Importance of Roleplay in Teaching English free essay sample

Non-scripted ones are when students are given a role each and must use whatever knowledge they have in order to speak with that partner. Below is a list of ideas for a general English class. This can be adapted to suit a situation. Try These Fresh Role Play Activities With Your Class 1 Telephone Conversation Speaking on the phone is different to a face-to-face conversation because one relies solely on language to communicate. Get the students who are practicing to sit back to back in order for this to work properly. There is a whole range of ideas which one can use to act this out. Examples include: phoning to make a complaint, speaking to a friend or inquiring about a job position. 2 Going to the Shop A great one for younger learners as it will teach them the basics of interacting with people. Children generally rely on their parents to buy things for them, therefore this will boost their overall general confidence in buying. We will write a custom essay sample on Importance of Roleplay in Teaching English or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page It can be as simple or as complex as one wishes, depending on the situation. Key phrases are often important here, such as â€Å"I would like†¦Ã¢â‚¬  â€Å"How much are†¦Ã¢â‚¬  â€Å"Good morning†¦Ã¢â‚¬  and so forth. 3 Booking a Hotel This will allow students to practise a specific type of language. Usually this will be formal language as it is a business conversation. This can also be done in the format of a telephone conversation, or it could be someone approaching a text. There is a wide range of opportunity here for the students to learn new forms of vocabulary. 4 Sharing Opinions Choose a topic that everyone appears to be interested in. Get the students to pair up and give them a list of questions to follow (for example, see our ‘130 Topics for Discussion (more than 2000 questions) For Any Level’). This will allow them to come up with their own phrases and use language in a much more practical way. Job Interview Work is usually a good topic to begin with when teaching adults. Many are learning English in order to improve their career prospects. As a result, a job interview role play is an excellent way to get the class learning that all important material. Again, this can be scripted or non-scripted. A good idea would be to have the interviewer have a list of s et questions, and the students can take it from there. 6 Getting Everyone to Speak A traditional method is to ask the class to pair off. Of course, one cannot monitor every student particularly if the class is quite large. Therefore, it is important to make sure everyone is speaking and getting the most out of the language they know. If one has time, have each individual group come up to the top of the class and speak in front of everyone else. This will allow people to use their language more creatively. 7 Argument Between Neighbours Again, this is a new opportunity for learning different types of vocabulary. This could be between two neighbours who are having an argument. Perhaps one plays music too loudly in the middle of the night and is disturbing the rest of the apartment block. This can be as absurd or ridiculous as the students’ want, as long as they are speaking and using the language correctly. Some of the situations thought up can be quite amusing. See some suggested situations here: â€Å"Neighbour Problems Role Play†. 8 Body Language Body language is just as important as spoken language, so in their role plays try and let the students get into the role. Of course, one does not have to be an expert at acting but it is important for them to get a feel of the flow of the conversation. Using body language effectively will allow them to become a lot more in tune with the language they are using. Debate Debates are a brilliant way of encouraging language use. This is because they can become somewhat heated, and many new words can come up. It is important to choose a topic which might not be too controversial to some students. Remember to be sensitive to their age group and the general attitude of the particular country. Divide the class into t wo sides and give them each a side of an argument to defend. 10 Have Fun When it comes to role plays, it is all about the creative use of language. The student must put what they know to the test. This doesn’t mean they have to list off a boring dialogue. Allow them to be as creative as they can. Put them into challenging situations, and this will allow them to think of new ways of saying things. Role plays can work as a great ice breaker for the beginning of the class. Always remember to be sensitive to any particular issues at the time, however, and be wary of the students’ age. Usually, the likes of filing a complaint will not really be of interest to children. Once the students are having fun and speaking English, there are no limits to their own learning!

Accepting Yourself essays

Accepting Yourself essays It is easy in the world to live after the worlds opinion; it is easy in solitude to live after our own; but the great man is he who in the midst of the crowd keeps with perfect sweetness the independence of the solitude. That was once said by Emerson in his Self-Reliance essay. The phrase above states that its easy to forget who you are when you are in among a crowd of people or your friends, but the one who can be him or herself when they are around a crowd is the real you. I was transferred from a work farm out in the south to the Oregon psychiatric hospital all of the other patients in the ward notice something different about him. I caused most of the disturbance during the night calling the nurses and the aides inappropriate names. I placed many bets that I could get transferred out of that ward just as fast as I did the one before that, and the one before that. There was this one nurse who I couldnt stand at all so I bet I could make her go off on me by the end of the week, for sure I could get kicked out then. I didnt like any of the other men in my ward, they were very different than me. They acted as if they were in there and havent did a thing wrong in their entire life and act as if they were fine. I know I have done wrong and I know that I will have to pay the consequences now, I learned to accept thats who I am and I am not willing to change for anyone. The best solution I could have done was when I was myself, I do not regret one thing I said or one thing I did while I was in the ward. I was myself, I was who I wanted to be, I did what I wanted when I was around everyone else. I had many people who didnt like me and many people said Well, Randle if you want them to think you are cured, you better change or you are never going to get out here. I did not care if I got out or not, that is who I was. The other men in the ward learned to accept m ...

Please write a summary of I BELIVE IN THA HOLY SPIRIT vol. 3 pp Essay

Please write a summary of I BELIVE IN THA HOLY SPIRIT vol. 3 pp. 174-214 written by Yves Congar. I mean only this part fro - Essay Example Anselm decided that the Greeks and Latins were on the same page when it came time to discuss Trinitarian doctrines. Augustine stated that the Greeks believed in one essence and three substances while the Latin people believed in one essence or substance brings three persons. Augustine stated that the difference is only in the wording, however, Abelard believed that this difference was crucial in deciding how well the Greeks practiced their faith. Abelard stated that "hypostasis" was a dangerous word to Jerome. There had been a problem in the way that Greeks followed the doctrines on the Holy Spirit according to the non-Greek religious leaders. These non-Greek religious leaders felt it impossible that the Greeks were genuine when their vocabulary was inappropriate. They believed that the Greeks did not practice in the right way since the vocabulary they used tended to be so radically different, that it was impossible that they followed the right path. The non-Greek religious groups fe lt that this was only a vocabulary issue and that they did still believe in the Holy Spirit in the right way, however, it was too difficult to think that if there is a vocabulary error, there must also be a method in practicing faith error as well. During Anselm's time, it was believed that most of the doctrines were in agreement between the Latin people and the Greeks. Wording seemed to be the only problems encountered by Anselm's opinion of how the Greeks practiced. Thomas believed that the wording was incredibly different but the meanings were almost the same. The Greeks deny the procession of the Holy Spirit a Filio, however they concede it in its antecedent. This problem has lasted since the year 325 and it is now the fourteenth century. This dispute is quite strong still by the fourteenth century and no conclusions have yet been made about whether the Greeks and Latins can come to an agreement of how they practice their faith. Alexander Hales came up with his own opinion and h is comments about how the Latins and Greeks differ are as follows: Augustine (Latin leader at the time) considered the inner structure of the spirit and therefore maintained that it was from the mens that the cogitatio or word proceeded and the latter was followed by the spiration of the affectus. The Damascene (Greek leader at the time), on the other hand, considered the external word so that the point of departure was the intellect, followed by the word, which emerged as a word with a breath, which was connected in an immediate way to the intellect. The spirit, then, was Spiritus Verbi, non a Verbo. Alexander believed that these were the opposing views between the Latins and the Greeks of how the word and the Holy Spirit were related. Bonaventure was a commentator and he came up with an interesting perspective about this controversial debate. The first part is the fact that both the Greeks and the Latins agreed on the aspects of faith in divine revelation found in the scriptures. The second part is concerning the fact that the Greeks and Latins differ in their viewpoints on categories and terminology. The third and final aspect is that of the teaching in a formula which led to the controversy in the first place. He actually figured out where the similarities and differences were and wrote them out to help clear this debate once and for all. The items they both agreed on are as follows: the scriptural basis of the procession and the spirit belongs to the son and is sent by the son. The Latins

Social and Cultural Factors Affecting Early Year's Education Provision Essay

Social and Cultural Factors Affecting Early Year's Education Provision in UK - Essay Example In practice, United Kingdom’s education system has a holistic purpose. United Kingdom’s education curriculum states that education is a conventional process in which the society intentionally channels its amassed dexterity, skills, knowledge, values and customs from one coeval to the other. Education is one of the fundamental units for an individual’s development and immiseration reduction. For the child to learn effectively, there are various factors that need to be weighed and evaluated (Hodgeson & Spours, 2008, p. 12). Children surrounded by a strong learning environment that is supportive and informative improve on their educational improvement. When considering the role of education and the desired goal and the result, it is necessary to observe where the current education system stands and the effects that have impacted upon it (Hodgeson & Spours, 2008, p. 20). Students exposed to underprivileged, and poor educational surrounding are at a high peril of a ne gative learning effect. United Kingdom has distinct metropolitan boroughs. Each borough has a different social set up. This paper will focus on Barking and Dagenham borough. The fact that children are particularly vulnerable makes early childhood education accomplishment a rough and tough experience. This is because there are social, cultural and economic factors that affect the provision of early childhood education. ... In adapting to the environment, the child assimilates and accommodates the new experiences within her or himself. Social factors are the elements within the society or social environment (Pugh & Duffy, 2006, p. 25). These elements include family, locality, political system, mobility rate and the child’s relations. Barking and Dagenham borough has a high number of educational institutions and a high number of learned and affluent adults. It is one of the most developing metropolitan boroughs in the region. Barking and Dagenham borough consists of affluent families and learned adults. A family is a social unit where related people live together. It can either affect early year’s education of a child positively or negatively (Pugh & Duffy, 2006, p. 30). Relatively, a parent’s education will affect the child’s education. An affluent parent has a high consideration for education and sets academic goals for the child. The educated parent has a higher access to e ducational resources for the child. A child with either one of the parents as a doctor or an engineer is motivated to attain a higher education level than the parent (Pugh & Duffy, 2006, p. 38). A community with educated and learned parents, such as Barking and Dagenham community will have a higher demand for education. From this fact, we can conclude that the parent's level of education in Barking and Dagenham determines a child’s early education provision in a given society or community. The family environment affects a child’s education (Pugh & Duffy, 2006, p. 45). From various studies conducted by the not-for-profit organizations across all the boroughs, most of families are peaceful, and cases of family violence are minimal. A peaceful

Information security legislation Essay Example | Topics and Well Written Essays - 4750 words

Information security legislation - Essay Example Never the less, times have changed and the recent past has seen a lot of regulations and legislation which impacts information security. Some of these legislations are the European Data Protection Directive, Sarbanes-Oxley Act, and the Capital Adequacy Directive, just to mention but a few. In the event of these new compliance rules organization are being forced to resort a range of codes and standards to control their information systems. (Purtell, 2007) Information security is an organization problem, and not a technologically one. With increasing spotlight on information security in legislation and the media all over the world, companies are being faced with a complex need to conform to privacy and security regulations and standards. This is making information security issues to be discussed in the boardrooms and many executives and directors becoming aware of their responsibility in ensuring information security in an organization. Information security is driven by; The knowledge of issues and challenges being faced in information security currently has increased. Through, the government, the media, crimes, cyber attacks and proliferation of products that are vulnerable, information security has continued to receive more attention (Purtell, 2007) Through successful attacks for example code red and Nimrod, companies are realizing that security technology product is not the overall solution to information security. Information security is an organization problem and technology is only but a small element in the organization. (Purtell, 2007) Companies are facing complex needs and requirements to conform to numerous regulation/standards. Even those vertical organizations such as financial services organizations, complication to adhere to security measures brought about by different regulations, for example the US Gramm-Leach Biley Act, 1999 (GLBA),

Asset Returns in African Stock Market Indexes

Asset Returns in African Stock Market Indexes 1.0 INTRODUCTION Financial markets are important in an economy in that they involve lots of monetary funds in the capital markets. These funds enable firms to raise finance in the form of equities and debts as means to finance expansion or expenses. Hence they serve the intermediation process and also provide a means for investors to diversify their portfolio of assets. African stock markets have been subject to economic restructuration as well as stock exchange modernisation these recent years. They now face regional and global integration and so the need to investigate their returns characteristics. Efficiency is an integral part of investment valuation. When markets are efficient, security prices are properly valued as they absorb all information at each point of time. This leads to optimal allocation of private and social resources. Moreover, investors may not beat the market and make abnormally higher returns than others, based on information asymmetry. Conversely, inefficiency leads to market prices deviating from actual value. Hence, those having reasonable level of expertise in the field of valuation will be able to spot and exploit above and under-valued stocks. Efficiency in equity markets is of significance to investors and policymakers in African markets. The concept has been widely applied to developed countries but less attention has been devoted to less developed ones. These researches indicate the importance of developing stock markets for countries which are at appropriate stage of economic growth. Indeed, it is more convenient to test for weak form efficiency of market rather than testing for semi-strong or strong forms of efficiency due to lack of data and supervision pertaining to those markets. 1.1 Organisation of the paper The objective of this study is to examine the possibility of both short- and long-term memory in asset returns in selected African markets stock indexes. Besides South Africa, all the other markets are still in developing state so that efficiency can be gauged on basis of market development and size. The paper is organised as follows: * Section 2 describes informational efficiency with emphasis on weak-form efficiency and random walk. Critics relating to the latter are then raised to emphasise on non-linearity and long-term dimensions. * Section 3 provides a brief description of the characteristics of the selected African stock markets as well as their respective indices. * A methodological discussion based on the different random walks and long-term analysis is then presented in the fourth section. * Tests, results and discussions are provided in section 5. The possible explanations for efficiency or inefficiency pertaining to the respective markets are also made. * Finally, we conclude in section 6 and make policy recommendations as well as future scope for research. 1.2 Limitations of the Study This paper in centered on market efficiency. However, given the excessive literature that exists in this field, it is beyond the scope this study to review all the previous works related to the study. We therefore provide only a short discussion on the main findings associated to the weak-form efficiency or random walk hypothesis to provide a general overview of the paper. Besides, the main limitation of this paper is that we restrict to the weak-form efficiency using time series analysis. Consequently, the statistical tests are only used to test for market efficiency excluding any transaction costs adjustment such as the bid-ask spread. Finally, we use daily data for the analysis though it may lead to possible biasness in the observations. We believe that using a longer time period would help to reduce this problem. LITERATURE REVIEW 2.0 Introduction Efficient market hypothesis is one of the most researched topics in the realm of the stock market. While most of the early studies have previously been centered on developed stock markets like USA, Japan and Europe, developing and emerging stock markets have been brushed aside. Before proceeding with a systematic and ordered approach, it might be useful to present a general review of the theory under study, which in turn aims at defining the main concepts and demonstrating familiarity with previous relevant findings concerning the same field of research. 2.1 Theoretical review In this section, we develop a formal view of the weak-form efficiency as well as the random walk hypothesis. Starting with the martingale model, necessary assumptions are made to develop a model consistent with Lo and McKinley (1997) model specification. Making the necessary assumptions about the model, a formal presentation of the different random walks is made and criticised. 2.1.1 Market efficiency Efficiency has various different contextual meanings but analysis of financial markets assumes an informational dimension. The attribute of those markets by virtue of which they respond to new information, is called informational efficiency. This implies that current market price reacts instantaneously to new information so that it incorporates all relevant information. Since, by definition, new information is unpredictable, it follows that change in stock price cannot be anticipated and thus move in a random manner. Informational efficiency can be related to the hypothesis of random walk which assumes that prices do not exhibit predictive patterns over time and follow a random walk. Hence, prediction of future prices in absolute terms, based singly on information about historical price, will be unsuccessful. The theory had its roots from the early works of Bachelier (1900). In his own words, Bachelier argued that â€Å"past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes†. This emphasises the informational content of stock prices. In his paper on the behaviour of stock and commodity prices, Maurice Kendall (1953) further supported the random walk theory. The findings, unexpectedly, showed that prices follow a random walk and not regular cycles. His conclusion was that the series appeared ‘wandering, ‘Almost as if once a week the Demon of Chance drew a random number from a symmetrical population of fixed dispersion and added it to the current price to determine the next weeks price In his thesis, Behaviour of stock market prices, Fama supported the random walk theory where he reviewed previous works on stock price movements. He concluded that â€Å"it seems safe to say that this paper has presented strong and voluminous evidence in favour of the random walk hypothesis.† Indeed in a market where prices are determined rationally, only new information will cause them to change. Hence prices follow a random walk to reflect all current knowledge. If price prediction were possible, this would have caused market inefficiency as prices dont incorporate all information. Fama (1965) was the first one who coined the term efficient market. He held that such a market is one constituting of a large number of competing rational and active profit-maximisers who try to predict individual values of securities. Information in those markets tends to be almost free. He argued that the essence of ‘instantaneous adjustment in actual prices to new information is competition leading to efficiency in the market. Later, the random walk theory was broadened into a concept called the efficient market theory. Based on the works of Samuelson (1965) and Roberts (1967), Fama (1970) developed a second paper: Efficient capital markets: A review of theory and empirical work. He distinguished between three levels of efficiency, as earlier initiated by Roberts (1967), based on three sets of information reflected in the price. He posited that a market is efficient in the weak-form if any information which might be contained in past price movements is already reflected in the security prices. It is semi-strong efficient when all relevant publicly available information is impounded in security prices while strong form efficiency suggests that security prices already reflect all available information, even private information. In this stream of literature, Malkiel (1992) contribution is elaborated in his essay Efficient market hypothesis in the New Palgrave Dictionary of Money and Finance. He defines a capital market as efficient when it fully and correctly reflects all relevant information in security price determination. Hence, for some information set, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, the market is efficient if security prices are unaffected by unveiling that information to market participants. Then it becomes impossible to make economic profits by exploiting the information set. Hence, both the random walk theory and the EMH are related to informational efficiency. Then the form of efficiency under consideration will depend upon the information set, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, which determines the level of efficiency. 2.1.2 Weak Form Efficiency: Random walk and its critics Weak-form efficiency focuses on the informational content of the previous sequence of stock price movements. An informational efficient market postulates that excess return cannot be realised from information contained in past prices. The rationale behind weak-form efficiency is that stock prices are the most publicly available information so that an investor may not be able to use information, which is already available to others, to beat the market. A long considered necessary condition for an efficient asset market is the martingale process. Under market efficiency, the conditional expectation of future price changes, conditional on the price history, cannot be either positive or negative and therefore must be zero. In fact the martingale originated from gambling and the concept of fair game. Samuelson (1965) and Mandelbrot (1966) independently demonstrated that a sequence of prices of an asset is a martingale (or a fair game) if it has unbiased price changes. Danthine (1977), LeRoy (1976, 1989), Huang (1985) and Neftci (2000) held that if a security market can be equilibrium and for sure be a fair game, then the following equations must hold: Ept+1ÃŽ ©t=pt (1) Ept+1-ptÃŽ ©t=0 (1.1) Where t denotes the price of an asset at date t, à ¢Ã¢â‚¬Å¾Ã‚ ¦t is a set of all past and current information regarding prices pt,pt-1,pt-2†¦.. and pt+1-pt=rt. Hence, the directions of the future movements in martingales are impossible to forecast. If pt is a martingale in equation (1), the best forecast of pt+1 that could be derived on basis of current information ÃŽ ©t, equals pt. For equation (1.1), rt is a fair game if the forecast is zero for any possible value of ÃŽ ©t. Then pt is a martingale only if rt is a fair game. In this case, asset price evolves in a random process so that the correlation coefficient between the successive price changes will be zero given information about current and past prices. However, most assets are expected to yield a non-zero and positive returns. The martingale hypothesis does not take into account the trade-off between risk and return as pointed out in financial economics. The model implicitly assumes risk neutrality while investors are generally risk averse. In fact, an investor is likely to hold more risky assets provided they are compensated in terms of higher expected returns. In this case, knowledge of the riskiness of current information set implies some awareness about the expected returns. Hence the equilibrium model shall predict a positive price change in the assets price though the actual return is still unforecastable under market efficiency. Then an asset model, considering positive returns, may be formulated as Fama (1970). He suggested the sub-martingale process: Ept+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t≠¥pt or alternatively Ert+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t≠¥0 (1.2) This states that the expected value of next periods price based on the information available at time t, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, is equal to or greater than the current price. Equivalently, it stipulates that the expected returns and price changes are greater or equal to zero. Market efficiency plus an equilibrium model for asset pricing normally produces a random character to asset prices or returns or excess returns. The equilibrium model generally shows how the assets expected return varies with its risk and this can be closely related to Famas sub-martingale model. However, the representative model for the asset uses log prices and the expected continuously compounded return, rt+1. Ert+1ÃŽ ©t=pt+1-pt (1.3) Under the efficient market hypothesis, investors cannot earn abnormal profits on the available information set other than by chance. This is in line with Jensen (1978) who defines a market as efficient with respect to the information set, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, if it not possible to make economic profits on the basis of this set of information. Hence, defining excess returns as zt+1: zt+1=rt+1-Ert+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t (1.4) Since market efficiency implies that all information is already impounded in stock prices, the following applies: Ezt+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t=0 (1.5) Under the assumption that the equilibrium model determining asset prices in (1.3) is assumed to be constant over time, the deduction is that expected return does not depend on the information available at time t such that: pt+1-pt=Ert+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t=Ert+1=r (1.6) Therefore market efficiency produces a result that implies that the changes in asset prices follow a random walk. The appropriate model would then be a random walk with drift where the arbitrary drift parameter, reflects how prices change on average to provide returns to holding the asset over time. The following equation sets the random walk model similar to the one defined by Lo and MacKinlay (1997): pt+1= ÃŽ ¼+pt+ ÃŽ µt+1 (1.7) rt= ÃŽ ¼+ÃŽ ±rt-1+ ÃŽ µt (1.8) If the stock price index follows a random walk, then, ÃŽ ± = 0. Generally, if stock prices and returns are unpredictable then time series have the property of random walk and white noise implying the validity of EMH. Thus, given an equilibrium model for asset pricing, the test for weak-form efficiency is that of random walk tests of market efficiency. Ko and lee (1991) maintained that â€Å"If the random walk hypothesis holds, the weak form of the efficient market hypothesis must hold, but not vice versa. Thus, evidence supporting the random walk model is the evidence of market efficiency. But violation of the random walk model need not be evidence of market inefficiency in the weak form†. Depending on the restrictions put on the increments,ÃŽ µt+1, different forms of the random walk are tested. Within the random walk hypothesis, three successively more restrictive sub-hypotheses with sequentially stronger tests for random walks exists (Campbell et al. 1997). These are range from the most restrictive form of Random Walk 1 (RW1) to the least restrictive one which is the Random Walk 3 (RW3). Based on their extensive research, the orthogonality condition for the random walk is: covfrtgrt+k=0 (1.8) Where frt and grt+k are two arbitrary functions and rt and rt+k refers to the returns for period t and t+k respectively. If (1.9) holds for all functions frt,grt+k this corresponds to RW1 and RW2. The former is the most restrictive version of random walk model implying it is not possible to predict either future price movements or volatility based on past prices. It states that returns are serially uncorrelated with independently and identically distributed increments with mean, zero and variance, ÏÆ'2. Under RW2, the returns are serially uncorrelated, corresponding with a random walk hypothesis with increments that are independent but not identically distributed. In case frt,grt+k are arbitrary linear functions, the RW3 applies so that it is not possible to use information on the basis of past prices to predict future prices. Hence, returns in a market conforming to this standard of random walk are serially uncorrelated, corresponding to a random walk hypothesis with dependent but uncorrelated increments. The foundation of traditional tests of random walk rests on the assumption of IID. The most famous tests remain the sequences and reversals test proposed by Cowles and Jones (1937) and the runs test. Tests of RW2 and RW3 encompass the variance ratio tests and unit root tests which are more recent tools. Developed by Lo and MacKinlay (1988), hereby LM, the variance ratio tests out that the variance of the innovations pertaining to a random walk model is linear functions of time. This popular test does not restrict only to the RW1 but also to the RW2 and RW3. However, exclusion of non-linear analysis in financial series could lead to inappropriate deductions as regards weak-form efficiency. Indeed, the application of non-linear dynamics and chaos theory to financial series has shown that they evidence non-linear structure. In practice, returns distributions exhibit leptokurtic behaviours as opposed to normal distribution. They often reflect volatility clustering thereby the level of volatility in the next period tends to be positively correlated with its current level. Then it may be possible for information on the variance of past prices to predict the future volatility of the market. Indeed, share price movements could be unpredictable when using linear models but forecastable under non-linear models in the ‘short-run. This contradicts the use of linear models for testing the efficient market hypothesis. Further departures from the random walk hypothesis exist in the long-range dependence. This is analogous to high autocorrelation structure in a series so that there is persistent dependence between distant observations. In this case covfrtgrt+k does not tend to zero at higher lags. As regards market efficiency, persistence implies that past data contain useful information for prediction so that long memory violates the concept. Several tests have been developed for this purpose including the rescaled statistic to test for long-term ‘randomness of the market series and the ARFIMA-FIGARCH which categorises the long- and short-term memory based on the estimated value of the fractional difference. 2.2 Empirical Review Following the work of Fama (1965) â€Å"Random walk in stock prices† arguing for random walk hypothesis, a multitude of research has been performed throughout the world. While most of the well developed markets were found to be efficient, research findings of developing and less developed markets are mixed and controversial too. Most of the less developed market encounters the problem of thin trading. Besides, it is easier for large traders to manipulate small markets. Though emerging markets are generally assumed to be less efficient, empirical evidence does not always support the idea. Some previous research aiming at testing the weak-form efficiency of a particular group of stock markets are presented below. A research that aims at testing weak-form market efficiency in the equity markets of the three main Central European transition economies (the Czech Republic, Hungary, and Poland) is that of Gilmore and McManus (2001). Using different approaches comprising of univariate, multivariate tests as well as the model-comparison approach for the period July 1995 to September 2000 different conclusion were drawn. While the serial correlation-based tests largely support a conclusion that these markets are weak-form efficient, the results of comparing forecasts of alternative models are consistent in rejecting the random walk hypothesis. Examining the existence of weak-form efficiency in European stock market, Worthington and Higgs (2003) used daily returns for sixteen developed markets (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom) and four emerging markets (Czech Republic, Hungary, Poland and Russia) to perform a number of testing procedures of random walk. They started with the serial correlation coefficient test and the runs test, and found that Netherlands and Germany do follow a random walk while the United Kingdom, Ireland and Portugal were efficient under one test or the other. All remaining markets were weak form inefficient. Beside unit root tests (ADF, PP statistics and KPSS), the multiple variance ratio tests rejected the presence of random walk in most of the markets. While in the developed markets only the United Kingdom, Portugal, Ireland, Sweden and Germany satisfied the most stringent rand om walk criteria, in emerging markets only Hungary did so. Weak-form efficiency for emerging equity markets were also tested by Chang, Lima and Tabak (2003). They deduced that random walk hypothesis is not consistent with Asian equity markets while left apart Chile, Latin American indices resemble a random walk. Using daily prices from January 1992 to December 2002, multivariate variance ratios using heteroscedastic robust bootstrap procedures and test trading rules using trading range break (TRB) levels were employed. Taking the US and Japan as yardsticks, they were not able to reject the random walk hypothesis. Another study considering a group of selected Asian markets; Kim and Shamsuddin (2008) argues that market efficiency varies with the level of stock market development. Using new multiple variance ratio tests based on the wild bootstrap and signs as well as the conventional Chow-Denning test, they found that the Hong Kong, Japanese, Korean and Taiwanese markets adhere to the martingale property while Indonesia, Malaysia, Philippines markets are inefficient. Besides, the results revealed evidence that the Singaporean and Thai markets followed a random walk after the Asian crisis. As regards the Gulf Co-operation Council (GCC) stock markets, Elango and Hussein (2008) tested whether daily returns series are an approximation of normal distribution or not. Dubai, AbuDhabi, Saudi Arabia, Qatar, Kuwait, Oman and Bahrain stock market indices were examined using the Kolmogorov-Smirnov test, Runs test, Autocorrelation Function and Partial Autocorrelation Functions. The results revealed that the distribution of daily returns on these markets deviated from the normal distribution during the study period. Also, the runs test rejected the hypothesis of random walk for all seven markets. In his paper investigating the random walk hypothesis, Urrutia (1995), used monthly data from December 1975 to March 1991 for four Latin American equity markets: Argentina, Brazil, Chile, and Mexico to observe whether they are weak-form efficient. He made use of the Variance-ratio tests and the runs tests. While results of the variance ratio estimatespixel rejects the random walk hypothesis, runs tests specify that Latin American equity markets are weak-form efficient. These empirical findings suggest that domestic investors might not be able to develop trading strategies that would allow them to earn excess returns. Using Lo-MacKinlay Variance ratio, Wrights rank and sign VR and the standard runs tests; Al-Khazali, Ding and Pyun (2007) revisited the validity of random walk hypothesis in eight emerging markets in the Middle East and North Africa (MENA): Bahrain, Egypt, Jordan, Kuwait, Morocco, Oman, Saudi Arabia, and Tunisia. When assessed by Wrights (2000) rank and sign VR test, all the markets rejected the hypothesis of random walk. However, once data are reconciled for distortions from thinly and infrequently traded stocks, all eight stock markets do follow a random walk. African countries were investigated in the paper ‘How Efficient are Africas Emerging Stock Markets by Magnusson and Wydick (2002). Testing procedures considered monthly data for eight African markets in comparison with nine other developing countries in Latin America and Asia. Distinguishing among the three types of random walk models, they started by testing the RW 3, by investigating the Partial Auto-Correlation Function(PACF) of the historical series and examining whether they are statistically different from zero. Markets in Botswana, Cote dIvoire, Kenya, Mauritius and South Africa did conform to the RW3 while those of Ghana, Nigeria and Zimbabwe were rejected. Proceeding with the RW2, excluding Botswana, results did not change. However none of the African Markets were conform to the RW1 White test for heteroscedasticity. They conclude that African countries do conform quite favourably to some regions of the developing world. Another research which focuses on African markets was that of Jefferis and Smith (2005). It covers seven African stock markets: South Africa, Egypt, Morocco, Nigeria, Zimbabwe, Mauritius and Kenya and use a GARCH approach with time-varying parameters to detect changes in weak-form efficiency through time. They emphasised on RW 3 model with volatilities changing over time and found that Johannesburg stock market was weak-form efficient with no tendency to change like many other developed markets. On the other hand, the stock markets of Egypt, Morocco and Nigeria showed changing levels of inefficiencies to become weak-form efficient towards the end of the period. The results for Kenya, Zimbabwe and Mauritius, however, showed tendency towards efficiency and rejected the hypothesis of weak-form efficiency. Recently, McMillan and Thupayagale (2009) in their paper â€Å"The efficiency of African equity markets† examined long memory effects of both equity returns and volatility for eleven African countries, taking the UK and US as reference. They made use of unit roots test and the GARCH(1,1) models before proceeding with ARFIMA-FIGARCH and ARFIMA-HYGARCH models. They ended up with mixed results. The ARFIMA-FIGARCH models provide evidence for long term memory in African equity markets with the exception of Mauritius, Morocco, Botswana and Nigeria where the results were unpredictable. Also, the US stock return volatility was marked by long memory process while the UK was non-stationary. These results were further supported by the ARFIMA-HYGARCH models. 2.3 Conclusion During the course of the literature review, limited evidence on weak form efficiency of African markets was found. These countries have attracted significant investment these last years and are of much importance to portfolio managers. Univariate time series analysis might be important tool for technical analysts in trying to outperform these markets. Indeed, the battery of econometrics software now paves the way for investigation of the random walk hypothesis based on different sets of assumption. A preliminary analysis of the African markets shall provide us with an insight to efficiency based on their attributes and consultation of previous works. GENERAL OVERVIEW OF THE AFRICAN STOCK MARKETS 3.0 Introduction African stock markets, following in the wake of the surge in the world stock markets over the few decades, are starting to take off. Recognizing the importance of stock markets in economic development, several African countries launched stock exchanges during the past two decades. The African Stock Exchange Association (ASEA) was, hence, set up in 1993 so as to promote the development of stock markets. Prior to 1989, there were just five stock markets in Sub-Saharan Africa and three in North Africa. Today, Africa has about 20 active stock markets, with some exchanges more established than others, depending on when they were established. Alongside the rapid expansion of stock markets in the continent, there has also been a significant growth in market capitalization and the number of listed companies. However, with the exception of the well established markets, stock markets in Africa remain thin and illiquid. This study covers four African stock markets namely South Africa, Mauritius , Morocco and Egypt over periods for which data is available. Mauritius Stock Exchange Since its start of trading on the 5th July 1989 under the Stock Exchange Act of 1988, the Mauritius Stock Exchange (SEM) has come a long way. From a pre-emerging market with trading taking place only once a week, the SEM has emerged as one of the leading exchanges in Africa. It operates two markets namely the Official and the Development and Enterprise market (DEM), established in August 2006 to replace the over-the-counter market. The exchange is regulated by the Financial Services Commission. As the second sub-Saharan stock exchange member of the World Federation of Exchanges, SEM operates in line with international standards. In addition, its developing institutional and retail investor base make it an attractive investment destination for foreign investors. The SEM offers quite a limited range of products to its investors and the aim for the next few years would be to increase the range of products offered. The three main indices of the official market are namely the SEMDEX, SEM- 7 and the SEMTRI. As at 30 June 2009, some 40 companies, with a market capitalisation of Rs 130.77 bn, are listed on the Official market and 52 companies, with a market capitalisation of Rs 45.41 bn, are listed on the Development and Enterprise Market (DEM). The SEM maintained an upward momentum, amidst typical market fluctuations, until the end of February 2008. The total market capitalization of the Official Market and the DEM was Rs 173.1 bn at end 2007. This is in line with the levels observed in well-established emerging stock markets. However, like other exchanges, the SEM experienced market volatility since the start of the financial crisis in September 2008. The main pillars of the Mauritian economy were adversely affected and this reflected on hotels and banks stocks listed on the SEM. The market then picked-up by mid-March 2009 on the back of interest rate cuts and stimulus packages put forward by the Government of Mauritius. Johannesburg Stock Exchange The Johannesburg Stock Exchange (JSE), regulated by the Financial Services Board under the Securities Services Act 2004, is the largest exchange in Africa and among the top twenty largest in the world in terms of market capitalisation. JSE Securities Exchange existed since November 1887 and was incorporated as a public limited company on 1st July 2005, pursuant to its demutualization. Since then, the JSE has evolved from a traditional floor based equities trading market to a modern securities exchange providing fully electronic trading, clearing and settlement in equities, financial and agricultural derivatives and other associated instruments and has extensive surveillance capabilities. Technical agreement with the London Stock Exchange (LSE) enables dual primary listings on both exchanges since 2001. Between the listed entity and its trusted trading platforms the South African economy becomes an active hub of activity where expansion is encouraged, businesses are enhanced, performa nce is driven and shareholder value is created. The JSE currently operates four boards for the equities market and the South African bond market is a leader among emerging-market economies. The main market indices are Top 40, Industrial 25, All Share, Oil and Gas Index. As the gateway to Africas economy, the JSE provides the link between international markets and the continent. In 2008, a daily average of 334 million shares was traded on the JSE. At year-end, there were 992 listed securities on the JSE with a total market capitalisation of R4,514 billion compared to R5,696 billion in 2007. Casablanca Stock Exchange Founded in 1929, the Casablanca Stock Exchange (CSE) in Morocco is relatively modern, having experienced reform in 1993. The exchange is well regulated by the Conseil Deontologique des Valeurs Mobilieres (CDVM). Originally, CSE had the Index de la Bourse des Valeurs de Casablanca (IGB) but this was replaced on January 2002 by two indexes: MASI (Moroccan All Shares Index) which comprises all listed shares, allows to follow up all listed values and to have a long-term visibility and MADEX (Moroccan Most Active Shares Index), comprisi Asset Returns in African Stock Market Indexes Asset Returns in African Stock Market Indexes 1.0 INTRODUCTION Financial markets are important in an economy in that they involve lots of monetary funds in the capital markets. These funds enable firms to raise finance in the form of equities and debts as means to finance expansion or expenses. Hence they serve the intermediation process and also provide a means for investors to diversify their portfolio of assets. African stock markets have been subject to economic restructuration as well as stock exchange modernisation these recent years. They now face regional and global integration and so the need to investigate their returns characteristics. Efficiency is an integral part of investment valuation. When markets are efficient, security prices are properly valued as they absorb all information at each point of time. This leads to optimal allocation of private and social resources. Moreover, investors may not beat the market and make abnormally higher returns than others, based on information asymmetry. Conversely, inefficiency leads to market prices deviating from actual value. Hence, those having reasonable level of expertise in the field of valuation will be able to spot and exploit above and under-valued stocks. Efficiency in equity markets is of significance to investors and policymakers in African markets. The concept has been widely applied to developed countries but less attention has been devoted to less developed ones. These researches indicate the importance of developing stock markets for countries which are at appropriate stage of economic growth. Indeed, it is more convenient to test for weak form efficiency of market rather than testing for semi-strong or strong forms of efficiency due to lack of data and supervision pertaining to those markets. 1.1 Organisation of the paper The objective of this study is to examine the possibility of both short- and long-term memory in asset returns in selected African markets stock indexes. Besides South Africa, all the other markets are still in developing state so that efficiency can be gauged on basis of market development and size. The paper is organised as follows: * Section 2 describes informational efficiency with emphasis on weak-form efficiency and random walk. Critics relating to the latter are then raised to emphasise on non-linearity and long-term dimensions. * Section 3 provides a brief description of the characteristics of the selected African stock markets as well as their respective indices. * A methodological discussion based on the different random walks and long-term analysis is then presented in the fourth section. * Tests, results and discussions are provided in section 5. The possible explanations for efficiency or inefficiency pertaining to the respective markets are also made. * Finally, we conclude in section 6 and make policy recommendations as well as future scope for research. 1.2 Limitations of the Study This paper in centered on market efficiency. However, given the excessive literature that exists in this field, it is beyond the scope this study to review all the previous works related to the study. We therefore provide only a short discussion on the main findings associated to the weak-form efficiency or random walk hypothesis to provide a general overview of the paper. Besides, the main limitation of this paper is that we restrict to the weak-form efficiency using time series analysis. Consequently, the statistical tests are only used to test for market efficiency excluding any transaction costs adjustment such as the bid-ask spread. Finally, we use daily data for the analysis though it may lead to possible biasness in the observations. We believe that using a longer time period would help to reduce this problem. LITERATURE REVIEW 2.0 Introduction Efficient market hypothesis is one of the most researched topics in the realm of the stock market. While most of the early studies have previously been centered on developed stock markets like USA, Japan and Europe, developing and emerging stock markets have been brushed aside. Before proceeding with a systematic and ordered approach, it might be useful to present a general review of the theory under study, which in turn aims at defining the main concepts and demonstrating familiarity with previous relevant findings concerning the same field of research. 2.1 Theoretical review In this section, we develop a formal view of the weak-form efficiency as well as the random walk hypothesis. Starting with the martingale model, necessary assumptions are made to develop a model consistent with Lo and McKinley (1997) model specification. Making the necessary assumptions about the model, a formal presentation of the different random walks is made and criticised. 2.1.1 Market efficiency Efficiency has various different contextual meanings but analysis of financial markets assumes an informational dimension. The attribute of those markets by virtue of which they respond to new information, is called informational efficiency. This implies that current market price reacts instantaneously to new information so that it incorporates all relevant information. Since, by definition, new information is unpredictable, it follows that change in stock price cannot be anticipated and thus move in a random manner. Informational efficiency can be related to the hypothesis of random walk which assumes that prices do not exhibit predictive patterns over time and follow a random walk. Hence, prediction of future prices in absolute terms, based singly on information about historical price, will be unsuccessful. The theory had its roots from the early works of Bachelier (1900). In his own words, Bachelier argued that â€Å"past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes†. This emphasises the informational content of stock prices. In his paper on the behaviour of stock and commodity prices, Maurice Kendall (1953) further supported the random walk theory. The findings, unexpectedly, showed that prices follow a random walk and not regular cycles. His conclusion was that the series appeared ‘wandering, ‘Almost as if once a week the Demon of Chance drew a random number from a symmetrical population of fixed dispersion and added it to the current price to determine the next weeks price In his thesis, Behaviour of stock market prices, Fama supported the random walk theory where he reviewed previous works on stock price movements. He concluded that â€Å"it seems safe to say that this paper has presented strong and voluminous evidence in favour of the random walk hypothesis.† Indeed in a market where prices are determined rationally, only new information will cause them to change. Hence prices follow a random walk to reflect all current knowledge. If price prediction were possible, this would have caused market inefficiency as prices dont incorporate all information. Fama (1965) was the first one who coined the term efficient market. He held that such a market is one constituting of a large number of competing rational and active profit-maximisers who try to predict individual values of securities. Information in those markets tends to be almost free. He argued that the essence of ‘instantaneous adjustment in actual prices to new information is competition leading to efficiency in the market. Later, the random walk theory was broadened into a concept called the efficient market theory. Based on the works of Samuelson (1965) and Roberts (1967), Fama (1970) developed a second paper: Efficient capital markets: A review of theory and empirical work. He distinguished between three levels of efficiency, as earlier initiated by Roberts (1967), based on three sets of information reflected in the price. He posited that a market is efficient in the weak-form if any information which might be contained in past price movements is already reflected in the security prices. It is semi-strong efficient when all relevant publicly available information is impounded in security prices while strong form efficiency suggests that security prices already reflect all available information, even private information. In this stream of literature, Malkiel (1992) contribution is elaborated in his essay Efficient market hypothesis in the New Palgrave Dictionary of Money and Finance. He defines a capital market as efficient when it fully and correctly reflects all relevant information in security price determination. Hence, for some information set, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, the market is efficient if security prices are unaffected by unveiling that information to market participants. Then it becomes impossible to make economic profits by exploiting the information set. Hence, both the random walk theory and the EMH are related to informational efficiency. Then the form of efficiency under consideration will depend upon the information set, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, which determines the level of efficiency. 2.1.2 Weak Form Efficiency: Random walk and its critics Weak-form efficiency focuses on the informational content of the previous sequence of stock price movements. An informational efficient market postulates that excess return cannot be realised from information contained in past prices. The rationale behind weak-form efficiency is that stock prices are the most publicly available information so that an investor may not be able to use information, which is already available to others, to beat the market. A long considered necessary condition for an efficient asset market is the martingale process. Under market efficiency, the conditional expectation of future price changes, conditional on the price history, cannot be either positive or negative and therefore must be zero. In fact the martingale originated from gambling and the concept of fair game. Samuelson (1965) and Mandelbrot (1966) independently demonstrated that a sequence of prices of an asset is a martingale (or a fair game) if it has unbiased price changes. Danthine (1977), LeRoy (1976, 1989), Huang (1985) and Neftci (2000) held that if a security market can be equilibrium and for sure be a fair game, then the following equations must hold: Ept+1ÃŽ ©t=pt (1) Ept+1-ptÃŽ ©t=0 (1.1) Where t denotes the price of an asset at date t, à ¢Ã¢â‚¬Å¾Ã‚ ¦t is a set of all past and current information regarding prices pt,pt-1,pt-2†¦.. and pt+1-pt=rt. Hence, the directions of the future movements in martingales are impossible to forecast. If pt is a martingale in equation (1), the best forecast of pt+1 that could be derived on basis of current information ÃŽ ©t, equals pt. For equation (1.1), rt is a fair game if the forecast is zero for any possible value of ÃŽ ©t. Then pt is a martingale only if rt is a fair game. In this case, asset price evolves in a random process so that the correlation coefficient between the successive price changes will be zero given information about current and past prices. However, most assets are expected to yield a non-zero and positive returns. The martingale hypothesis does not take into account the trade-off between risk and return as pointed out in financial economics. The model implicitly assumes risk neutrality while investors are generally risk averse. In fact, an investor is likely to hold more risky assets provided they are compensated in terms of higher expected returns. In this case, knowledge of the riskiness of current information set implies some awareness about the expected returns. Hence the equilibrium model shall predict a positive price change in the assets price though the actual return is still unforecastable under market efficiency. Then an asset model, considering positive returns, may be formulated as Fama (1970). He suggested the sub-martingale process: Ept+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t≠¥pt or alternatively Ert+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t≠¥0 (1.2) This states that the expected value of next periods price based on the information available at time t, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, is equal to or greater than the current price. Equivalently, it stipulates that the expected returns and price changes are greater or equal to zero. Market efficiency plus an equilibrium model for asset pricing normally produces a random character to asset prices or returns or excess returns. The equilibrium model generally shows how the assets expected return varies with its risk and this can be closely related to Famas sub-martingale model. However, the representative model for the asset uses log prices and the expected continuously compounded return, rt+1. Ert+1ÃŽ ©t=pt+1-pt (1.3) Under the efficient market hypothesis, investors cannot earn abnormal profits on the available information set other than by chance. This is in line with Jensen (1978) who defines a market as efficient with respect to the information set, à ¢Ã¢â‚¬Å¾Ã‚ ¦t, if it not possible to make economic profits on the basis of this set of information. Hence, defining excess returns as zt+1: zt+1=rt+1-Ert+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t (1.4) Since market efficiency implies that all information is already impounded in stock prices, the following applies: Ezt+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t=0 (1.5) Under the assumption that the equilibrium model determining asset prices in (1.3) is assumed to be constant over time, the deduction is that expected return does not depend on the information available at time t such that: pt+1-pt=Ert+1à ¢Ã†â€™Ã¢â‚¬Å"à ¢Ã¢â‚¬Å¾Ã‚ ¦t=Ert+1=r (1.6) Therefore market efficiency produces a result that implies that the changes in asset prices follow a random walk. The appropriate model would then be a random walk with drift where the arbitrary drift parameter, reflects how prices change on average to provide returns to holding the asset over time. The following equation sets the random walk model similar to the one defined by Lo and MacKinlay (1997): pt+1= ÃŽ ¼+pt+ ÃŽ µt+1 (1.7) rt= ÃŽ ¼+ÃŽ ±rt-1+ ÃŽ µt (1.8) If the stock price index follows a random walk, then, ÃŽ ± = 0. Generally, if stock prices and returns are unpredictable then time series have the property of random walk and white noise implying the validity of EMH. Thus, given an equilibrium model for asset pricing, the test for weak-form efficiency is that of random walk tests of market efficiency. Ko and lee (1991) maintained that â€Å"If the random walk hypothesis holds, the weak form of the efficient market hypothesis must hold, but not vice versa. Thus, evidence supporting the random walk model is the evidence of market efficiency. But violation of the random walk model need not be evidence of market inefficiency in the weak form†. Depending on the restrictions put on the increments,ÃŽ µt+1, different forms of the random walk are tested. Within the random walk hypothesis, three successively more restrictive sub-hypotheses with sequentially stronger tests for random walks exists (Campbell et al. 1997). These are range from the most restrictive form of Random Walk 1 (RW1) to the least restrictive one which is the Random Walk 3 (RW3). Based on their extensive research, the orthogonality condition for the random walk is: covfrtgrt+k=0 (1.8) Where frt and grt+k are two arbitrary functions and rt and rt+k refers to the returns for period t and t+k respectively. If (1.9) holds for all functions frt,grt+k this corresponds to RW1 and RW2. The former is the most restrictive version of random walk model implying it is not possible to predict either future price movements or volatility based on past prices. It states that returns are serially uncorrelated with independently and identically distributed increments with mean, zero and variance, ÏÆ'2. Under RW2, the returns are serially uncorrelated, corresponding with a random walk hypothesis with increments that are independent but not identically distributed. In case frt,grt+k are arbitrary linear functions, the RW3 applies so that it is not possible to use information on the basis of past prices to predict future prices. Hence, returns in a market conforming to this standard of random walk are serially uncorrelated, corresponding to a random walk hypothesis with dependent but uncorrelated increments. The foundation of traditional tests of random walk rests on the assumption of IID. The most famous tests remain the sequences and reversals test proposed by Cowles and Jones (1937) and the runs test. Tests of RW2 and RW3 encompass the variance ratio tests and unit root tests which are more recent tools. Developed by Lo and MacKinlay (1988), hereby LM, the variance ratio tests out that the variance of the innovations pertaining to a random walk model is linear functions of time. This popular test does not restrict only to the RW1 but also to the RW2 and RW3. However, exclusion of non-linear analysis in financial series could lead to inappropriate deductions as regards weak-form efficiency. Indeed, the application of non-linear dynamics and chaos theory to financial series has shown that they evidence non-linear structure. In practice, returns distributions exhibit leptokurtic behaviours as opposed to normal distribution. They often reflect volatility clustering thereby the level of volatility in the next period tends to be positively correlated with its current level. Then it may be possible for information on the variance of past prices to predict the future volatility of the market. Indeed, share price movements could be unpredictable when using linear models but forecastable under non-linear models in the ‘short-run. This contradicts the use of linear models for testing the efficient market hypothesis. Further departures from the random walk hypothesis exist in the long-range dependence. This is analogous to high autocorrelation structure in a series so that there is persistent dependence between distant observations. In this case covfrtgrt+k does not tend to zero at higher lags. As regards market efficiency, persistence implies that past data contain useful information for prediction so that long memory violates the concept. Several tests have been developed for this purpose including the rescaled statistic to test for long-term ‘randomness of the market series and the ARFIMA-FIGARCH which categorises the long- and short-term memory based on the estimated value of the fractional difference. 2.2 Empirical Review Following the work of Fama (1965) â€Å"Random walk in stock prices† arguing for random walk hypothesis, a multitude of research has been performed throughout the world. While most of the well developed markets were found to be efficient, research findings of developing and less developed markets are mixed and controversial too. Most of the less developed market encounters the problem of thin trading. Besides, it is easier for large traders to manipulate small markets. Though emerging markets are generally assumed to be less efficient, empirical evidence does not always support the idea. Some previous research aiming at testing the weak-form efficiency of a particular group of stock markets are presented below. A research that aims at testing weak-form market efficiency in the equity markets of the three main Central European transition economies (the Czech Republic, Hungary, and Poland) is that of Gilmore and McManus (2001). Using different approaches comprising of univariate, multivariate tests as well as the model-comparison approach for the period July 1995 to September 2000 different conclusion were drawn. While the serial correlation-based tests largely support a conclusion that these markets are weak-form efficient, the results of comparing forecasts of alternative models are consistent in rejecting the random walk hypothesis. Examining the existence of weak-form efficiency in European stock market, Worthington and Higgs (2003) used daily returns for sixteen developed markets (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom) and four emerging markets (Czech Republic, Hungary, Poland and Russia) to perform a number of testing procedures of random walk. They started with the serial correlation coefficient test and the runs test, and found that Netherlands and Germany do follow a random walk while the United Kingdom, Ireland and Portugal were efficient under one test or the other. All remaining markets were weak form inefficient. Beside unit root tests (ADF, PP statistics and KPSS), the multiple variance ratio tests rejected the presence of random walk in most of the markets. While in the developed markets only the United Kingdom, Portugal, Ireland, Sweden and Germany satisfied the most stringent rand om walk criteria, in emerging markets only Hungary did so. Weak-form efficiency for emerging equity markets were also tested by Chang, Lima and Tabak (2003). They deduced that random walk hypothesis is not consistent with Asian equity markets while left apart Chile, Latin American indices resemble a random walk. Using daily prices from January 1992 to December 2002, multivariate variance ratios using heteroscedastic robust bootstrap procedures and test trading rules using trading range break (TRB) levels were employed. Taking the US and Japan as yardsticks, they were not able to reject the random walk hypothesis. Another study considering a group of selected Asian markets; Kim and Shamsuddin (2008) argues that market efficiency varies with the level of stock market development. Using new multiple variance ratio tests based on the wild bootstrap and signs as well as the conventional Chow-Denning test, they found that the Hong Kong, Japanese, Korean and Taiwanese markets adhere to the martingale property while Indonesia, Malaysia, Philippines markets are inefficient. Besides, the results revealed evidence that the Singaporean and Thai markets followed a random walk after the Asian crisis. As regards the Gulf Co-operation Council (GCC) stock markets, Elango and Hussein (2008) tested whether daily returns series are an approximation of normal distribution or not. Dubai, AbuDhabi, Saudi Arabia, Qatar, Kuwait, Oman and Bahrain stock market indices were examined using the Kolmogorov-Smirnov test, Runs test, Autocorrelation Function and Partial Autocorrelation Functions. The results revealed that the distribution of daily returns on these markets deviated from the normal distribution during the study period. Also, the runs test rejected the hypothesis of random walk for all seven markets. In his paper investigating the random walk hypothesis, Urrutia (1995), used monthly data from December 1975 to March 1991 for four Latin American equity markets: Argentina, Brazil, Chile, and Mexico to observe whether they are weak-form efficient. He made use of the Variance-ratio tests and the runs tests. While results of the variance ratio estimatespixel rejects the random walk hypothesis, runs tests specify that Latin American equity markets are weak-form efficient. These empirical findings suggest that domestic investors might not be able to develop trading strategies that would allow them to earn excess returns. Using Lo-MacKinlay Variance ratio, Wrights rank and sign VR and the standard runs tests; Al-Khazali, Ding and Pyun (2007) revisited the validity of random walk hypothesis in eight emerging markets in the Middle East and North Africa (MENA): Bahrain, Egypt, Jordan, Kuwait, Morocco, Oman, Saudi Arabia, and Tunisia. When assessed by Wrights (2000) rank and sign VR test, all the markets rejected the hypothesis of random walk. However, once data are reconciled for distortions from thinly and infrequently traded stocks, all eight stock markets do follow a random walk. African countries were investigated in the paper ‘How Efficient are Africas Emerging Stock Markets by Magnusson and Wydick (2002). Testing procedures considered monthly data for eight African markets in comparison with nine other developing countries in Latin America and Asia. Distinguishing among the three types of random walk models, they started by testing the RW 3, by investigating the Partial Auto-Correlation Function(PACF) of the historical series and examining whether they are statistically different from zero. Markets in Botswana, Cote dIvoire, Kenya, Mauritius and South Africa did conform to the RW3 while those of Ghana, Nigeria and Zimbabwe were rejected. Proceeding with the RW2, excluding Botswana, results did not change. However none of the African Markets were conform to the RW1 White test for heteroscedasticity. They conclude that African countries do conform quite favourably to some regions of the developing world. Another research which focuses on African markets was that of Jefferis and Smith (2005). It covers seven African stock markets: South Africa, Egypt, Morocco, Nigeria, Zimbabwe, Mauritius and Kenya and use a GARCH approach with time-varying parameters to detect changes in weak-form efficiency through time. They emphasised on RW 3 model with volatilities changing over time and found that Johannesburg stock market was weak-form efficient with no tendency to change like many other developed markets. On the other hand, the stock markets of Egypt, Morocco and Nigeria showed changing levels of inefficiencies to become weak-form efficient towards the end of the period. The results for Kenya, Zimbabwe and Mauritius, however, showed tendency towards efficiency and rejected the hypothesis of weak-form efficiency. Recently, McMillan and Thupayagale (2009) in their paper â€Å"The efficiency of African equity markets† examined long memory effects of both equity returns and volatility for eleven African countries, taking the UK and US as reference. They made use of unit roots test and the GARCH(1,1) models before proceeding with ARFIMA-FIGARCH and ARFIMA-HYGARCH models. They ended up with mixed results. The ARFIMA-FIGARCH models provide evidence for long term memory in African equity markets with the exception of Mauritius, Morocco, Botswana and Nigeria where the results were unpredictable. Also, the US stock return volatility was marked by long memory process while the UK was non-stationary. These results were further supported by the ARFIMA-HYGARCH models. 2.3 Conclusion During the course of the literature review, limited evidence on weak form efficiency of African markets was found. These countries have attracted significant investment these last years and are of much importance to portfolio managers. Univariate time series analysis might be important tool for technical analysts in trying to outperform these markets. Indeed, the battery of econometrics software now paves the way for investigation of the random walk hypothesis based on different sets of assumption. A preliminary analysis of the African markets shall provide us with an insight to efficiency based on their attributes and consultation of previous works. GENERAL OVERVIEW OF THE AFRICAN STOCK MARKETS 3.0 Introduction African stock markets, following in the wake of the surge in the world stock markets over the few decades, are starting to take off. Recognizing the importance of stock markets in economic development, several African countries launched stock exchanges during the past two decades. The African Stock Exchange Association (ASEA) was, hence, set up in 1993 so as to promote the development of stock markets. Prior to 1989, there were just five stock markets in Sub-Saharan Africa and three in North Africa. Today, Africa has about 20 active stock markets, with some exchanges more established than others, depending on when they were established. Alongside the rapid expansion of stock markets in the continent, there has also been a significant growth in market capitalization and the number of listed companies. However, with the exception of the well established markets, stock markets in Africa remain thin and illiquid. This study covers four African stock markets namely South Africa, Mauritius , Morocco and Egypt over periods for which data is available. Mauritius Stock Exchange Since its start of trading on the 5th July 1989 under the Stock Exchange Act of 1988, the Mauritius Stock Exchange (SEM) has come a long way. From a pre-emerging market with trading taking place only once a week, the SEM has emerged as one of the leading exchanges in Africa. It operates two markets namely the Official and the Development and Enterprise market (DEM), established in August 2006 to replace the over-the-counter market. The exchange is regulated by the Financial Services Commission. As the second sub-Saharan stock exchange member of the World Federation of Exchanges, SEM operates in line with international standards. In addition, its developing institutional and retail investor base make it an attractive investment destination for foreign investors. The SEM offers quite a limited range of products to its investors and the aim for the next few years would be to increase the range of products offered. The three main indices of the official market are namely the SEMDEX, SEM- 7 and the SEMTRI. As at 30 June 2009, some 40 companies, with a market capitalisation of Rs 130.77 bn, are listed on the Official market and 52 companies, with a market capitalisation of Rs 45.41 bn, are listed on the Development and Enterprise Market (DEM). The SEM maintained an upward momentum, amidst typical market fluctuations, until the end of February 2008. The total market capitalization of the Official Market and the DEM was Rs 173.1 bn at end 2007. This is in line with the levels observed in well-established emerging stock markets. However, like other exchanges, the SEM experienced market volatility since the start of the financial crisis in September 2008. The main pillars of the Mauritian economy were adversely affected and this reflected on hotels and banks stocks listed on the SEM. The market then picked-up by mid-March 2009 on the back of interest rate cuts and stimulus packages put forward by the Government of Mauritius. Johannesburg Stock Exchange The Johannesburg Stock Exchange (JSE), regulated by the Financial Services Board under the Securities Services Act 2004, is the largest exchange in Africa and among the top twenty largest in the world in terms of market capitalisation. JSE Securities Exchange existed since November 1887 and was incorporated as a public limited company on 1st July 2005, pursuant to its demutualization. Since then, the JSE has evolved from a traditional floor based equities trading market to a modern securities exchange providing fully electronic trading, clearing and settlement in equities, financial and agricultural derivatives and other associated instruments and has extensive surveillance capabilities. Technical agreement with the London Stock Exchange (LSE) enables dual primary listings on both exchanges since 2001. Between the listed entity and its trusted trading platforms the South African economy becomes an active hub of activity where expansion is encouraged, businesses are enhanced, performa nce is driven and shareholder value is created. The JSE currently operates four boards for the equities market and the South African bond market is a leader among emerging-market economies. The main market indices are Top 40, Industrial 25, All Share, Oil and Gas Index. As the gateway to Africas economy, the JSE provides the link between international markets and the continent. In 2008, a daily average of 334 million shares was traded on the JSE. At year-end, there were 992 listed securities on the JSE with a total market capitalisation of R4,514 billion compared to R5,696 billion in 2007. Casablanca Stock Exchange Founded in 1929, the Casablanca Stock Exchange (CSE) in Morocco is relatively modern, having experienced reform in 1993. The exchange is well regulated by the Conseil Deontologique des Valeurs Mobilieres (CDVM). Originally, CSE had the Index de la Bourse des Valeurs de Casablanca (IGB) but this was replaced on January 2002 by two indexes: MASI (Moroccan All Shares Index) which comprises all listed shares, allows to follow up all listed values and to have a long-term visibility and MADEX (Moroccan Most Active Shares Index), comprisi

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Fast ‘n Fresh Premium Ice Cream Parlor Fast ‘n Fresh Ice Cream â€Å"Fast ‘n Fresh- - good for you!† Statement of Purpose   Ã‚  Ã‚  Ã‚  Ã‚  The purpose of this business plan is to support a request for a 75,000 five-year bank loan to purchase equipment and inventory as part of the financing for a start-up sole proprietorship, Fast ‘n Fresh Premiun Ice Cream Parlor. The business will be owned by Daniel W. Beese and will be located in leased space at 858 Success Ave in the new Riverside Faire shopping center, Jacksonville, FL 32211. The owner will provide a minimum of 75,00 in initial equity.   Ã‚  Ã‚  Ã‚  Ã‚  The business will serve healthy and premium ice cream, yogurt, sandwiches, and nonalcholic beverages to the generally upscale target market of Riverside Faire. Based on the financial and competive analysis presented in this plan, Fast ‘n Fresh Premium Ice Cream Parlor will be sucessful.   Ã‚  Ã‚  Ã‚  Ã‚  It is anticipated that Fast ‘n Fresh Premium Ice Cream Parlor will become established in Jacksonville, FL within two years and will become known throughout the North Florida area within five years with the potential of multiple locations. The Fast ‘n Fresh Premium Ice Cream Parlor’s distinct logo, it’s reputation for fast service and only the freshest ingredients, plus it’s slogan, â€Å"Fast ‘n Fresh- good for you!† will provide a distinctive competive edge.   Ã‚  Ã‚  Ã‚  Ã‚  The owner, Daniel W. Beese, has founded three highly successful food service businesses in the North Florida area. The owner holds an undergraduate degree and a MBA from the University of Florida. The Business Description   Ã‚  Ã‚  Ã‚  Ã‚  Fast ‘n Fresh Premium Ice Cream Parlor will be a start-up ice cream parlor located in leased space at 858 Success Ave in the new Riverside Faire shopping Center, Jacksonville, FL 32211. A ninety-day option has been taken on this location. The estimated opening day is April 2002.   Ã‚  Ã‚  Ã‚  Ã‚  Daniel W. Beese will own the business as a sole proprietorship. Each of the business owned by Daniel W. Beese has broken even after only six months and was sold for a minimum of three times the owners investment. Fast ‘n Frsh Ice Cream Parlor will be an upscale restaurant selling premium ice cream, yogurt, sandwiches, and hot... ...ations in Jacksonville, FL. The closest Superior Flavors is four miles away . Superior Flavors is well known for their creative yogurt and ice cream flavors. Their products are priced moderately and they do not serve sandwiches. Superior Flavors has a competive advantage with it’s name recognition. Fast ‘n Fresh has a advantage beacuse it offers sandwiches. Personnel   Ã‚  Ã‚  Ã‚  Ã‚  The business will operate using local University, Community College, and high school students as it’s principle employees. This will reflect a youthful, invigorating image consistent with its â€Å"Fast ‘n Fresh -- good for you!† slogan. The manager will be an experienced person from one of the owner’s other businesses. A special employee benefit will be Fast ‘n Fresh Premium Ice Cream Parlor scholarships covering tuition and books. This offer will only be good after employees complete the ninety day probation period. The majority of the employees will be part time with a full time manager. Student employees will earn 6.50/hr with oppurtunities for pay increases. The manager will be paid 10% above prevailing salary levels. A policy of promotion form within will be adopted.