficiency is significant for single factor, three factor and four factor model. CAPM results shows that market premium is significant and positively related to all portfolios returns and the intercept is found insignificant. Three factor model and four factor model results shows that size premium is significant and positively related to all portfolios returns. It is also found that value premium is significant and positive for portfolio having high BTM ratio and significant and negative for portfolio having low BTM ratio.

The explanatory power of four factor model based on information efficiency premium is higher than single factor model CAPM and three factor Fama and French (1992) model. Size and value premium results are in line with the previous study of Hassan and Javed (2011). Therefore, SMB, HML and IEP factor cannot be ignored for low R square stocks also. Whereas, information efficiency premium is found significant and negative for low R square stocks. Results of low SPS stocks are consistent with Lambert, et al. (2012), who suggest that prevision of public and private information is an increasing function and it is negatively associated with the cost of equity. Farooq and Ahmed (2014) argue that SPS is an increasing function of governance environment of a firm and better governance mechanism reveal higher SPS. Findings of high SPS stocks are in line with this argument. Therefore, information premium is present in the market.

Overall result of first pass regression shows that traditional CAPM is a valid model for Pakistani equity market. However, as discussed above, it does not capture prescribed information regarding firm specific factors and its explanatory power is lower. So the remaining information can be captured by using premium associated with difference of SPS. The empirical results also documented that Fama and Macbeth (1973) second pass regression report that past betas can explain current returns. It is evident that three factor and four factor model raise adjusted R square which explains the model better than the single factor CAPM based on market premium.

Ahmad Fraz <aahmadfraz@gmail.com> is Assistant Professor, Capital University of Science and Technology, Islamabad. Arshad Hassan <aarshad.hasan@gmail.com> is Associate Professor, Capital University of Science and Technology, Islamabad.

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Table 1
Descriptive Statistics of Monthly Returns of
Stylised Portfolios 2002 to 2012

Portfolio   Mean    Standard    Kurtosis
                    Deviation

P           0.005     0.063      0.299
S           0.006     0.072      0.309
B           0.004     0.067      0.868
S/H         0.011     0.073      0.183
S/L         0.001     0.076      0.480
B/H         0.003     0.074      1.034
B/L         0.005     0.063      0.920
S/H/HR      0.015     0.084      0.817
S/H/LR      0.006     0.074      0.797
S/L/HR      0.002     0.083      0.624
S/L/LR      0.001     0.082      0.828
B/H/HR      0.002     0.093      2.587
B/H/LR      0.004     0.064      0.048
B/L/HR      0.005     0.084      3.531
B/L/LR      0.006     0.058      0.882
Rm-Rf       0.010     0.087      6.228
SMB         0.002     0.049      2.197
HML         0.004     0.027      -0.107
IEP         0.002     0.045      7.027

Portfolio   Skewness   Minimum   Maximum

P            -0.286    -0.189     0.151
S            0.116     -0.183     0.187
B            -0.449    -0.226     0.193
S/H          0.034     -0.184     0.196
S/L          0.180     -0.226     0.210
B/H          -0.431    -0.270     0.211
B/L          -0.415    -0.220     0.175
S/H/HR       0.046     -0.237     0.239
S/H/LR       -0.138    -0.266     0.203
S/L/HR       0.066     -0.213     0.242
S/L/LR       0.003     -0.245     0.232
B/H/HR       -0.318    -0.384     0.318
B/H/LR       -0.341    -0.186     0.153
B/L/HR       -0.650    -0.384     0.293
B/L/LR       -0.365    -0.186     0.184
Rm-Rf        -1.249    -0.460     0.236
SMB          -0.441    -0.214     0.120
HML          0.204     -0.052     0.078
IEP          0.663     -0.186     0.233

Note: P is the portfolio consists of all 152 stocks;
S portfolio consists of those stocks having low market
capitalisation; B portfolio consists of those stocks having
large market capitalisation; S/H portfolio consists of those
small stocks having high BTM ratio; S/L portfolio consists
of those small stocks having low BTM ratio; B/H portfolio
consists of those big stocks having high BTM ratio; B/L
portfolio consists of those big stocks having low BTM ratio;
S/H/HR portfolio consists of those small stocks having high
BTM ratio and high R square and S/H/LR portfolio consists of
those small stocks having high BTM ratio and low R square;
S/L/HR portfolio consists of those small stocks having low
BTM ratio and high R square and S/L/LR portfolio consists of
those small stocks having low BTM ratio and low R square;
B/H/HR portfolio consists of those big stocks having high
BTM ratio and high R square; B/H/LR portfolio consists of
those big stocks having high BTM ratio and low R square;
B/L/HR portfolio consists of those big stocks having low
BTM ratio; high R square and B/L/LR portfolio consists of
those big stocks having low BTM ratio and low R square;
HML, high minus low; IEP, High R Square minus Low R square
and Rm-Rf, return to the market portfolio minus risk-free
rate..

Table 2
Regression Analysis of Low R-square Portfolio from 2002 to 2012

[R.sub.it]-[R.sub.ft] = [alpha] + [[beta].sub.1][MKT.sub.t] +
[[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] +
[[beta].sub.4][IEP.sub.t] + [e.sub.t]

                 S/H/     S/H/     S/H/     S/L/
                  LR       LR       LR       LR

a                0.003   -0.005   -0.005   -0.002
T value          0.458   -1.384   -1.766   -0.364
[[beta].sub.1]   0.368   0.592    0.761    0.339
T value          5.474   13.638   16.279   4.381
[[beta].sub.2]           1.097    0.938
T value                  14.471   13.181
[[beta].sub.3]           0.804    0.835
T value                  6.192    7.315
[[beta].sub.4]                    -0.601
T value                           -6.252
Adj. R 2         0.18     0.72     0.78     0.12
F stat           29.97   110.63   117.43   19.19
F sig            0.00     0.00     0.00     0.00

[R.sub.it]-[R.sub.ft] = [alpha] + [[beta].sub.1][MKT.sub.t] +
[[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] +
[[beta].sub.4][IEP.sub.t] + [e.sub.t]

                  S/L/     S/L/     B/H/     B/H/
                   LR       LR       LR       LR

A                -0.006   -0.007   -0.001   -0.004
T value          -1.851   -2.034   -0.207   -0.961
[[beta].sub.1]   0.683    0.783    0.514    0.561
T value          16.243   15.801   10.968   11.715
[[beta].sub.2]   1.421    1.328             0.272
T value          19.350   17.614            3.252
[[beta].sub.3]   -0.627   -0.609            0.480
T value          -4.983   -5.040            3.353
[[beta].sub.4]            -0.353
T value                   -3.473
Adj. R 2          0.78     0.80     0.48     0.55
F stat           159.90   133.30   120.30   53.33
F sig             0.00     0.00     0.00     0.00

[R.sub.it]-[R.sub.ft] = [alpha] + [[beta].sub.1][MKT.sub.t] +
[[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] +
[[beta].sub.4][IEP.sub.t] + [e.sub.t]

                  B/H/     B/U     B/L/     B/L/
                   LR      LR       LR       LR

a                -0.004   0.001   0.001    0.001
T value          -1.058   0.268   0.326    0.244
[[beta].sub.1]   0.645    0.437   0.481    0.581
T value          11.212   9.920   10.182   10.327
[[beta].sub.2]   0.193            0.161    0.068
T value          2.200            1.955    0.800
[[beta].sub.3]   0.495            -0.253   -0.235
T value          3.529            -1.791   -1.716
[[beta].sub.4]   -0.300                    -0.353
T value          -2.537                    -3.051
Adj. R 2          0.56    0.43     0.45     0.48
F stat           43.30    98.41   36.46    31.45
F sig             0.00    0.00     0.00     0.00

Mole: S/H/LR portfolio consists of those small stocks having
high BTM ratio and low R square; S/L/LR portfolio consists of
those small stocks having low BTM ratio and low R square; B/H/LR
portfolio consists of those big stocks having high BTM ratio and
low R square; B/L/LR portfolio consists of those big stocks having
low BTM ratio and low R square; a, a-coefficient; [[beta].sub.1],
[[beta].sub.1]-coefiicient; [[beta].sub.2], [[beta].sub.2]-
coefficient; [[beta].sub.3], [[beta].sub.3]-coefficient;
[[beta].sub.4], [[beta].sub.4]-coefficient Adj. [R.sup.2],
Adjusted R square; F stat., F statistics ; F sig.,
F significance.

Table 3
Regression Analysis of High R square
Portfolio from 2002 to 2012

[R.sub.it]-[R.sub.ft] = [alpha] + [[beta].sub.1][MKT.sub.t] +
[[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] +
[[beta].sub.4][IEP.sub.t] + [e.sub.t]

                 S/H/     S/H/     S/W      S/L/
                  HR       HR       HR       HR

a                0.009   0.002    0.003    -0.004
T value          1.548   0.533    0.837    -0.801
[[beta].sub.1]   0.564   0.775    0.558    0.620
T value          8.132   15.162   10.413   9.637
[[beta].sub.2]           1.036    1.239
T value                  11.603   15.201
[[beta].sub.3]           0.775    0.735
T value                  5.059    5.625
[[beta].sub.4]                    0.770
T value                           6.995
Adj. R 2         0.33     0.70     0.78     0.41
F stat           66 13   101.62   116.98   92.88
F sig            0.00     0.00     0.00     0.00

[R.sub.it]-[R.sub.ft] = [alpha] + [[beta].sub.1][MKT.sub.t] +
[[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] +
[[beta].sub.4][IEP.sub.t] + [e.sub.t]

                  S/L/     S/L/     B/H/     B/H/
                   HR       HR       HR       HR

a                -0.007   -0.006   -0.007   -0.009
T value          -1.518   -1.492   -2.098   -2.626
[[beta].sub.1]   0.832    0.668    0.964    0.954
T value          15.414   10.839   23.495   28.024
[[beta].sub.2]   0.870    1.022             0.019
T value          9.227    10.889            0.245
[[beta].sub.3]   -0,446   -0.475            0.447
T value          -2.760   -3,159            3.447
[[beta].sub.4]            0.578
T value                   4.562
Adj. R 2          0.65     0.70     0.81     0.82
F stat           83.83    77.80    552.01   202.02
F sig             0.00     0.00     0.00     0.00

[R.sub.it]-[R.sub.ft] = [alpha] + [[beta].sub.1][MKT.sub.t] +
[[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] +
[[beta].sub.4][IEP.sub.t] + [e.sub.t]

                  B/H/     B/L/     B/L/     B/L/
                   HR       HR       HR       HR

a                -0.009   -0.005   -0.004   -0.003
T value          -2.727   -1.519   -1.267   -1.251
[[beta].sub.1]   0.806    0.887    0.886    0.738
T value          16.661   25 480   23.265   17.931
[[beta].sub.2]   0.157             -0.028   0.109
T value          2.130             -0.427   1.741
[[beta].sub.3]   0.420             -0.168   -0.195
T value          3.562             -1.473   -1.936
[[beta].sub.4]   0.524                      0.522
T value          5.280                      6.169
Adj. R 2          0.85     0.83     0.83     0.87
F stat           190.30   649.23   217.75   220.10
F sig             0.00     0.00     0.00     0.00

Note: S/H/HR portfolio consists of those small
stocks having high BTM ratio and high R square; S/L/HR
portfolio consists of those small stocks having low BTM
ratio and high R square; a, a-coefficient; [[beta].sub.1],
[[beta].sub.1]-coefficient; [[beta].sub.2], [[beta].sub.2]-
coefficient; [[beta].sub.3], [[beta].sub.3]- coefficient;
[[beta].sub.4], [[beta].sub.4]-coefficient Adj. [R.sup.2],
Adjusted R square; F stat., F statistics; F sig.,
F significance.

Table 4
Regression Analysis ofpast Betas on
all portfolios from 2002 to 2012

[R.sub.it] - [R.sub.ft] = [alpha] + [[lambda].sub.1]
[[beta].sub.1i][MKT.sub.i] + [[lambda].sub.2][[beta].sub.2i]
[SMB.sub.ii] + [[lambda].sub.3][[beta].sub.3i][HML.sub.i] +
[[lambda].sub.4][[beta].sub.4i][IEP.sub.i] + [e.sub.i]

                a     [[lambda].sub.1]   [[lambda].sub.2]

Coefficient   0.022        -0.028             0.002
T value       2.976        -2.600             1.163
coefficient   0.021        -0.026             0.002
T value       2.686        -2.349             1.094

[R.sub.it] - [R.sub.ft] = [alpha] + [[lambda].sub.1]
[[beta].sub.1i][MKT.sub.i] + [[lambda].sub.2][[beta].sub.2i]
[SMB.sub.ii] + [[lambda].sub.3][[beta].sub.3i][HML.sub.i] +
[[lambda].sub.4][[beta].sub.4i][IEP.sub.i] + [e.sub.i]

              [[lambda].sub.3]   [[lambda].sub.4]   Adj.R 2   F stat

Coefficient        0.004                             0.652    5.367
T value            2.537
coefficient        0.005              0.002          0.626    3.932
T value            2.477              0.853

Note: a, a-coefficient; [[lambda].sub.1],
[[lambda].sub.1]-coefficient; [[lambda].sub.2],
[[lambda].sub.2]-coefficient; [[lambda].sub.3],
[[lambda].sub.3]-coefficient; [[lambda].sub.4],
[[lambda].sub.4]-coefficient Adj. [R.sup.2], Adjusted
R square; F stat., F statistics ; F sig., F significance.