Cultures Research Assignment Essay

As requested, here is the research assignment describing the culture of Mexico, Japan, and Kenya. This assignment will help guide you in understanding the basic communication styles, business etiquettes, and conflict management styles within their corresponding countries. Sincerely, Christian, Candace, and Fabiola Mexico As you travel to Mexico, there are a few tips you should consider to ensure a smooth visit. The communication styles, business etiquette, and conflict management styles vary differently with whoever you are dealing with. Mexicans place great value upon personal relationships. You should always properly address the appropriate Mexican within the organization. If they do not retain a professional title, then always address them with a courteous Mr. Mrs. or Miss (Senor, Senora, or Senorita, respectively). Business attire resembles that of the rest of North America. Men will usually shake hands during greetings, whereas Women will often pat each other on the right forearm or shoulder. Mexican men may exchange a hug, called an â€Å"abrazo†. Usually used among closer acquaintances; it is a sign of good will. To avoid being pushy or rude, never use a direct â€Å"no† for a response. Disguise the â€Å"no† within a â€Å"maybe† or â€Å"we’ll see†. If a conversation topic is outside the purpose of the business meeting, refrain from such topics as Mexican Politics, the Mexican-American war, and comparing Mexico unfavourably to the United States. You may, however, cover such topics as the City and its people, culture and history, and Mexican landmarks. It is not unusual for Mexican business meetings to take place during breakfast, lunch, or dinner. In Mexico, lunch is the biggest meal of the day and it can last for several hours. Dinner is usually served around 9 pm and is usually a light meal. The conflict resolution style used most frequently in Mexico is either by accommodating or by compromising. Japan Today, working in this fast-paced business environment, allows individuals living in different cultures to have business interactions with new clients and build a network of international colleagues. In Japan, they value business people that represent themselves as trustworthy and humble. Japanese primarily use the collaborating conflict management styles in the business environment. Collaboration generates new ideas, and allows both parties to effectively cooperate to on focuses on building a team. In the Japanese culture it is common for business people to ask direct questions with a new person business partner in order to familiarize themselves with one another. At the beginning of a meeting, when business cards are exchanged, a person must bow slightly when handing out their card, and they should place the Japanese translation facing up and toward their business partners. In Japan, business meetings have seating arrangements which is always determined by the status of the participants. Therefore, as a guest you will be directed to the appropriate seat. Always remember, to wait for the head executive to take his/her seat before you will be seated, also when the meeting is finished wait until the head executive leaves his seat before you can exit the room. Japan has similarities and differences in compared to North Americans; however by becoming aware of Japan’s cultural norms it will be easier to understand Japan’s business etiquettes. Kenya Kenya has different business interactions than what we have in North America. The most common greeting in Kenya is by handshake. When greeting an elder or someone with a higher status, lower your eyes and grasp their right wrist with your left hand while shaking hands to demonstrate respect. Right after the hand shake they typically greet you with â€Å"Jambo?† which means â€Å"How are you?† It is mandatory to ask about family, health, and business right after the handshake, rushing or skipping questions will be seen as poor manners and rude. Unless specified by the person, greet them with their professional title followed by their last name. Kenyans mostly have a compromiser, and avoider conflict management style. Kenyans often use stories, metaphors or analogies to get their points across. Direct statements make them really uncomfortable. Kenyans will say what they think it is expected to be said or agree with someone, even if it is the complete opposite in order to not embarrass the other person. Showing anger during a conversation in Kenya it is seemed as a sign for mental instability. When exchanging business cards present and give them with two hands. Following these rules of etiquette when conducting business will result in achieving a successful meeting.

Play and Game Essay

The title of this article kind of makes it seem like I’m about to encourage you to cheat, but that’s not what I’m here to do. I’m here to tell you what you can do when it comes to poker that allows you to get ahead of the game. While some of these tips might not be necessarily applicable to online poker, for poker where you are sitting around a table, these tips can tip the scales into your favor. Know the People If you find yourself at a table somewhere where you don’t know the other players, take a little time to know the tendencies of each player. One might only bet big if he has a good hand, one might be very hesitant no matter what card he has and the other might flick his hair when he is lying. Every single person at that table has a ‘tell’ for when they have something good or for when they are bluffing, especially in Poker, when you are all trying to beat each other. Take some time, get to know the people at the table and even get them talking. It could create a way in which you can win more money, just from being able to read the other players. Be conscious of your own tells If you have the chance, play a friendly game of Poker and have a friend watch you as you play. Have them after the game tell them what you are doing in the way of body movement depending on the hand you are on. It’s extremely important to know what you do, and be able to stop it. Especially if you know you touch your face when you might be able to use this to your advantage in ways I don’t even want to explain. While these two tips don’t work online, they can change the balance in your favor during an offline game of poker. Just Give Up If it is not your night, if you have been fighting with your significant other, just don’t play. Whether offline or online you might feel the urge to do so, but try to resist. While it might act as your stress reliever; your mind will not focus on the game and in a game where your money is on the line, this is a serious issue. From here you have to make sure to change any habit that you think is costing you money, whether that is staying up until 3 in the morning to play and feeling fatigued while playing or not drinking enough water. If you feel you aren’t in peak Physical condition, don’t bother playing. It’ll end up being a waste of time and money. Know the Rules; Know the Hands. In Poker, the best hand is a four of a kind and an ace combination. That is the best possible hand (figuratively) but the probability of getting it is very low. Know this when you go into a game and you will see your play improve dramatically. Know what you can have and what your opponents can have. Use probability and their reactions to make sure that if you are going into a hand that you can win, but going into a hand that is a calculated risk and has a chance of winning is better than hoping for the best. Just watch your play and keep everything in mind. Poker is as much a game of outwitting your opponent as staying mentally sharp yourself. You have to know what to do and when to do it. You have to make sure you are watching your own play as well as others. You have to know when to ‘hold’em’ and when to ‘fold’em’ Author Bio: Jeremy Henderson is an expert in all forms of poker and this is possibly because he is so passionate about the game. His expertise has helped him win at a number of tournaments and in turn he has made a comfortable living playing the game. He is also a voracious reader and an avid writer.

Marketing Essay Example | Topics and Well Written Essays - 750 words - 49

Marketing - Essay Example In addition to Andrew’s competitive market analysis could be seen as a huge opportunity by increasing awareness through a different target audience, product development and to avoid the retaliation of competitors. However stealing competitor’s clients could result in the retaliation of other competitors on the long run and an increase in costs. Overall in this case SPARK has more opportunities than problems to deal with (Quinn, 56). The company tends to spend a lot of money in marketing their services. The aim is to draw the attention of clients who would somewhat not think about insurance. Professionals say a number of people only consider policies when they are befallen with an accident, purchase a new car, move, or renew their current agreement, which normally happens twice a year, at most. This otherwise could led to poor sales profit of the company which has devastating effects to its economic growth. The advertisement mean to be used should be those that can reach the majority of the people. Because of this, SPARK Company lacked correct management where the means used in the advertisement were not of availability to all the esteemed and prospective customers. This reduced their selling power hence a reduction in the profits gained by the company. This calls for a changing in its strategic management so that newer ways could be obtained to facilitate maximum publicity so as all the clients can be reached a nd may develop interests in investing with the company (Quinn, 78). The reduction in interest earned by the company is articulated to poor management and management strategy taken by the company in the advertising sector. The advertisement is always the key to any business. This is because advertisement is always the selling strategy of the company as it helps publicize itself to its prospective customers. For any business organization or firm, advertisement helps to bring

Returning to the Trenches 1914 by C.R.W. Nevinson Essay

Returning to the Trenches 1914 by C.R.W. Nevinson - Essay Example While in the process of recovering he made several paintings based on his wartime experience with the army in France. In his own words, he confirms to have seen the Great War as an event that was so tragic. Nevinson still made the argument that the only way to express violence, brutality and the crude form is to use the futuristic technique. This technique is used to express emotions that appear in battle fields in Europe. This is clearly seen through his painting called, Returning to the Trenches, which he painted concerning the Western Front. One of its critics, P.G. Konody on the 14th March 1915 noted that â€Å"returning to the trenches† is rather a different but interesting picture where he found an extreme formula for the rhythm of a marching body, which is of a French infantry man who is armed fully. Shown first during the Galleries exhibition in Leicester the year 1916, Returning to the Trenches was among Nevinson’s paintings of the Great War that are recognized immediately. The futurism language that the artist proclaimed prior to 1914 is clearly carried in the image of the column of marching French soldiers together with the recurring pattern of the soldier’s legs and the exaggeration and animation of their movements by the extended force lines.2 The use of such manner by Nevinson, however, becomes more powerful in the monochrome of etching by combining the experimental techniques used to express movement with a great emotive subject. This kind of combination is able to simultaneously suggest.

Using ACE to Improve Communication Results Case Study

Using ACE to Improve Communication Results - Case Study Example I would also issues a direct answer to Q2 and inform the employees that, attending the workshop is very essentials because the management plans to revise the working procedures and those that fail to adhere to the new working conditions might be laid off. The internal website is reliable and covers a wider audience as opposed to using the Memo. The information communication will reach to the employees present and those that are absent. In addition, the information provided is detailed and the employee’s questions and objections are responded to before even they ask them. In essence, the information provided is clear and can be reviewed from time to time, as opposed to using the Memos which are issued once. Even though, most companies may prefer using company’s internal website in communication, it is not a reliable communication channel. Some employees may not get a chance to visit the website. Together with that, those that are not within the company and do not have an access to the internet may not get the information. In addition, in case the websites breaks down, the communication also breaks down and it becomes difficult to reach out to everyone. It is an efficient way of communicating to each employee since the management is aware that every person is aware of the meeting held. The employees prepare in advance and lack an excuse of failing to attend. It is a clear indication that the meeting is vital and intendance is least expected. It is ineffective and one is not quite certain to reach out to all the employees. There is likelihood that the absent employees may not get the information. It is expensive considering that memos are to be printed and issued to all the employees. In connection to that, it is tiresome to address a memo to each and every employee within the company. The information sent via the email is detailed and responds to the possible questions and objections that the employees might have. Also, employees have a chance of asking

Analyse and model engineering situations and solve problems using Math Problem - 1

Analyse and model engineering situations and solve problems using Ordinary differential equations - Math Problem Example This empirical observation coincides to the Newton’s Law of Cooling which states that â€Å"the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature.† For instance, when a hot metal ball is placed in a bath of tap water at temperature of T0, it gradually cools. In this process which takes time to complete, naturally the metal ball gives off heat to the surrounding water so that the bath gets warm due to the heat released to it. However, as time proceeds, since the bath of water is open to the larger environment at T0, the system consisting of it and the material it contains would in time establish equilibrium with its environment. In which case, the Newton’s Law of Cooling applies such that, for the heated object being cooled within a room, the temperature of the hot body changes so that it approaches the room’s temperature which is T0. b. Formulate mathematical model for t he cooling process. According to Newton’s Law of Cooling with which the problem statement proves to be consistent, a first-order differential equation may be set up as follows: = -kT where ‘k’ refers to the constant of proportionality. The negative sign accounts for the difference in temperature since the object being cooled would have a lower final temperature compared to its initial temperature. Then on solving the equation: = -k Where Tf = final temperature difference T(t) - T0 Ti = initial temperature difference T1 - T0 Here, T0 = ambient room temperature T1 = initial temperature of heated object T(t) = temperature of the object (under cooling) at anytime ‘t’ So that upon evaluation of the integral, ln Tf - ln Ti = -kt By exponent property, ln = -kt ---? = ---? = Then, substituting expressions for Tf and Ti: ----? T(t) - T0 = (T1 - T0) 2. At time t = 0 water begins to leak from a tank of constant cross-sectional area A. The rate of outflow is pro portional to h, the depth of water in the tank at time t. Write the constant of proportion kA where k is constant. a. Analyse the tank leaking process. Since water leaks out of the tank from an initial height say h0 which corresponds to water volume of V(h0) in the tank, the finite change in this volume per unit change in time, beginning at t = 0 would be (?V/t). The tank is not being filled in so this merely represents the rate of water outflow which is proportional to the water depth in the tank. Essentially, the water depth may be expressed as the finite change in height h(t) - h0 as the water leaks out of the tank where h0 refers to the initial height in the tank and h(t) is the height of the water measured at any time ‘t’. b. Formulate mathematical model for the leaking process. The leaking process may be mathematically modelled as follows: = - k A ?h in which A pertains to the constant area of cross-section through water depth The factors kA serve as the constant of proportionality and the negative sign is used to signify the value of h(t) that is lower than h0. For depth ?h = h(t) - h0, it follows that ?V = V[h(t)] - V(h0). Thus, = -k A [ h(t) - h0 ] which on arranging yields to: Write conclusions based on your formulated mathematical model for leaking process. Task 2 – Learning Outcome 4.2 Solve first order differential equations using analytical and numerical methods. 3. Find the solution of the following equations: a. Separating variables, = t dt Integrating both sides, let u

Race and the White American Community Term Paper

Race and the White American Community - Term Paper Example One factor that is common amongst all people in my community is that we have all immigrated to America three, four or five generations ago. We have been struggling over the generations in order to decide whether we want to adopt the identity of a pure American or at least remain, in part, associated with our background. There are few people amongst our community that is reluctant to break ties with their original homeland and thus, introduce themselves to the society as Italian Americans, French Americans or Scottish Americans. In my own family, we prefer to be called Americans, although we are originally Dutch. A vast majority of White Americans like me choose to be called Americans because this is what we are today. My ancestors were Dutch, but I am as American as anybody with the ancestors residing in this place for centuries is. In an attempt to adjust in this society, my ancestors have been working quite hard trying to dismantle their original identity, and I want to take their efforts to a further level. From the very moment my ancestors entered America, they were strongly urged by the society to forget their past, their original language and also make sure that we don’t get to learn or speak that. ...   Many people in my community are xenophobic, and they have the most unusual and strangest reason for being xenophobic than anyone can imagine. Conventionally, people develop xenophobia because they fear that the immigrants would consume the job and other opportunities that would otherwise have been available to them, but in this case, people of my community are xenophobic because they think that in-pour of the immigrants into the US from all parts of the world would suppress white Americans as a community. White Americans have conventionally maintained an edge over other races in America because of the white American majority. Whenever we talk about minority, we generally mean the people of color. However, with the rapid increase in the number of immigrants, multiculturalism is heavily cultivating in America and people of my community fear that one day, the population of the people of color would be so much that it would be sufficient to outnumber the white Americans as a majority . Thus, people of my community are xenophobic because they see themselves as a minority in the near future (Blake, 2011). This is the fundamental reason why many amongst them want to make racism a norm because they see the display of racism as a way out of the problem. I am anti-racist. I am a white American but my thoughts are way different from those of the majority of people in my community. When I tend to study the cultural experiences of people belonging to other races, I find that they are quite inconsistent with the way we suppose a democratic nation to be.  

Sociology Assignment Example | Topics and Well Written Essays - 1250 words

Sociology - Assignment Example Similarly G.S. Thompson notes that education is how the environment influences an individual to bring about permanent changes in the behavior as well as habits of an individual. Therefore, the term education is a pedagogical process as well as a component that nourishes the body, mind, soul of ignorance. This study focuses on different key aspects as well the as the context of education. This is coupled by objectives and importance of having education in place (Brayl & Murray, 1998). The concept of education This study views education in two aspects. These are the narrow aspect and the wider aspect. Narrow aspect In the narrow education aspect, the field of education is necessary in imparting instructions in schools or colleges. Here, there is direct involvement between the teacher and the student interacting with one another. There is a well stipulated order in which the education process has to be delivered. For instance, the key areas of focus include; objectives of education, cur riculum, teaching methodology, including discipline in the educational process as well as application of evaluation techniques. The narrower aspect of education is purposefully directed to the development of a child through schooling. ... According to Dewey, education is the progressive acquisition of experiences and abilities in which one incorporates throughout his life in the control of environment as well as reaching the limits of possibilities. These two approaches are very important in development of human beings in particular. Generally, the understanding of the concept of education can be viewed in the most appropriate way. There are two concepts of education that are most relevant in the contemporary human development. First, we have the ‘Banking concept’ and then the ‘Modern concept’. The modern concept In the modern concept of education, there is a great emphasis on the shift individual development to national development. Here, education does not only focus on the social change but also on the national development. It is believed through national revolution, there will be realization of economic gains. This is a concept that most countries have adopted and others being encouraged to adopt in order ascertain national development that is now thriving the development process of the modern countries. This has been particularly important in social, economic and political interests of national development. The banking concept The banking concept of education is teacher-student interactive concept. This is the most important in the formal or non-formal modes of education. The teacher is perceived to give or deposit knowledge while the student is the receiver of that particular knowledge. The teacher communicates and gives instructions as the student listens, memorizes and practices the communique of the teacher. Here, the teacher uses evaluation methods to find out if the communicated information was well incorporated by the student. The information that would have been well

Week 5 Essay Example | Topics and Well Written Essays - 250 words - 2

Week 5 - Essay Example In some cases however, there have been reported cases where terrorists form political parties, which makes it easy for them to manipulate people behind democratic symbols. Terrorists desired outcomes require them to use force in order to induce fear to anyone who does not agree with them. For instance, ISIL executed two American journalists, in order to warn the American Government about its activities in the Middle East (Steinsson, 2014). In other cases, the Alshabaab from Somalia have become a common threat to the Kenyan Government. In April, they attacked a university college in Garrisa town and murdered 148 students, with the aim of threatening the Kenyan government to withdraw its military forces in Somalia. Between 1960 and 1980, the Tupamaros used violence as a strategy to turn things around in Uruguay. In their strategy laid down by a Latin American Revolutionary Carlos Marighela, the terrorist organization used bombing and widespread killings to turn the government against its citizens. The government quickly reacted by infringing civil liberties, as a tactic to combat the attack and further threats (Kydd & Walter, 2006). However, the public ended up perceiving the government as an enemy and not the terrorist organization. Currently, the same strategy is being used in Peru by Shining Path and Ulster’s PIRA, though on low scale. In most cases, use of violence in achieving their goals looks like the most viable method used by terrorist organizations. It does not matter whether they are aligned to a political party or a religious cult. Their motives come out clear through executions, kidnapping, inhuman acts, piracy, and propaganda. However, whoever accepts their demands suffers further losses because they take control when their rival submits to their terms. Steinsson Sverrir. (2014, Jun 22). Is Terrorism an Effective Way to Attain Political Goals? Retrieved Jun 7,

Black Feminist Theory Essay Example for Free

Black Feminist Theory Essay Sula is Morrison’s main character and is a perfect example of a Liberated woman. According to Lois Tysons definition of a Liberated Woman, Sula has â€Å"discovered her abilities, knows what she needs, and goes about getting it. † Along with all these activities, comes pride and independence. It began when Sula was younger as she had Nel, her best friend, by her side. â€Å"In the safe harbor of each others company they could afford to abandon the ways of other people and concentrate on their own perceptions of things,† (55). Her friendship gave her the comfort to be herself and confident on acting on her own terms. Sula continued this attitude into adulthood but not everyone agreed with her actions towards getting what she wants. Sula leaves for 10 years to go to college and live her life beyond the Bottom. When she finally comes back, she and Eva get into an argument. Eva brings up her disappointment in Sula for not settling down with a family and Sula lashes back with, †I don’t want to make somebody else. I want to make myself, † (92). She displays her aversion to not have anyone dependent on her and she wants to only care for herself. Having a family and a husband, in her opinion, would stop her from getting what she wants or needs and would put herself second in her life. Sula doesn’t want to be tied down and oppressed by a man, she wants to be independent and she’s not ashamed about being the only woman wanting her independence . When Nel finally confronts Sula about her affair with Jude, Nel accuses Sula of being proud but she responds with â€Å"‘What you talking about? I like my own dirt, Nellie. I’m not proud’,† (142). This shows how Nel, along with everyone in the bottom, thinks she’s proud or conceded, but in actuality, she’s just not ashamed of her decisions or life style. Lois Tyson continues the definition of a liberated woman with â€Å"the ‘liberated woman’ has already found herself and likes what she has found. † When sula says â€Å"I like my own dirt† she supports Tyson’s definition because Sula also â€Å"likes what she has found. † Sula’s independence, and her pride in being so, fully supports Tyson’s complete definition of a Liberated Woman. Nel’s character fits into an Emergent Woman as she â€Å"[comes] to an awareness of her own psychological and political oppresion usually through a harsh experience of initiation that makes her ready for change. † On Nel’s trip to meet her grandmother, Nel witnesses her mother’s â€Å"custard† being revealed. From then on Nel â€Å"resolved to be on guard- always. She wanted to make certain that no man ever looked at her that way. That no midnight eyes of marbled flesh would accost her and turn her into jelly† (22). Ashamed of the â€Å"jelly† or the weak substance â€Å"custard† that Morrison also associates with Helene, Nel makes certain that no man shall look at her, and make her into anything weak. In this secne, she becomes aware of her mother’s oppression and makes the decision to never allow it in her life. At the end of their trip, Nel lays in bed thinking about the possibility of ending up like her mother. To establish her independence separate from her mother, Nel states, †I’m me. I’m not their daughter. I’m not Nel. I’m me. Me,† (28). As an Emergent woman, she demonstrates her ability to make her own choices and establish her own independence. Years Later, filled with resentment towards Sula, Nel visits ill Sula in her deathbed. For years, her depression was encouraged by the thought that her husband was taken and now she is alone to take care of her children. She believed it was all Sula’s fault and she hated her for this, but one day she confronts Sula about taking Jude away from her, and Sula asks â€Å"What you mean take him away? I didn’t kill him, I just fucked him. If we were such good friends, how come you couldn’t get over it? † Nel starts to think of the idea of it not being Sula’s fault, that Jude was the one who put her through the heart break of being alone. Sula dies and Nel attends her burial. There she realizes that â€Å"all that time, [she] thought [she] was missing Jude,† but actually, she missed her friendship with Sula (174). Their friendship was more supportive than her marriage as Sula helped bring out the ’me’ in Nel that she lost in her marriage to Jude. Her epiphany helps her to notice how Jude was the one who hurt her , and now she can move on. Toni Morrison portrays Eva Peace as a suspended woman. According to Mary Helen Washington, a suspended woman is a â€Å"victim of men and of society as a whole, with few or no options. † Morrison starts off Eva’s story with her discontented marriage to her husband, BoyBoy. BoyBoy â€Å"liked womanizing best, drinking second, and abusing Eva third,† (32). Eva, disappointingly, tolerates all his abuse, because of her dependency on BoyBoy. One day, when he leaves her and their three children, her dependency becomes clear. Being inconsiderate of his family’s welfare, he leaves as his worst affliction to his wife. Now, abandoned with nearly no money,Eva realizes that â€Å"the children needed her† and â€Å"she needed money,† (32). This shows her desperation and how BoyBoy belittled her as she had to beg and rely on the neighbors for basic necessities like food for her children. Her Neighbors â€Å"were very willing to help, but Eva felt she would soon run her welcome out† and the fact that she had to continue begging, knowing she had ask for enough, embarrassed her. Eva struggles to raise them on her own and one day her son, Plum, stopps having his bowel movements. When all the stress and pressure gets to her, â€Å"Eva squatted there wondering what was she doing down on her haunches She shook her head as though to juggle her brains around, then said aloud, ‘Uh uh. Nooo,’†(34). Eva leaves her children with her neighbor for more than a year and comes back with one leg, losing the other for money to care for her children. If BoyBoy had never abused or had left her, she would have never been a victim and never would have had to sacrifice her pride and her leg. This proves she’s a suspended woman because BoyBoy’s abuse and abandonment left her with the only option to leave her children and sell her leg, because as a black woman in their society, she had very few options. Toni Morrison exemplifies Mary Helen Washington’s definitions in Nel, Sula, and Eva through out Sula, using their experiences and personalities. Sula’s independence, Nel’s epiphany, and Eva’s abuse all characterize them into their type of African American female character, making Sula a Liberated Woman, Nel an Emergent Woman, and Eva a suspended woman.

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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People from all over come to experience the Grand Canyon National Park, located exclusively in North Arizona. Covered with unexplored caves and valleys, and immense canyons, the Grand Canyon is very well liked for hikers, whether that hiker is experience of a beginner. This park offers recreational events for everyone. Today, the Grand Canyon stretches out to be eighteen miles long in some places. The Grand Canyon has much to offer from hiking along a rough, yet narrow landscape, bringing the family out to camp for a few days, gazing at the amazing scenery, or visiting the Indian reservations. This area contains several ecosystems and also hundreds to thousands of unique plants and animals. â€Å"It contains fossils of corals, crinoids, and brachiopods that indicate warm tropical conditions in a sea that once stretched across the continent. The stone looks different from the red wall, because 500 million years ago the ocean was closer to the ancient continent, and any mud and sand t hat washed off the land mixed in with the lime, making it crumbly and yellow† (Weintraub 24). The rock layers in the canyon make a magnificent color of stripes in the canyon walls that could be seen miles and miles away. Not only is this canyon enormous, but also this vast canyon can be seen from space. Although the canyon is not the deepest canyon in the world, it is known for its tremendous dimension and its vibrant landscape. This terrain reserves more than two thousand archeological sites of Native Americans, who have also resided there for four thousand years. The park itself became a National Park in the year 1919. The Grand Canyon is a stunning place to visit for all ages, and for the family to see the remarkable canyon formed not only by the erosi... ... patches along the river† (Halvorsen 5). Separate from the eroding motion of the Colorado River, the flow of the debris played a major, yet foremost role in the broadening and expanding of the Grand Canyon. All these elements contributed to the creation of the Grand Canyon, which still till this day remains a fascinating story and feature for every one of us, especially geologists, who still have many thoughts as to how the Grand Canyon was even formed. Rock layers that have formed the Grand Canyon, as everyone has seen, are created due to the sedimentations of the seas and the oceans. All of this is precisely evident of the fact that the rocks that are found on the sides of the canyon are made of sedimentary rocks. Scientists have said that the erosion is how the Grand Canyon was form, but there can always be something new to every evaluation of the Grand Canyon.