This chapter aims at reexamining the literature on the undermentioned issues. First, the theory underlying the efficient market hypothesis will be reviewed with an accent on the random walk theoretical account. Secondly, some surveies analyzing the weak signifier efficiency of markets around the universe will be reviewed and in conclusion researches made on the presence of twenty-four hours of the hebdomad consequence and month of the twelvemonth anomalousness will be discussed.

The EMH attempts to explicate why stock market monetary values appear to follow a random walk i.e. ; that their day-to-day fluctuation is a random value following the Gaussian distribution. The history of the efficient market hypothesis started with Bachelier ( 1900 ) who laid the theoretical basis for the efficient market hypothesis, which was postulated half a century subsequently by Maurice Kendall. Kendall ( 1953 ) found that stock monetary values evolved indiscriminately and that his informations offered no manner to foretell future monetary value motions. The account for this phenomenon, the efficient market hypothesis, ab initio seemed counterintuitive to the academic community. However, after the first daze had passed, bookmans rapidly embraced the theory and began to document its cogency in real-world markets by analyzing empirical informations. To make so, they developed different models to pattern the features of market monetary values. The first type of model – based on expected return efficient markets – includes such well-known theoretical accounts as the just game theoretical account, the random walk and the submartingale theoretical accounts, every bit good as the market theoretical account and the celebrated capital plus pricing theoretical account ( CAPM ) of Sharpe ( 1964 ) ; Lintner ( 1965 ) ; Mossin ( 1996 ) .

## 3.1.1 Random-walk theoretical account

Harmonizing to Fama ( 1970 ) an efficient market is a market in which monetary values reflect all available information. In the stock market, the intrinsic value of a portion is equivalently measured by the hereafter discounted value of hard currency flows that will accrue to investors. If the stock market is efficient, portion monetary values must reflect all available information which is relevant for the rating of a company ‘s future public presentation, and hence the market monetary value of portion must be equal to its intrinsic value. Any new information, which is expected to alter a company ‘s future profitableness, must be instantly reflected in the portion monetary value because any hold in the diffusion of information to monetary value would ensue in unreason, as some subsets of available information could be exploited to calculate future profitableness. Therefore, in an efficient market, monetary value alterations must be a response merely to new information. Since information arrives indiscriminately, portion monetary values must besides fluctuate erratically. The Random Walk theoretical account can be stated in the undermentioned equation:

Where

Pt+1: monetary value of portion at clip t+1 ;

Platinum: monetary value of portion at clip T ;

i??t+1: random mistake with nothing mean and finite discrepancy.

The above equation indicates that the monetary value of a portion at clip t+1 is equal to the monetary value of a portion at clip t plus given value that depends on the new information ( unpredictable ) geting between clip T and t+1. In other word, the alteration of monetary value, i??t+1 = Pt+1- Pt, is independent of past monetary value alterations.

Fama ( 1970 ) argued that the random walk theoretical account is an extension of the expected return or just game theoretical account. Specifically, the just game theoretical account merely indicates that the conditions of market equilibrium can be stated in footings of expected returns while the random walk theoretical account gives the inside informations of the stochastic procedure bring forthing returns. Therefore, he concluded that empirical trials of the random walk theoretical account are more powerful in support of the EMH than trials of the just game theoretical account.

## 3.2 Empirical on EMH

In the old ages from the 1950s to the 1970s, most surveies found grounds consistent with the efficient market hypothesis. Despite some grounds undertakings the contrary, by the early 1970s markets had hence mostly come to be considered to be efficient in the semi strong signifier, as defined by Fama ( 1970 ) .

However, in order to reason that a market is semi strong efficient, it is critical that the market is first and first weak-form efficient. As mentioned earlier, a market is efficient in the weak signifier if stock monetary values follow a random walk procedure. Therefore, trials of weak signifier efficiency are of course based on an scrutiny of the interrelatedness between current and past stock monetary values ( Fawson et al. , 1996 ) .

## 3.2.1 Testing for weak signifier efficiency

In finance literature, surveies proving for weak-form market efficiency should trust entirely on past trading informations. Most research workers formulate a trading regulation based on yesteryear monetary values which they test to see whether extra market returns are obtained. Practically, several statistical techniques, such as tallies test, unit root trial, consecutive correlativity trials, and spectral analysis, have been normally used for proving weak signifier efficiency.

## 3.2.1.1 Weak-form Efficient Markets

Kim and Shamsuddin ( 2008 ) examined whether a group of Asiatic stock market returns ( Hong Kong, Indonesia, Japan, Korea, Malaysia, Philippines, Taiwan, Thailand and Singapore ) follow the random walk theoretical account. In their survey, new multiple discrepancy ratio trials based on the wild bootstrap and marks were adopted. They used both day-to-day and hebdomadal monetary value indices from 1990 to 2005.

It was found that the developed markets like Hong Kong, Japanese, Korean and Chinese markets show weak signifier efficiency. While the emerging markets of Indonesia, Malaysia and Philippines have shown no mark of market efficiency. They have besides found grounds that the Singaporean and Thai markets have become efficient after the Asiatic crisis in 1997.

Using both the multiple variance-ratio and the auto-regressive fractionally incorporate moving-average trials, Ojah and karemera ( 1999 ) documented grounds demoing that equity monetary values in major Latin American emerging equity markets-Argentina, Brazil, Chile and Mexico- follow a random walk. Hence they are by and large weak-form efficient.

A survey undertaken by Khazali et Al ( 2008 ) tried to happen grounds of the weak-form efficient market hypothesis in several emerging markets in the Middle-East and North Africa. Using the new Wright ( 2000 ) variance-ratio every bit good as the classical VR trial and the tallies trial, they revisited the empirical cogency of the random walk hypothesis in eight emerging markets in the Middle East and North Africa ( MENA ) viz. Bahrain, Egypt, Jordan, Kuwait, Morocco, Oman, Saudi Arabia, and Tunisia. All the three proving methods used gave consistent consequence that the equity markets follow the random-walk theoretical account.

## 3.2.1.2 Weak-form inefficient markets

There are other cases where the markets for both developed and rising states are found to be inefficient. The market does non react to new information outright and this may happen due to a hold in airing to new monetary value sensitive information or prejudices ( under or over reaction ) in the response of market participants to such information. This implies stock markets are non weak signifier efficient therefore extra net incomes can be earned by working trading chances.

For case, the weak-form market efficiency of Latin American equity markets was studied by Worthington and Higgs ( 2008 ) . It constituted of seven emerging markets viz. Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela. The day-to-day returns for these states were examined for random walk utilizing the consecutive correlativity coefficient and runs trials, Augmented Dickey-Fuller ( ADF ) , Phillips-Perron ( PP ) and Kwiatkowski, Phillips, Schmidt and Shin ( KPSS ) unit root trials and multiple discrepancy ratio ( MVR ) trials.

The consequences from the three different processs employed concluded that none of these markets are observed to follow the random walk theoretical account and hence are non weak-form efficient.

The emerging market of Bangladesh that is the Dhaka Stock Exchange ( DSE ) was examined by Mobarek et Al ( 2008 ) to happen grounds on whether the return series follow the random walk theoretical account. The day-to-day monetary value index over the period 1988 to 2000 was used as sample.

The writer concluded that the consequences from both trial implemented, the non-parametric ( Kolmogrov-Smirnov: normalcy trial and run trial ) and parametric trial ( Auto-correlation trial, Autoregressive theoretical account, ARIMA theoretical account ) provided grounds that the security returns do non follow the random walk theoretical account.

Another survey was conducted by Kashif Hamid et Al. ( 2010 ) to prove the weak-form market efficiency in the Asian Pacific part. The sample consisted of 14 equity markets from that part viz. Pakistan, India, Sri Lanka, China, Korea, Hong Kong, Indonesia, Malaysia, Philippine, Singapore, Thailand, Taiwan, Japan and Australia. They used monthly observations for the period January 2004 to December 2009. In order to prove the hypothesis that the stock market follow the random walk theoretical account, the autocorrelation, Ljung-Box Q-statistic Test, Runs Test, Unit Root Test and the Variance Ratio trials were applied.

They concluded that the monthly monetary values are non weak signifier efficient in all the states of the Asian-Pacific part. Therefore, investors can gain arbitrage net income due to the fact that all the markets are inefficient.

## 3.3 Return Seasonality

Return seasonality are characterized by forms in stock returns. Seasonality has been found in intraday, hebdomadally, monthly and one-year return informations. It was claimed by Fama ( 1991 ) that this may be caused by seasonal in the chances that measured whether monetary values are at ask or command, due to seasonal in investors ‘ trading forms.

## 3.3.1 Testing Day of the hebdomad consequence

Several surveies were carried out in order to prove for the presence of the twenty-four hours of the hebdomad anomalousness in stock returns. Some surveies discovered that stock returns are random while others obtained important presence of the market anomalousness on some specific yearss of the hebdomad.

## 3.3.1.1 Evidence of market efficiency

Aly and Perry ( 2004 ) investigated the Egyptian stock market utilizing the Capital Market Authority Index ( CMA ) , in order to prove for day-to-day stock anomalousness in an emerging capital market where trading takes topographic point on a four-day hebdomad footing reverse to the traditional five-day hebdomad. The day-to-day returns for the CMA Index from 1998-2001 was used. The undermentioned arrested development equation was estimated by utilizing the ordinary least square ( OLS ) theoretical account:

Where Rt is the day-to-day return, D1 through D4 are dummy variables such that if t is a Monday, so D1=1 or otherwise 0 for all other yearss ; Iµt is a random term and I?1-I?4 are coefficients to be estimated utilizing ordinary least squares ( OLS ) . If the Monday consequence exists in the Egyptian stock market, the estimated coefficient I?1 is expected to be negative and statistically important and the returns on Monday should besides be significantly less than returns during the remainder of the hebdomad.

The consequences showed that the Egyptian stock market return on Monday are positive and important on mean nevertheless it was non significantly different from the returns of the other trading yearss. Therefore, bespeaking that the stock market is weak-form efficient.

In the same spirit, Suliman Zakaria Suliman Abdalla ( 2012 ) studied the day-to-day stock anomalousness on the Khartoum stock exchange ( KSE ) from Sudan. They examined this anomalousness on both the stock market returns and the conditional volatility over the period of 2nd January 2006 to 30th October 2011 utilizing day-to-day observations.

Three different theoretical accounts have been used to prove for possible being of twenty-four hours of the hebdomad viz. the Ordinary Lease Squares ( OLS ) and two different Generalized Autoregressive Conditional Heteroscedastic ( GARCH ) theoretical account.

A silent person variable attack based on a additive arrested development with 5 silent person variables was employed in the first theoretical account. The writer included lagged values of the return variable to extinguish the possibility of holding car correlative mistakes. Hence the first theoretical account is illustrated as follows:

The 2nd theoretical account is the GARCH ( 1,1 ) . This was used to turn to the possibility of holding heteroscedasticity job. This is as follows:

The Generalized Autoregressive Conditional Heteroscedasticity in Mean ( GARCH-M ) was used as the 3rd theoretical account, which include some exogenic variable in the discrepancy equation in order to take into consideration incorporate volatility consequence every bit good as hazard premium. The equation is in the undermentioned signifier:

: The discrepancy of the error term ;

: Last period ‘s volatility ( the ARCH term ) ;

: Last period ‘s discrepancy ( the GARCH term ) ;

and i?¬ is called the hazard premium parametric quantity.

The empirical findings from the OLS and GARCH theoretical accounts indicated the absence of the twenty-four hours of the hebdomad consequence in both returns and volatility equations for the Khartoum stock exchange. Thus, during that period of survey the Khartoum stock exchange was non affected by the twenty-four hours of the hebdomad consequence.

Another survey was conducted by Kenourgios and Samitas ( 2008 ) in the Athens Stock Exchange ( ASE ) General Index. Daily stock returns over a period of 10 old ages were used. The sample was divided into two subperiods: 1995-2000 and 2001-2004. In the first bomber periods three major indices was besides considered viz. banking, insurance and assorted piece for the 2nd period FTSE-20 and FTSE-40 was examined. The writers tested for possible being of twenty-four hours of the hebdomad utilizing the GARCH ( 1,1 ) and Modified-GARCH ( 1,1 ) theoretical account.

The findings indicated the presence of such anomalousness over the period 1995-2000. However, due to the Grecian entry to the Euro-Zone and the market has developed into an upgraded one ; this stock market anomalousness seemed to lose its strength over the period 1995-2000 in the ASE.

## 3.3.1.2 Evidence of market inefficiency

Faryad, Kashif and Rana ( 2011 ) focused on the twenty-four hours of the hebdomad consequence on the equity market in Pakistan. This research consists of day-to-day stock monetary values of the KSE-100 Index, for the period January 2006 to December 2010. The Ordinary Least Square ( OLS ) theoretical account was used and the undermentioned arrested development equation was estimated:

Where Rt is the day-to-day returns and Mt, Tt, Wt, THt and Ft are dummy variables for Monday, Tuesday, Wednesday, Thursday, and Friday severally. If it is a Monday, than M=1 and “ 0 ” for all other yearss and so forth I is a random term. B1-B5 are co-efficient to be estimated utilizing OLS.

The consequence obtained suggested that the Tuesday returns are quite important and positive. The Tuesday return on norm are greater compared to the other yearss of the hebdomad. Hence, it can be concluded that there exists twenty-four hours of the hebdomad consequence in the stock market of Pakistan.

Similarly, the Kuwait stock exchange index was studied by Al-Loughani and Chappel ( 2001 ) for grounds of a day-of-the-week consequence. The day-to-day stock return for the period 1993 to 1997 was investigated. A nonlinear GARCH ( 1,1 ) was employed to prove day-of-the-week anomalousness.

The findings obtained significantly showed that the returns on the five different trading yearss were non similar. Hence, it can be concluded that the Kuwait stock market face the twenty-four hours of the hebdomad consequence.

Choudhry ( 2000 ) on the other manus examined the twenty-four hours of the hebdomad consequence on seven emerging Asiatic stock markets returns viz. . Daily stock monetary values of from India, Indonesia, Malaysia, Philippines, South Korea, Taiwan, and Thailand was used from January 1990 to June 1995. The research was done utilizing the GARCH theoretical account. Empirical consequences obtained indicate that both the mean and conditional discrepancy ( volatility ) of stock return showed important presence of the twenty-four hours of the hebdomad consequence.

## 3.4 Testing month-of-the twelvemonth consequence

In several research documents, grounds was found of statistically important differences in stock returns during peculiar months of the twelvemonth. The ‘January consequence ‘ is the most researched anomalousness but in the recent old ages the month of the twelvemonth consequence could be found in the other months as good.

## 3.4.1 Evidence of efficiency

Al-Jarrah, Khamees and Qteishat ( 2011 ) investigated the presence of the month of the twelvemonth consequence on the Amman stock exchange ( ASE ) . The day-to-day stock return for a sample period from 1992 to 2007 was examined. They employed the methodological analysiss followed by by Jaffe and Westerfield ( 1989 ) , Boudreaux ( 1995 ) , Compton et Al. ( 2006 ) and Floros ( 2008 ) by utilizing the undermentioned equation:

Where Rt is the stock index return, Dt is a dummy variable taking the value of 1 for t1 and 0 for t2. Since stock index returns are serially correlated, the arrested development equation takes the first difference and is the first order consecutive correlativity coefficient of the mistake footings. This process is the Cochrane-Orcutt method. The arrested development theoretical account tests the difference between average returns for the beginning of the month and at the terminal of the month.

The consequences obtained indicate that the month of the twelvemonth anomalousness is non present in the Amman stock exchange. These findings may hold favorable impact on pulling foreign investing besides these consequences have of import deductions for investors and bargainers who base their investing schemes on how the ASE index move overtime.

The impact of the planetary fiscal crisis on the monthly consequence of the stock market returns was examined by Al-Jafari ( 2011 ) on the Bahrain Bourse. The sample period consisted of day-to-day returns from 1 January 2003 until 31 July 2011.It was divided into two bomber periods, the first period from 1 January 2003 to 30 November 2007 characterised the period before the planetary fiscal crisis while the 2nd 1 is the crisis period and spanned from 1 December 2007 until 31 July 2011.The equality for agencies trials ( F-test, Chi-square trial, and Kruskal-Wallis trial ) and the equality for discrepancy trials ( Bartlett trial, Levene trial, and Brown- Forsythe trial ) was employed to prove the sample. The empirical findings demonstrated that there were no important differences of the monthly consequence for day-to-day returns of the Bahrain stock market in the two bomber periods.

Using an ordinary least square ( OLS ) theoretical account, Christos Floros ( 2008 ) focused on the month of the twelvemonth in the Grecian stock market. Daily returns of the General ASE Index, FTSE/ASE-20 and FTSE/ASE Mid 40 were used. The sample period consisted of informations from 26 November 1996 to 12 July 2002 for General ASE Index, 23 September 1997 to 30 August 2001 for FTSE/ASE-20 and 8 December 1999 to 30 August 2001 for FTSE/ASE Mid 40. The consequences showed that there is no January consequence. In other words, day-to-day returns are non higher in January than in any other month.

The emerging stock market of Jordan was examined by Maghayereh ( 2003 ) for seasonality of monthly stock returns and January consequence anomalousness. Daily returns on the Amman Stock Exchange ( ASE ) were employed for the period 1994-2002. This survey employed the standard GARCH, exponential GARCH ( EGARCH ) and the GJR theoretical accounts. Maghayereh ( 2003 ) illustrated that there were no grounds in favour monthly seasonality every bit good as January consequence in the ASE returns. This indicated that investors can non gain unnatural return when puting in the ASE.

## 3.4.2 Evidence of inefficiency

Wyeme and Olfa ( 2011 ) focused on the being on the month of the twelvemonth anomalousness in the Tunis stock exchange ( TSE ) . Using arrested development analysis of silent person variable ( Gultekin and Gultekin, 1983 ) , they investigated the month of the twelvemonth consequence on the day-to-day stock return of TSE over the period January 2003 to December 2008. The undermentioned arrested development was estimated:

Where Rm, T is the market return on twenty-four hours T ; D1, T through D12, t are dummy variables for each month of the twelvemonth such that D1, t = 1 if twenty-four hours t falls in January and 0 and so on. The coefficients a1 through a12 are the estimation of the average returns for January to December severally and is a random mistake term.

The writers found grounds of the month of the anomalousness in the stock market of Tunis for the whole sample period. Furthermore, they documented an April consequence, significance that the average day-to-day market returns were significantly higher in the month of April than the staying months.

In a survey undertaken by Giovanis ( 2009 ) , he analysed the month of the twelvemonth and January consequence in 50 five stock market indices from 50 one states. The symmetric GARCH theoretical accounts was employed and based on dissymmetries trials asymmetric GARCH theoretical accounts were estimated. In order to gauge arrested development the GARCH theoretical accounts were applied.

The first theoretical account is the simple symmetric GARCH ( 1,1 ) recommended by Bollerslev ( 1986 ) and is every bit follows

Where is the disturbance term of the average equation and

The standard GARCH theoretical account is symmetric in its response to past inventions. Good intelligence and bad intelligence may hold different effects on the volatility therefore two alternate GARCH theoretical accounts were estimated in order to capture the asymmetric nature of volatility responses.

The asymmetric EGARCH and GJR theoretical accounts were the other two GARCH theoretical accounts considered Nelson ( 1991 ) proposed the EGARCH ( 1,1 ) theoretical account and was defined as:

where is the disturbance term of the average equation. It is expected, “ good intelligence ” generate less volatility than “ bad intelligence ” , where reflects the purchase consequence.

The 2nd asymmetric GARCH theoretical account estimated was the GJR-GARCH ( 1,1 ) . This was proposed by Glosten et Al. ( 1993 )

is a dummy variable, where if and otherwise. Besides for a purchase consequence is expected that, so that the “ bad intelligence ” have larger impacts, and is required that and for non-negativity status.

Empirical findings suggested grounds of December consequence on 20 stock markets, February consequence is found in nine stock markets while January and April effects in seven and six stock markets severally. This suggested that the returns on those specific months are higher than the staying months.

Fountas and Segredakis ( 2002 ) focussed on the month of the twelvemonth and January consequence anomalousness on returns in 18 emerging stock markets. A monthly stock return for the period 1987 to 1995 was used. The findings showed grounds of monthly seasonality in stock returns. However, really small grounds in favor of the January consequence has been found.

## Decision

After analyzing legion research documents from the literature, certain issues can be clearly spotted. Some markets were found to be weak form efficient while others did non fulfill the random walk theoretical account. With regard to the presence of a certain tendency in stock market returns, being the twenty-four hours of the hebdomad consequence and month of the twelvemonth consequence, assorted decision were reached. Importantly, it can be seen that different statistical methods were employed to set about these analysis including the usage of simple OLS arrested development and GARCH theoretical accounts every bit good. The following chapter provides informations specification used in the survey and description of some of the methods employed by the above-named writers, in inside informations, to help in accomplishing the research objectives of this research.