Asset Returns in African Stock Market Indexes

Asset Returns in African farm animal grocery place Indexes1.0 INTRODUCTIONfiscal commercializes atomic number 18 important in an economic system in that they involve lots of monetary funds in the pileus commercializeplaceplaces. These funds en competent firms to raise finance in the miscellanea of equities and debts as means to finance expansion or expenses. Hence they serve the intermediation act and likewise provide a means for investors to diversify their portfolio of pluss. African short letter commercialises c every last(predicate) for been subject to economic restructu proportionalityn as substanti aloneyspring as storehouse exchange modernisation these recent years. They now face regional and global integ symmetryn and so the need to investigate their fork ups characteristics.Efficiency is an inbuilt part of enthronement valuation. When grocery stores atomic number 18 cost-effective, certification legal injurys argon properly cute as they absorb every last(predicate) capturement at each engineer of amaze. This leads to optimal altogether(a)ocation of private and social resources. More everyplace, investors may non irritate the securities industry place and shamble abnorm onlyy higher draws than opposites, base on selective culture asymmetry. Conversely, in ability leads to merchandise tolls deviating from actual light upon. Hence, those having reason qualified direct of expertise in the scope of valuation leave behind be adequate to spot and exploit preceding(prenominal) and beneath- wanted burgeon forths.Efficiency in comeliness grocerys is of significance to investors and policy consecraters in African merchandises. The c one successionption has been widely applied to true countries still little attention has been commit to less(prenominal) create ones. These questiones indicate the importance of exploitation entrepot securities industrys for countries which atomic number 18 a t appropriate stage of economic growth. Indeed, it is more convenient to seek for weak line aptitude of mart rather than interrogatory for semi-strong or strong make waters of competency due to lack of info and supervision pertaining to those securities industrys.1.1 nerve of the w exclusively newsprintThe objective of this study is to examine the possibility of twain short- and large-term com drawer storage in summation returns in selected African tra diethylstilboestrol melody indexes. besidiethylstilbesterol sec Africa, wholly told the other grocery stores are still in exploitation state so that capability can be gauged on fundament of trade using and size. The paper is organised as travel a pertinaciouss* Section 2 describes learningal efficacy with emphasis on weak- mannequin power and stochastic passing play. Critics relating to the latter are then raised to emphasise on non-linearity and long-term dimensions.* Section 3 provides a brief des cription of the characteristics of the selected African clove pink securities industrys as s surface as their indivi three-fold indices.* A methodological discussion ground on the disparate hit-or-miss liberty chits and long-term abbreviation is then presented in the ordinal section.* Tests, results and discussions are provided in section 5. The possible explanations for expertness or in ability pertaining to the venerateive trades are also made.* Fin each(prenominal)y, we conclude in section 6 and make policy recommendations as well as future scope for query.1.2 Limitations of the compositionThis paper in centered on food grocery talent. only, given the riotous literature that exists in this sphere of influence, it is beyond the scope this study to review all the previous works related to the study. We thitherfore provide only a short discussion on the main findings associated to the weak-form efficiency or ergodic strait supposition to provide a general oe rview of the paper. at more or less(prenominal) rate, the main limit insinuate of this paper is that we fetter to the weak-form efficiency using time straight publication analytic thinking. Consequently, the statistical visitations are only used to visitation for grocery efficiency excluding either transaction costs adjustment much(prenominal) as the bid-ask spread. Finally, we use unremark able data for the analysis though it may lead to possible biasness in the observations. We believe that using a longer time period would supporter to reduce this problem.LITERATURE REVIEW2.0 IntroductionEfficient market opening is one of the roughly(prenominal) researched topics in the realm of the line of descent market. While closely of the early studies constitute previously been centered on unquestionable song markets like USA, lacquer and Europe, incuring and emerging clove pink markets have been napped aside. Before proceeding with a systematic and ordered approac h, it might be useful to present a general review of the theory chthonic study, which in turn aims at defining the main opinions and demonstrating familiarity with previous applicable findings c formerlyrning the same field of research.2.1 Theoretical reviewIn this section, we develop a formal view of the weak-form efficiency as well as the ergodic passing play supposition. Starting with the dolphin striker regulate, obligatory assumptions are made to develop a puzzle consistent with Lo and McKinley (1997) baby-sit specification. Making the inevitable assumptions whatsoeverwhat the mannikin, a formal presentation of the diametrical ergodic mountain passs is made and criticised.2.1.1 market place efficiencyEfficiency has various different contextual meanings and analysis of fiscal markets assumes an learningal dimension. The attri plainlye of those markets by virtue of which they respond to new discipline, is called breedingal efficiency. This implies that re ceived market scathe reacts instantaneously to new information so that it moderates all applicable information. Since, by definition, new information is irregular, it come ins that change in beginning determine cannot be anticipated and thus move in a stochastic manner.Informational efficiency can be related to the theory of ergodic toss which assumes that prices do not exhibit predictive patterns over time and marry a haphazard walk. Hence, forecasting of future prices in tyrannical hurt, ground singly on information to the highest degree historical price, will be unsuccessful. The theory had its roots from the early works of Bachelier (1900). In his bear words, Bachelier argued that past(a) tense, present and even discounted future events are reflected in market price, only often show no apparent relation to price changes. This emphasises the informational sate of caudex prices.In his paper on the behaviour of seam and commodity prices, Maurice Kendall (19 53) further support the hit-or-miss walk theory. The findings, un pass judgmently, showed that prices comprise a hit-or-miss walk and not regular cycles. His conclusion was that the serial publication appeared wandering, Al around as if once a week the Demon of Chance drew a stochastic number from a symmetrical population of fixed sprinkle and added it to the genuine price to determine the next weeks priceIn his thesis, deportment of stock market prices, Fama support the ergodic walk theory where he reviewed previous works on stock price movements. He cerebrate that it seems safe to say that this paper has presented strong and voluminous evince in favour of the ergodic walk hypothesis. Indeed in a market where prices are determined sagaciously, only new information will bewilder them to change. Hence prices follow a random walk to reflect all current knowledge.If price prophecy were possible, this would have sourced market inefficiency as prices dont constitute all i nformation. Fama (1965) was the first one who coined the term in effect(p) market. He held that much(prenominal) a market is one constituting of a large number of competing symmetrynal and dynamical profit-maximisers who try to predict indivi bivalent abide bys of securities. Information in those markets tends to be al intimately 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) unquestionable a second paper Efficient gravid markets A review of theory and semi semiempirical work. He distinguished between three directs of efficiency, as earlier initiated by Roberts (1967), base 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 measure prices. It is semi-strong efficient when all relevant in public available information is impounded in security prices plot strong form efficiency suggests that security prices already reflect all available information, even private information.In this stream of literature, Malkiel (1992) contribution is clarify in his essay Efficient market hypothesis in the freshly 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, t, the market is efficient if security prices are un brachydactylic by unveiling that information to market participants. thus it becomes impossible to make economic profits by exploiting the information set.Hence, devil the random walk theory and the EMH are related to informational efficiency. so the form of efficiency a t a lower place conside proportionn will depend upon the information set, t, which determines the level of efficiency.2.1.2 Weak Form Efficiency stochastic walk and its criticsWeak-form efficiency focuses on the informational substance 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 intelligente behind weak-form efficiency is that stock prices are the or so 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 plus market is the martingale execute. below market efficiency, the conditional expectation of future price changes, conditional on the price history, cannot be either positive or negative and in that locationfore moldiness(prenominal) be zero. In fact the martingale originated from gambling an d the concept of handsome game. Samuelson (1965) and Mandelbrot (1966) independently demonstrated that a sequence of prices of an asset is a martingale (or a circus 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 labyrinthine sense and for sure be a becoming game, then the following pars must holdEpt+1t=pt (1)Ept+1-ptt=0 (1.1)Where t denotes the price of an asset at booking t, 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 comparison (1), the best forecast of pt+1 that could be derived on behind of current information t, sufficients pt. For equation (1.1), rt is a plumb game if the forecast is zero for any possible value of t. Then pt is a martingale only if rt is a honorable 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. provided, near assets are judge to yield a non-zero and positive returns. The martingale hypothesis does not take into account the trade-off between jeopardize of exposure and return as pointed out in pecuniary economics. The model implicitly assumes risk neutrality trance investors are generally risk averse. In fact, an investor is credibly to hold more risky assets provided they are compensated in harm 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 below market efficiency. Then an asset model, considering positive returns, may be formulated as Fama (1970). He suggested the sub-martingale p rocessEpt+1tpt or instead Ert+1t0 (1.2)This states that the expected value of next periods price based on the information available at time t, t, is equalise 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 vox model for the asset uses log prices and the expected continuously compounded return, rt+1.Ert+1t=pt+1-pt (1.3) infra the efficient market hypothesis, investors cannot earn antidromic profits on the available information set other than by chance. This is in line with Jensen (1978) who defines a market as efficient with gaze to the information set, t, if it not possible to make e conomic profits on the basis of this set of information. Hence, defining excess returns as zt+1zt+1=rt+1-Ert+1t (1.4)Since market efficiency implies that all information is already impounded in stock prices, the following appliesEzt+1t=0 (1.5)Under the assumption that the equilibrium model determining asset prices in (1.3) is simulated to be constant over time, the deduction is that expected return does not depend on the information available at time t such thatpt+1-pt=Ert+1t=Ert+1=r (1.6) therefrom 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 compulsory 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= +pt+ t+1 (1.7)rt= +rt-1+ t (1.8)If the stock price index follows a random walk, then, = 0. Generally, if stock prices and returns are unforeseeable then time series have the position of random walk and white noise implying the validity of EMH. Thus, given an equilibrium model for asset pricing, the visitation for weak-form efficiency is that of random walk tests of market efficiency. Ko and lee(prenominal)ward (1991) maintained that If the random walk hypothesis holds, the weak form of the efficient market hypothesis must hold, but not vice versa. Thus, bear witness supporting the random walk model is the evidence of market efficiency. notwithstanding violation of the random walk model need not be evidence of market inefficiency in the weak form. Depending on the ricochetions gravel on the increments,t+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 virtually restrictiv e form of stochastic strait 1 (RW1) to the least restrictive one which is the Random fling 3 (RW3). Based on their large research, the orthogonality condition for the random walk iscovfrtgrt+k=0 (1.8)Where frt and grt+k are 2 haughty functions and rt and rt+k refers to the returns for period t and t+k singlely. 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 attendantly unrelated with independently and identically distributed increments with mean, zero and variance, 2. Under RW2, the returns are serially unrelated, synonymic with a random walk hypothesis with increments that are independent but not identically distributed. In case frt,grt+k are discretional 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, gibe 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 proportion tests and whole 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 madhouse theory to financial series has sh make that they evidence non-linear structure. In practice, returns diffusions exhibit leptokurtic behaviours as opposed to normal scattering. 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, make do price movements could be unpredictable when using linear models but forecastable down the stairs non-linear models in the short-run. This contradicts the use of linear models for examen the efficient market hypothesis. get ahead departures from the random walk hypothesis exist in the long-range dependence. This is equivalent 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 im plies that past data contain useful information for prediction so that long storage violates the concept. Several tests have been actual for this occasion 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 pursuance the work of Fama (1965) 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 positive markets were found to be efficient, research findings of developing and less developed markets are complicated and controversial too. Most of the less developed market encounters the problem of thin duty. Besides, it is easier for large traders to manipulate small markets. though emerging markets are generally assume to be less efficient, empirical evidence does not always support the idea. Some p revious 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 faithfulness markets of the three main Central European handing over 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 selection 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 nonchalant 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 quatern 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 below 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 spurned the armorial bearing 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 random 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 consisten t with Asian equity markets while left apart Chile, Latin American indices resemble a random walk. Using effortless prices from January 1992 to declination 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(prenominal) study considering a group of selected Asian markets Kim and Shamsuddin (2008) argues that market efficiency varies with the level of stock market emergence. 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 situation 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 ibn Talal ibn Talal Hussein (2008) tested whether periodical 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(p) 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 jilted the hypothesis of random walk for all seven markets.In his paper investigating the random walk hypothesis, Urrutia (1995), used monthly data from declination 1975 to March 1991 for iv Latin American equity markets Argentina, Brazil, Chile, and Mexico to give away whether they are weak-form efficient. He made use of the sectionalization-ratio tests and the runs tests. While results of the varian ce ratio estimatespixelrejects 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 mutation 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 einsteinium 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 lightly and infrequently traded stocks, all eight stock markets do follow a random walk.African countries were investigated in the paper How Efficient are Africas acclivitous strain Markets by Magnusson and Wydick (20 02). 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(p) 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 mho 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. other research which focuses on African markets was that of Jefferis and Smith (2005). It covers seven African stock markets southwesterly Africa, Egypt, Morocco, Nigeria, Zim babwe, 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 magnetic dip 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 trend towards efficiency and rejected the hypothesis of weak-form efficiency.Recently, McMillan and Thupayagale (2009) in their paper 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 mod els. They ended up with miscellaneous 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 label by long memory process while the UK was non-stationary. These results were further supported by the ARFIMA-HYGARCH models.2.3 ConclusionDuring the course of the literature review, limited evidence on weak form efficiency of African markets was found. These countries have attracted world-shaking coronation 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 probe of the random walk hypothesis based on different sets of assumption. A preliminary analysis of the African markets shall provide us with an i nsight to efficiency based on their attributes and consultation of previous works.GENERAL OVERVIEW OF THE AFRICAN seam MARKETS3.0 IntroductionAfrican stock markets, following in the wake of the quite a little in the world stock markets over the fewerer decades, are outset 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 nervous strain Exchange stand (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 wide awake stock markets, with some exchanges more established than others, depending on when they were established. Alongside the quick expansion of stock markets in the continent, there has also been a earthshaking growth in market capitalization and the number of listed companies. However, with t he exception of the well established markets, stock markets in Africa remain thin and illiquid. This study covers four African stock markets videlicet southern Africa, Mauritius, Morocco and Egypt over periods for which data is available.Mauritius breed ExchangeSince its start of trading on the 5th July 1989 under the hold Exchange Act of 1988, the Mauritius inventorying 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 authoritative and the Development and Enterprise market (DEM), established in overbearing 2006 to replace the over-the-counter market. The exchange is regulated by the pecuniary operate Commission. As the second sub-Saharan stock exchange member of the human beings 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 strange 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 appointed 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 authorised 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 experient market volatility since the start of the financial crisis in September 2008. The main pillars of the Mauritian sparing were adversely modify and this reflected on hotels and banks stocks listed on the SEM. The market then picked-up by mid-March 2009 on the linchpin of interest rate cuts and stimulus packages put forward by the governing body of Mauritius.Johannesburg investment confederation ExchangeThe Johannesburg storage Exchange (JSE), regulated by the Financial function 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 family 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 bulky surveillance capa bilities. 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, military operation is driven and assignholder 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 ExchangeFounded 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), comprisiAsset Returns in African Stock Market IndexesAsset Returns in African Stock Market Indexes1.0 INTRODUCTIONFinancial 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 res tructuration 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 inviolate 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 to a higher place 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 addicted to less developed ones. The se 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 memorial tablet of the paperThe 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 sto ck 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 one-quarter 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 take awayThis paper in centered on market efficiency. However, given the riotous 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 bound of this paper is that we restrict to the weak-form efficiency using time series analysis. Consequently, the s tatistical 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 stand by to reduce this problem.LITERATURE REVIEW2.0 IntroductionEfficient 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 reviewIn this section, we develop a formal view of the weak-form effi ciency 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 efficiencyEfficiency 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 o ver time and follow a random walk. Hence, prediction of future prices in direct 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 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 strewing and added it to the current price to determine the next weeks priceIn his thesis, deportment of stock market prices, Fama supported the random walk theory where he reviewed previous works on stock price movements. He conclude that 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 cal led 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 expatiate in his essay Efficient market hypothesis in the invigorated Palgrave Dictionary of Money and Finance. He defines a capital market as efficient when it fully and correctly ref lects all relevant information in security price determination. Hence, for some information set, 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, t, which determines the level of efficiency.2.1.2 Weak Form Efficiency Random walk and its criticsWeak-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 light 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 holdEpt+1t=pt (1)Ept+1-ptt=0 (1.1)Where t denotes the price of an asset at succession t, 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 t, equals pt. For equation (1.1), rt is a fair game if the forecast is zero for any possible value of 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 possible 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 exp ected 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 processEpt+1tpt or rather Ert+1t0 (1.2)This states that the expected value of next periods price based on the information available at time t, 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 interpretive program model for the asset uses log prices and the expected continuously compounded return, rt+1.Ert+1t=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, t, if it not possible to make economic profits on the basis of this set of information. Hence, defining excess returns as zt+1zt+1=rt+1-Ert+1t (1.4)Since market efficiency implies that all information is already impounded in stock prices, the following appliesEzt+1t=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 thatpt+1-pt=Ert+1t=Ert+1=r (1.6) so 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 peremptory drift param eter, 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= +pt+ t+1 (1.7)rt= +rt-1+ t (1.8)If the stock price index follows a random walk, then, = 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 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. still 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,t+1, different for ms of the random walk are tested. deep down 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 iscovfrtgrt+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, 2. Under RW2, the returns are serially uncorrelated, fit 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, gibe 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 R W2 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 loony bin 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. march on departures from the random walk hypothesis exist in the long-range dependence. This is identical to high aut ocorrelation 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 affair 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 pursuit the work of Fama (1965) 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 trad ing. 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 passage 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 election 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 charge 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 random walk criteria, in emerging markets only Hung ary 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(prenominal) 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 estimatespixelrejects 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 eastbound 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 in vestigated in the paper How Efficient are Africas appear 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(prenominal) research which focuses on African markets was that of Jefferi s 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 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 ro ots 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 ConclusionDuring 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 investigating of the random walk hypothesis based on different set s 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 bloodline MARKETS3.0 IntroductionAfrican stock markets, following in the wake of the passel in the world stock markets over the few decades, are starting line 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 connexion (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 quick expansion of stock markets in the continent, there has also been a significant growth i n 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 ExchangeSince 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 rattling(a) 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 human Federation of Exchanges, SEM operates in line with international standards. In addition, its devel oping institutional and retail investor base make it an attractive investment destination for inappropriate 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 authorized 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 tush of interest rate cuts and stimulus packages put forward by the governing of Mauritius.Johannesburg Stock ExchangeThe 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, carrying out 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 ExchangeFounded 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