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Return predictability in African stock markets Joe Appiah-Kusia, Kojo Menyahb,* a

Africa Financial Research Centre Ltd., London, UK Department of Accounting and Financial Services, London Guildhall University, 84 Moorgate, London EC2M 6SQ, UK

b

Received 5 October 2000; received in revised form 17 June 2002; accepted 21 August 2002

Abstract This paper models weekly index returns adjusted for thin trading as a nonlinear autoregressive process with conditional heteroscedasticity to investigate the weak-form pricing efficiency of 11 African stock markets. Specifically, the use of the EGARCH-M model allows us to capture how conditional volatility affects the pricing process without imposing undue restrictions on the parameters of the conditional variance equation. On the basis of such a robust model, we are able to reject the evidence in prior studies that the Nigerian stock market is weak-form efficient. On the other hand, we confirm extant results that the markets in Egypt, Kenya, and Zimbabwe are efficient while that of South Africa is not weak-form efficient. We also generate new results, which point to the efficiency of the stock markets in Mauritius and Morocco, while the markets in Botswana, Ghana, Ivory Coast, and Swaziland are not consistent with weak-form efficiency. D 2002 Elsevier Science Inc. All rights reserved. JEL classification: G15; G18 Keywords: African stock markets; Weak-form efficiency; Nonlinearity; EGARCH-M

1. Introduction Studies of return predictability in African stock markets are few and far between even though such markets were established in Egypt, South Africa, and Zimbabwe towards the end * Corresponding author. Tel.: +44-20-7320-1535; fax: +44-20-7320-1557. E-mail address: [email protected] (K. Menyah).

1058-3300/02/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved. doi:10.1016/S1058-3300(02)00073-3

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of the nineteenth century.1 The few studies that exist either include one or two markets such as Nigeria or Zimbabwe, as part of an emerging market sample (see, for instance, Claessens, Dasgupta, & Glen, 1995) or focus on one particular market such as Kenya (Dickinson & Muragu, 1994) or Nigeria (Olowe, 1999). Most of the previous studies—in accordance with contemporaneous approaches, assumed linearity in expected returns, and tested weak-form efficiency with serial correlation, runs tests, and spectral analysis models. Savit (1988) and Scheinkman and LeBaron (1989) among others, however, show that such studies may lack the power to accept or reject efficiency if asset returns are generated by deterministic chaos rather than by a stochastic process. Secondly, the linear models also assume that both the mean and the standard deviation of returns are constant over the estimation period, despite the evidence that asset prices, their variances, and covariances are not constant but change over time (see Christie, 1982 for a review). Thirdly, failure to account for thin trading in the calculation of returns can induce serial correlation in the returns that will confound the results of efficiency tests. This paper addresses the variable measurement and econometric problems associated with previous studies of weak-form efficiency in the markets of Egypt, Kenya, Nigeria, South Africa, and Zimbabwe by accounting for thin trading in the calculation of returns and allowing for nonlinearity and time-varying volatility in the return generation process. The paper also conducts empirical tests of weak-form efficiency in the stock markets of Botswana, Ghana, Ivory Coast, Mauritius, Morocco, and Swaziland that lack such studies. The innovation in the paper lies in the use of data adjustment methods and econometric modelling that have hitherto not been used in the study of weak-form market efficiency of African stock markets. This enables us to obtain robust results that will help to evaluate the findings of prior studies and provide new results for markets that have not been subjected to weak-form efficiency tests. The findings will be useful to those involved in investment decision making in African stock markets. In particular, country and emerging market fund managers concerned about the risk–return relationship in their African market portfolios will be able to identify which markets provide time-varying premium to compensate them for the risks they bear. Others keen to pursue international diversification will increase their understanding of the pricing process in African stock markets (especially those without prior efficiency studies) before committing significant amounts of capital to such markets. Local and other investors may also be able to devise strategies for generating profits from markets that exhibit return predictability. In the next section, we amplify the concept of efficiency tested in this paper and review the literature on weak-form efficiency with a focus on emerging stock markets. In Section 3, the factors that may induce nonlinearity in returns and how thin trading may affect efficiency

1 The Cairo Stock Exchange set up in 1883 was the busiest in Africa until the nationalisation programme of the early 1960s. Stock exchanges have operated in South Africa since 1881 largely to raise risk capital to fund mineral exploitation. The Bulawayo exchange was the first to be established in Zimbabwe in 1896. This and others that were later opened in Gwelo and Umtali were closed by 1924, when mineral deposits which they were expected to raise funds to exploit proved disappointing.

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tests are analysed. The empirical models appropriate for our tests are then specified. Section 4 provides the institutional background to the markets with a discussion of trading systems, trading costs, and foreign portfolio investment rules. In Section 5, we describe the sample and data sources. The empirical results are then reported and discussed. Section 6 provides a summary of the study and outlines its main contributions.

2. Weak-form efficiency in emerging stock markets 2.1. The concept of weak-form efficiency in an emerging market The concept of weak-form efficiency has its origins in the empirical tests for random walks in the changes in a time series carried out by Working (1934) and Kendall (1953). While these studies were essentially statistical in nature, Roberts (1959) provided the intuition for reformulating such results in terms of the standard economic theory of pricing in competitive markets. As a competitive market construct, statistical dependence in security returns is conceived as unexploited economic rent inconsistent with rational investor behaviour in such markets. Hence, the definition of weak-form inefficiency lies in the presence of unexploited economic rents rather than requiring all individuals in a market to be rational and informed. This is consistent with Hayek’s (1945) argument that no single individual can know the information that is embedded in prices. Therefore, the process of aggregating from the individual to the market is likely to be left as a ‘black box’ and the market is described as if it is acting as an entity in its own right in reacting to information. This implies that unexploited rents may exist in a market to induce price dependence not because of investor irrationality but as a result of the considerable costs of acquiring information about the presence of rents and of trading on such information. This conceptualisation of weak-form efficiency may help us to explore some of the factors that might account for the results of the econometric tests. Since the series of past prices is the information required to exploit weak-form inefficiency, the fact that it is not used by investors in inefficient markets may suggest the presence of significant transaction costs such as commissions and other market imperfections such as transfer and capital gains taxes. This way of analysing the issue avoids the presumption (see, for instance, Antoniou, Ergul, & Holmes, 1997) that emerging markets may be weak-form inefficient because they have weak institutional infrastructure.2 It should, however, be pointed out that institutional infrastructure efficiencies are desirable in their own right and ought to be pursued by regulators and market

2 Institutional infrastructure inefficiency exists where: (i) the local culture and political environment are not sympathetic to a market economy; (ii) a sophisticated and well-informed analyst profession does not exist; (iii) there are significant capital inflow – outflow restrictions; (iv) ineffective regulatory framework and inadequate investor protection system; (v) market participants have unrealistic expectations about the risks and returns from investments; (vi) insider trading rules are nonexistent or not enforced; and (vii) efficiency of stock price behaviour is not rigorously and regularly researched or tested through practices such as technical analysis trading.

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participants. They are, however, neither necessary nor sufficient conditions for weak-form efficiency in emerging markets. It is our view that rational investors are not likely to allow profitable opportunities to go unexploited simply because they are somehow not inclined to benefit from a weak institutional infrastructure. We therefore argue that there are real impediments to the exploitation of profitable opportunities, which induces the presence of price dependencies in some markets. 2.2. Prior studies of weak-form efficiency in emerging stock markets Market efficiency tests date back to the work of Kendall (1953). Fama (1970) described weak, semi-strong, and strong form tests to reflect the taxonomy of information sets in respect of which the efficiency concept can be defined. These were re-characterised as return predictability, event studies, and private information tests in Fama (1991). This study focuses on return predictability or weak-form efficiency using time series tests. It does not undertake anomaly tests that focus on seasonal or cross-sectional patterns in rates of return. A growing body of literature exists on weak-form efficiency on small and emerging stock markets. Barnes (1986) investigated the weak-form efficiency in the Kuala Lumpur Stock Exchange, with serial correlation tests and a sample of 30 actively traded stocks. The results showed little departure from a martingale within confidence intervals of two and three standard errors, suggesting a high degree of efficiency. These findings have been confirmed for the same exchange by the work of Annuar, Ariff, and Shamsher (1994) whose larger sample included 280 liquid and less liquid stocks. Ayadi and Pyun (1994) and Karemera, Ojah, and Cole (1999) have used variance ratio tests to confirm the earlier results of Cooper (1982) that the Korean Stock Exchange is weak-form efficient. Tests by Claessens et al. (1995) and Karemera et al. (1999) show consistent weak-form efficiency for markets in Indonesia and Malaysia while conflicting results have been found for the Philippines3, Thailand, and Taiwan. On the other hand, the work of Elyasiani, Perera, and Puri (1996), which used runs and variance ratio tests, found pricing on the Colombo Stock Exchange to be weak-form inefficient. Early studies on Latin American markets based on serial correlation and runs tests by Errunza and Losq (1985) show that the markets in Argentina, Brazil, Chile, and Mexico are weak-form efficient. Using monthly returns from 1975 to 1991, Urrutia (1995) confirms these previous findings for the four countries. On the other hand, Claessens et al. (1995) found evidence not consistent with weak-form efficiency for Chile and Mexico using monthly returns data from 1976 to 1992. The inefficiency result for Mexico has been confirmed in a recent study by Karemera et al. using monthly data for the 1986–1996 period. In the Middle East, Butler and Malaikah (1992), have investigated weak-form efficiency in the Kuwaiti and Saudi Arabian stock markets through autocorrelation tests. They found evidence of inefficiency in the Saudi Arabian stock market, but not in the Kuwaiti market.

3 Such conflicting results may be due to the different sample periods used as well as the fact that the test procedures do not account for time variation in expected returns.

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They argued that the institutional factors contributing to market inefficiency in the Saudi market included market fragmentation, trading and reporting delays, and the absence of official market makers. Markets in Jordan have been found to be weak-form efficient while others like those in Turkey and Israel show conflicting results in the papers of Claessens et al. and Karemera et al. Country studies of African markets have tended to focus on Kenya, Nigeria, and South Africa. Dickinson and Muragu (1994) tested the efficiency of the Nairobi Stock Exchange between 1979 and 1988 using serial correlation analysis. The empirical results were consistent with weak-form efficiency confirming the earlier study of Cooper (1982). Studies by Claessens et al. (1995) and Olowe (1999), among others, have all found the Nigerian stock market pricing to be consistent with weak-form efficiency whether weekly or monthly returns are used for the tests. Cooper, Errunza and Losq (1985), and Claessens et al. have obtained similar efficiency results for Zimbabwe. On the other hand, an early study of the Johannesburg Stock Exchange by Roux and Gilberston (1978) over the period 1971–1976 found it inconsistent with weak-form efficiency.

3. Modelling issues in testing efficiency in emerging markets 3.1. Return calculation and thin trading It is well known (see, for instance, Dimson, 1979; Miller, Muthuswamy, & Whaley, 1994) that thin trading can potentially lead to serial correlation in the return series. Thin trading may be the outcome of nonsynchronous trading where stocks trade at every consecutive interval, but not necessarily at the close of each interval. Alternatively, thin trading results from nontrading when stocks do not trade at every consecutive interval. Miller et al. (1994) model the effects of both types of thin trading of index portfolio stocks on the observed changes in the index level. They show that for a stock, an AR (1) model of the form can capture thin trading 0 þ ð1 jÞSt St0 ¼ jSt1

ð1Þ

where St is the true index level innovation, St0 is the observed index level change, and the parameter j measures the degree of trading infrequency. As j approaches zero, the observed index level change approaches the true index level change and infrequent trading does not affect the index level change measure. On the other hand, as j approaches 1, it implies that the last trade for a stock in the index may have taken place in some previous period. This has an impact on the return calculation. For nonsynchronous trading, this implies that the observed price change has a stale component j originating in period t 1 and a current component (1 j) originating in period t. In the nontrading case, the stale component j may be due to an infinite number of lagged price changes. Their analysis, therefore, establishes the fact that observed price changes can be adjusted by (1 j) to remove the impact of thin trading in the measurement of returns. In applying their model to

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index returns, they show (see Appendix A, pp. 507–510) that the returns follow a moving average process where the number of moving average components is equal to the number of nontrading days. However, by using the property that the weights decline geometrically with the order of the lag and sum to j, they show that the observed index price change process can be written as a modified AR (1) process and the residuals from such a model can be used to adjust the return calculation. Specifically, the following equation is estimated. Rt ¼ a0 þ jRt1 þ et

ð2Þ

The residuals from the above equation are used to estimate adjusted returns as follows: Radj t ¼ et =ð1 jÞ

ð3Þ

where Rtadj is the return at time t adjusted for thin trading. The main assumption underpinning the above correction model is that the thin trading adjustment is constant throughout the estimation period. To account for variation in the adjustment over time, Eq. (2) is estimated recursively to obtain the residuals used to calculate the adjusted returns in Eq. (3). In all the empirical tests of efficiency that follow, we use log returns adjusted for thin trading. 3.2. Nonlinearity in returns The efficient market hypothesis assumes that investors are rational, risk averse, unbiased in their forecast, and respond rapidly to price sensitive information. These assumptions provide a linear relationship that underpins the mechanics for testing market efficiency. According to Antoniou et al. (1997), ‘‘if these assumptions are not valid and if the return generating process is nonlinear and a linear model is used to test efficiency then the hypothesis of independence of successive price changes may be wrongly accepted.’’ A number of factors may induce nonlinearity in stock returns. For instance, where investors and markets overreact to bad news and underreact to good news (see, for example, DeBondt & Thaler, 1985), the feedback mechanism for returning the asset price to its equilibrium level may be nonlinear. This implies that the correction required to restore equilibrium might not always be proportional to the amount by which the price deviates from the asset’s real value. Efficiency tests that do not account for such nonlinearity are likely to draw inappropriate conclusions from test results. Secondly, investors may not react to information quickly because transaction costs make it unprofitable to trade or they may delay their response until other investors reveal their preferences. Such behaviour, likely to be prevalent in small order-driven markets, may also induce nonlinearity in returns. There are a number of studies that focus on nonlinearity in mature markets. Savit (1988) suggests that asset returns may not follow a stochastic process. He concludes that asset

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returns might be generated by deterministic chaos4 in which case the forecasting error grows exponentially so that the process appears stochastic. Scheinkman and LeBaron (1989) found support that stock market returns follow a nonlinear dynamic system. Hsieh (1991) found similar evidence of nonlinear dependence in stock returns induced by conditional heteroscedasticity. Hsieh (1989) also analysed daily exchange rate changes of five major currencies and found evidence of strong nonlinear dependence. He concluded that the nonlinear dependence was largely exerted through the variance rather than the mean of the series. Hence, a GARCH model could account for most of the nonlinearity in the data. Crato and de Lima (1994) studied data from the NYSE and Standard and Poor’s 500 index for 25 years. Their results indicated that the behaviour of stock market returns during the period displayed some nonlinearities. On the other hand, Stengos and Panas (1992) studied a number of selected banking stocks on the Athens Stock Exchange and found no noticeable presence of nonlinearity in the standardised residuals of the series. It is not unreasonable to assume that nonlinearities might exist in the returns of emerging markets, which are generally characterised by thin trading, high transaction costs, and regulatory problems. The regulatory problems encompass restrictions on short sales and weaknesses in information disclosure, investor protection, and foreign ownership rules. It is therefore appropriate to assume that conventional tests of market efficiency based on the linear model may wrongly lead to the acceptance or rejection of the null hypothesis. This is due to the fact that nonlinear time series, such as those following a GARCH process, may exhibit little or no serial correlation even though each realisation of the series in time t is not stochastically independent of its realisation in time t 1 (Hsieh, 1989). Hence, traditional tests of efficiency based on autocorrelation coefficients and runs tests will not detect nonlinear dependence. To deal with possible nonlinearities in emerging market returns, we follow the modelling approach of Antoniou et al. (1997) and use a logistic map that is capable of nesting both linear and nonlinear specifications. Consider the logistic map5 where a series evolves according to the following function: 2 Xt ¼ aXt1 ð1 Xt1 Þ ¼ aXt1 aXt1

This function maps the value at time t 1 into the value at time t. The second term in the equation is a negative nonlinear feedback term which competes with the linear term in stabilising the series. Even though the logistic map is only one of a number of possible

4

Deterministic chaos is a nonrandom generation of a price sequence, which is entirely dependent on its history. Such a sequence of prices can be generated by an explicit mathematical function. However, a chaotic sequence is unpredictable in the sense that it is impossible to have a perfect numerical estimate of the initial price. This feature of a chaotic system means that for any initial price Pa, one can find another price close to Pa such as Pb such that after some time t, the prices Pa and Pb will differ from each other by a large amount. 5 A logistic map is a type of nonlinear function that maps the price of an asset at time t 1 to the price at time t.

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nonlinear specifications, it has the advantage of capturing feedback mechanisms in emerging markets characterised by delays in information disclosure and trading. More importantly, the main purpose of using a model, which is able to capture both linear and nonlinear presence in the series, is not to determine the precise nature of the nonlinearity but to determine whether or not nonlinearities exist. The logistic map with an error term is a model that will allow for nonlinearities, but if the nonlinear term is found to be insignificant, a linear model is implied. Such a model will take the functional form ðadjÞ3

adj adj2 Radj t ¼ a0 þ a1 Rt1 þ a2 Rt1 þ a3 Rt1 þ 2t

ð4Þ

where, Radj is the thin trading adjusted return at time t calculated on the log of prices. Evidence of nonlinearity would not imply market inefficiency because if the market is characterised by change, the risk–return relationship may also change. Such changes in the risk–return relationship may induce a nonlinear return behaviour in accordance with the implications of the logistic map. 3.3. The empirical model Aggarwal, Inclan, and Leal (1999) and Bekaert and Harvey (1997), among others, point out that social, political, and economic factors can induce changes in the returns and volatility of emerging markets. It is therefore necessary to account for risk in the return process in a manner consistent with standard asset pricing theories such as the Capital Asset Pricing Model and the Arbitrage Pricing Theory. This therefore requires a modification of Eq. (4) to include risk as a determinant of return. The most appropriate way to do this is to use a GARCH-in-mean model that allows us to capture the impact of the conditional variance in the return generation process. Hentschel (1995) provides an extensive review of the variety of GARCH models. However, very few papers have studied return predictability in emerging markets with GARCH models. Antoniou et al. (1997) used a GARCH (1,1)-inmean model to investigate the return predictability of the Istanbul Stock Exchange. For the Athens Stock Exchange, Koutmous, Negakis, and Theodossiou (1993) find that returns are conditionally heteroscedastic with past returns correlated with current returns in violation of the martingale hypothesis. They also found that the EGARCH-M model captures the asymmetric impact of shocks on volatility effectively with positive shocks increasing volatility more than negative shocks. Poon and Fung (2000) also found that the exponential GARCH-in-mean model adequately described the return process in the emerging Chinese markets in Shanghai and Shenzhen. Su and Fleisher (1998) used various GARCH specifications to document that Chinese stock markets have time-varying volatility that is mildly persistent with a fat-tailed distribution. This paper uses the asymmetric EGARCH-in-mean model proposed by Nelson (1991) in the empirical tests, since it permits estimates that do not impose restrictions on the parameters of the conditional variance equation as required by the standard GARCH model

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of Bollerslev (1986).6 Secondly, the EGARCH specification takes care of the ‘leverage effect’ (noted by Black, 1976) through which negative shocks to the conditional mean equation tend to have a larger effect on volatility than positive shocks.7 To incorporate risk in the return process, we follow Antoniou et al. (1997) and substitute the square of the lagged adjusted return in Eq. (4) with the conditional standard deviation to get the mean Eq. (5).8 Eq. (5) specifies return as a function of risk and past returns and is consistent with standard asset pricing models where expected return is a function of ‘normal’ return (captured by the constant term in this instance) and a risk premium as noted by French, Schwert, and Stambaugh (1987). Eq. (6) is the EGARCH conditional variance equation that is estimated jointly with the mean equation to test the major hypothesis of weak-form efficiency in this paper. Hence, the return process in African stock markets is modelled as: ðadjÞ3

0:5 þ a1 Radj Radj t ¼ a0 þ lh t1 þ a2 Rt1 þ et

lnht ¼ b0 þ

p X s¼1

gs lnhts þ

q X

fs gðzts Þ

ð5Þ

ð6Þ

s¼1

p where g (zt)=[qzt + y( | zt | E( | zt|)]; E( | zt|) = 2/p; zt = et/st—the standardised innovation from the mean equation and ht is the conditional variance and the other variables are as previously defined. The mean equation (Eq. (5)) is specified as a first-order autoregressive process with a nonlinear variable. Statistically significant values for a1 would imply that past returns could be used to forecast current and future movement of returns—a result that would be inconsistent with weak-form market efficiency. The parameter l for the conditional standard deviation in the mean equation tests the linkage between return and conditional volatility.

6

The exponential form of the conditional variance equation of the EGARCH model allows for the asymmetric impact on conditional variance of positive and negative shocks to the conditional mean equation. This asymmetry is captured in the EGARCH model by the inclusion of et 1, normalised by the standard deviation of the errors. This contrasts with the GARCH model of Bollerslev where positive and negative innovations have an identical effect on conditional variance, since their sign becomes lost upon taking their square. Secondly, the restriction in the basic GARCH model, which requires the parameters of the conditional variance equation to be positive and sum up to less than 1 for the volatility process to be covariance stationary, is no longer necessary in the EGARCH specification. Therefore, in EGARCH, the presence of negative parameters does not cause the conditional variance itself to become negative. 7 However, as pointed out by Engle and Ng (1993), the conditional variance measures from the EGARCH model may tend to give rise to asymmetry that may be too high or low as measured by the ‘news impact curves’. This problem is not significant in this study since we do not focus on the impact of specific information other than the previously observed price, on the return generation process. 8 This substitution enables us to control for both time-varying volatility and nonlinearity in the return generation process without the need to test for all the specific exponents of the lagged return variable.

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Engle, Lilien, and Robins (1987) show that the sign and magnitude of this parameter depend on the utility functions of the agents and the supply conditions of the assets. A significant value for l means that volatility contributes to the risk premium and this may differ between periods of instability and tranquillity. The conditional variance equation (Eq. (6)) is the natural logarithm of past conditional variances, gi(ln ht 1) and past volatility shocks, fi( g(zt)). Significant values for gi and fi indicate that the volatility of index returns can be predicted by past volatility information and past unexpected volatility shocks.

4. Institutional background to the markets 4.1. Trading arrangements Table 1 summarises the information on the structure and operations of the stock markets—trading days, trading hours, and methods of trading during the period covered by the study. While most of the markets trade for 5 days a week, trading hours appear rather short on the majority of the markets. For five markets, the trading day only lasts for about 2 hours, with the exception of markets in South Africa and Zimbabwe that trade for about 6 hours a day. In the case of the Ivory Coast, trading does not appear to last for more than 30 min. Like exchanges in other parts of the world, stock-broking firms, usually local ones, are the intermediaries in stock trading in African stock markets. Trading methods, however, seem to vary across the continent. While most of the exchanges (six markets) use quotedriven open-outcry, three are call-over markets where orders are batched for simultaneous execution when the market is called once or twice a day. The remaining exchanges— Egypt and Morocco, were using some form of order-driven electronic trading platforms during the sample period. 4.2. Trading activity and trading costs Table 2 provides additional information on the actual operations of the markets as well as the sample period used in the empirical analysis. The number of firms on the exchanges varies from as little as four on the Swaziland exchange to 746 on the Egyptian exchange. Only two other countries, Nigeria and South Africa, have more than 100 firms listed on their markets. The small number of listed firms justifies why trading hours are relatively short on most of the markets. Unsurprisingly, the total market value of listed firms correlates highly with the number of listed firms with a rank correlation coefficient of .891( P value .000). Trading volume, however, has a lower correlation with the number of firms (rank correlation of .573, P value .066) reflecting the low levels of liquidity in the various markets. This is reinforced by the low turnover ratios that exceed 10 in only two markets—Egypt and Morocco. Apart from Morocco and South Africa, the average company size is under US$100 million. In light of the above statistics, the markets studied are generally small with low levels of liquidity.

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Table 1 Trading arrangements on African stock markets at the end of the sample period Market

Trading days

Trading hours

Trading method

Abidjan Stock Exchange

Shares: Tuesday and Thursday Bonds: Wednesday and Friday Monday to Friday

09.00 to 09.30 h

Shares: Open outcry Bonds: Screen-based quote system

Times of call over are 09.00 and 15.00 h 08.30 to 12.30 h

Open outcry

Botswana Stock Exchange The Casablanca Stock Exchange

The Egyptian Stock Exchange Ghana Stock Exchange Johannesburg Stock Exchange The Stock Exchange of Mauritius

Nairobi Stock Exchange The Nigerian Stock Exchange The Swaziland Stock Exchange Zimbabwe Stock Exchange

Monday to Friday

11.30 to 15.30 h

Electronic order-driven trading for the most liquid stocks. Fixing basis for the less liquid stocks Electronic order-driven trading

10.00 to 13.00 h

Call-over with a limited auction

09.00 to 16.00 h

Open outcry, continuous auction on a trading floor; order-driven Open outcry, order-driven and single price auction system

5 days—Sunday to Thursday Mondays, Wednesdays, and Fridays Monday to Friday Official market: Monday to Friday OTC market: Tuesday and Thursday Monday to Friday

Official market: 10.00 to 11.00 h OTC market: 14.00 to 15.00 h 10.00 to 12.00 h

Monday to Friday

Monday to Friday

Daily from 11.00 h onwards until all bids are done 10.00 to 12.00 h

Monday to Friday

08.00 to 16.30 h

Open outcry Call-over system

Matched bargain basis—broker acts as agent Open outcry

Source: The African Stock Exchanges Association. Apart from the markets in Ghana and Mauritius there were no price limits in force during the period of the study in the other markets. Short sales are only allowed in the markets of South Africa and Zimbabwe.

Government-imposed trading taxes were only levied on three exchanges—Egypt, Ghana, and Zimbabwe during the sample period. Of these, only the Ghanaian tax of 2% appeared excessive. Capital gains tax ranging from 2% in Egypt to 20% in the Ivory Coast and Nigeria were levied in only 5 of the 11 markets. Apart from Egypt, there were fixed brokerage commission rates on the other exchanges ranging from 3% of value traded on the smallest transactions to 0.2% on the largest value trades. The high commission rates for all transactions on the Nigerian market as well as the 20% capital gains tax may in part explain the low volume of trading on that market. Mauritius, Morocco, and South Africa had lower rates among the exchanges with fixed commissions.

258

Market capital in US$ millions—end of 1995

Country

Date index Date market established opened

Sample period No. of listed firms—end of 1995

Botswana Egypt Ghana Ivory Coast Kenya Mauritius Morocco Nigeria

1989 1898 1990 1976 1954 1989 1929 1960

1989 – 1995 1993 – 1995 1990 – 1995 1992 – 1995 1990 – 1995 1989 – 1995 1990 – 1994 1990 – 1995

11 746 19 31 56 28 44 181

397 8088 1680 867 1889 1381 5951 2033

1960 = 100 1990 – 1995 Jul 1990 = 100 1990 – 1995 1967 = 100 1990 – 1995

640 4 64

280,526 339 2038

South Africa 1887 Swaziland 1990 Zimbabwe 1896

1989 = 100 1992 = 100 1990 = 100 1985 = 100 1964 = 100 1989 = 100 1979 = 100 1993 = 100

Turnover Trading volume in US$ ratio—end millions—end of 1995 of 1995

Transfer Average taxes—end company of 1994 size in US$ millions—end of 1995

Commission Capital rates gains tax—end on tradesa of 1994

38 677 22.3 14.1 65 70 2426 14

10.0 10.9 1.3 2.2 2.8 4.6 45.9 0.8

33 11 88 28 34 49 135 11

None 0.2% 2% None None None None None

5% 2% None 20% None None None 20%

17,048 0.39 150

6.5 0.1 7.6

438 85 32

None None 0.35%

None None 10%

2% – 1% No fixed ratesb 3% – 1% N/A 2.5% – 1.1% 1% 0.6% – 0.3% 3% + 1% SEC fee 1.2% – 0.2% 2% – 1% 2% – 1%

Sources: IFC Emerging stock markets factbook. 1996 African Stock Exchanges. Trading volume is the number of shares traded multiplied by the price per share. The turnover ratio is calculated as market capitalisation divided by the trading volume. a All the exchanges had fixed commission rates for part of the sample periods. The first percentage number refers to the rates charged on small transactions and the last number is the maximum rate on large trades. Commission rates apply to the value of the transactions. b Fixed commission rates were abolished in 1994. Rates are now negotiated with the proviso that it should not exceed 0.5% on trades exceeding £10,000.

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Table 2 Descriptive data on African Stock Exchanges

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4.3. Foreign portfolio investment restrictions The participation of foreign investors in an emerging market can act as a catalyst for improvements in the operations of a stock market because they would require evidence of adequate workings of the trading, pricing, reporting, and surveillance systems before committing significant funds to a market. Whether or not an emerging market attracts foreign portfolio investors, however, depends crucially on its regulations towards such investors. Table 3 provides a summary of the foreign investment restrictions in African stock markets. Apart from the Ivory Coast market where foreign investors were severely restricted, four other markets allowed foreigners to collectively own a minority of the shares (up to 49%) in a single company. Egypt and Morocco had no restrictions on foreign investors while the restrictions in Mauritius, Nigeria, and South Africa applied to specific sectors of the economy. By allowing 74% of the shares in a single company to be owned by foreign investors, Ghana’s foreign investment rules appear very liberal. It is clear from the above that a majority of the stock exchanges studies are sufficiently open to encourage foreign investor participation. Since all the countries also allow repatriation of dividends and capital, this study will contribute to the understanding of these markets by providing empirical evidence on their weak-form informational efficiency.

Table 3 Foreign investment regulations Country

Restriction

Botswana

Foreigners may not collectively own more than 49% of a publicly quoted company’s share capital. No foreign individual may own more than 5% of a company’s shares. No restrictions. Foreign investors may not collectively own more than 74% of the shares in a quoted company. A nonresident portfolio investor may not own more than 11% of the shares in a company. Resident foreigners may invest without any limit. Restricted. Foreign investors as a group may not own more than 40% of the shares in a company. Individual foreign investors may not own more than 5% of the shares in a single company. Not more than 15% in a sugar company may be owned by foreign investors. Foreign investors may participate in unit trusts and mutual funds within approved limits. No restrictions. Foreigners may not own more than 40% of the shares of companies in some industrial sectors which were incorporated before 1990. Since the Industrial Policy Act of 1989, foreigners can incorporate companies as sole owners if they so wish. Total foreign ownership is limited to 15% for banks and 25% for insurance companies. There are no restrictions on foreign investors in other areas. Prior approval of central bank required before investment is undertaken if the investor wishes to buy 20% or more of a company. Foreign investors collectively may not own more than 40% of the shares in a company. Individual foreign investors may not own more than 5% of the shares in a company.

Egypt Ghana

Coˆte d’Ivoire Kenya Mauritius Morocco Nigeria

South Africa Swaziland Zimbabwe

Sources: African Stock Exchanges.

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5. Empirical results 5.1. Data sources and sample Prior empirical studies of return predictability in selected African stock markets were mostly based on monthly data. In this paper, we use weekly index data obtained directly from the various stock exchanges. Weekly data enable us to better capture the dynamic evolution of prices and returns, which may be glossed over in monthly observations. It also reduces the problems associated with nontrading which would arise with daily data. In a majority of countries, the index data used cover all the listed companies. In a few cases where the index did not include all quoted stocks, the companies covered represent more than 80% of the value of trades on the respective national stock exchanges. We use weekly closing index values measured in the domestic currency for the empirical tests. The time series of weekly observations used ranges from 175 for Egypt with 3 years data to 323 for Botswana. 5.2. Descriptive statistics and diagnostic tests on weekly returns Table 4 provides the descriptive statistics on the adjusted return data used in the empirical tests. Even a cursory look at the skewness and kurtosis of the series shows that the returns are not normally distributed. The high kurtosis for a number of countries such as Ivory Coast, Nigeria, and Swaziland implies that the returns have fatter tails than would be expected from a normally distributed variable. The Lagrange Multiplier test for the joint hypothesis of zero skewness and zero excess kurtosis rejects the normality assumption for all countries except Mauritius. This rejection of the normality assumption is inconsistent with a linear and constant conditional variance model. This is reinforced by the Ljung–Box ( Q2) statistics, which also shows the presence of conditional heteroscedasticity for most of the countries. Since all the diagnostic test results are consistent with nonlinearity and the presence of conditional heteroscedasticity, we conclude that the implementation of an EGARCH-M model will enable us to test our hypotheses of weak-form efficiency and nonlinearity in the return generation process. We choose EGARCH among other GARCH models because Nelson (1991) demonstrated that such a specification allows for asymmetric volatility, does not impose sign restrictions on the parameters of the past conditional variance and past volatility shocks, and does not require that the GARCH parameters must add up to less than 1 to ensure covariance stationarity of the volatility process. A growing number of studies such as Booth, Martikainen, and Tse (1997), Cheung and Ng (1992), and Poon and Fung (2000) have also found that the EGARCH specification adequately captures the stochastic behaviour of returns and volatility in developed and emerging stock markets. 5.2.1. Model diagnostic tests Eqs. (5) and (6) were estimated for each country using the BHHH algorithm in RATS5.01. The error process was modelled as a generalised error distribution (GED) to allow for the evidence of conditional heteroscedasticity in Table 4 of fat tails. The GED collapses into the normal distribution when the scale parameter d = 2. When d < 2, the distribution of the of the

Statistic

Botswana

Egypt

Ghana

Ivory Coast Kenya

Mauritius Moroccoa Nigeria

South Africa Swaziland Zimbabwe

Mean Variance Skewness Kurtosis LM (c2) testb LB ( Q) (12) LB ( Q2) (12) No. of observations

0.004103 0.000134 0.11484 1.08376 49.19 * * 43.91 * * 12.40 * 317

0.002789 0.000341 0.61027 5.41092 53.24 * * 20.85 * 34.84 * * 175

0.00428 0.00061 0.4266 8.0975 283 * * 40.91 * * 53.98 * * 255

0.0080 0.0029 6.2349 60.721 29,060 * * 8.34c 3.73e 200

0.00044 0.00026 0 0.09421 2.8373 0.834 29.08 * * 91.92 * * 323

0.00050 0.00042 0.37222 0.71754 70.60 * * 18.81d 24.34 * * 294

a

0.00185 0.00065 2.1632 19.662 3420 * * 35.36 * * 27.29 * * 277

0.00169 0.000841 0.39055 0.79488 12.54 * * 7.14 25.74 * * 55

Monthly returns for the period 1990 – 1994 were used since weekly data was not available. Tests the joint hypothesis of zero skewness and zero excess kurtosis. c Absence of serial correlation rejected at 5% or better for lags 2 and 3. d Absence of serial correlation was rejected up to 9 lags at 5% or better. e Absence of heteroscedasticity rejected at lag 1. * Normality, absence of serial correlation, and absence of heteroscedasticity rejected at 5%. ** Normality, absence of serial correlation, and absence of heteroscedasticity rejected at 1%. b

0.001114 0.000195 1.39527 11.67591 1038 * * 96.15 * * 59.22 * * 300

0.00025 0.00018 2.12019 25.1496 5573 * * 8.7556 11.26 263

0 0.00281 0.003454 0.74652 11.73094 948 * * 32.63 * * 76.07 * * 290

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Table 4 Descriptive statistics of adjusted weekly index returns

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error term has thicker tails than the normal distribution. On the other hand, when d > 2, the distribution of the error term has thinner tails than the normal distribution. The d values for the markets in Egypt, Kenya, Mauritius, South Africa, and Zimbabwe, which range from 1.9996 to 2.1490 in Table 5, suggest that the normal distribution is a good descriptor of the error process of the returns in these markets. With d values less than 2, the returns in the markets of Botswana, Ghana, Ivory Coast, Nigeria, and Swaziland have thicker tails than will be observed in a normal distribution. The value of d for Morocco suggests thinner tails than a normal distribution. The varied estimates of d justify the use of the GED in modelling the error process of Eqs. (5) and (6). From the analysis in Section 3, the specification of the mean equation was based on the objective of testing for weak-form efficiency, nonlinearity in returns, and the presence or otherwise of changing risk premium in the return generation process. On the other hand, the appropriate lag lengths for the conditional variance equation (Eq. (6)) for each of the 11 markets must be determined on the basis of appropriate specification tests. The tests used to determine the appropriate lag lengths of the p and q parameters are based on the Ljung–Box Q and Ljung–Box Q2 statistics of the standardised residuals generated from estimates of Eqs. (5) and (6). Since the findings of Engle and Ng (1993) suggest that the Ljung–Box test may not have the power to detect misspecifications related to asymmetric effects, we also use the asymmetric test statistics to verify the appropriateness of the models estimated. The results of the model specification diagnostic tests are reported in Table 5. All the LBQ statistics are not significant for all the countries as expected in a properly specified model with the exception of the LBQ (8) results for Ghana, Ivory Coast, and Zimbabwe and LBQ (24) for Morocco. The asymmetry tests, however, show that the models for Ghana, Ivory Coast, and Morocco are well specified. Only Zimbabwe has sign bias and negative size bias tests that appear significant at 10% even though the joint test is not significant. The results for Zimbabwe9 are similar to those of Booth et al. (1997) who also found in a study of Scandinavian countries that some of the same diagnostic tests for Finland were significant. In general, we conclude that the EGARCH-M ( p, q) estimates satisfy the appropriate diagnostic tests and are therefore used in the weak-form efficiency tests of 11 African stock markets. 5.2.2. Risk premium and nonlinearity tests Estimates of the mean equation parameters are reported in Table 6. The l parameter in the mean equation may be interpreted as the coefficient of relative risk aversion of a representative investor while the value of lht0.5 relates to the time-varying risk premium. A positive l should imply that investors are compensated for any additional risk as reported by Chou (1987) and French et al. (1987). Our estimates show positive and significant l values for Ghana, Ivory Coast, Nigeria, and Swaziland. Such results imply that these markets provide returns that compensate investors for time-varying risk premium—a finding that should be of interest to investors concerned about the risk–return relationship in African

9 The use of other p and q parameter combinations did not produce diagnostics that are better than those reported.

ðadjÞ3

ð5Þ

fs gðzts Þ

ð6Þ

0:5 Radj þ a1 Radj t ¼ a0 þ lh t1 þ a2 Rt1 þ et

lnht ¼ b0 þ

p X s¼1

gs lnhts þ

q X s¼1

p where g (zt)=[qzt+y(|zt|E(|zt|)]; E(|zt|)= 2/p; zt=et/st—the standardised innovation from the mean equation and ht is the conditional variance and the other variables are as defined in the text Statistic LBQ(8) LBQ(16) LBQ(24) LBQ2(8) LBQ2(16) LBQ2(24)

Botswana Egypt .54498 .50543 .27076 .78986 .79488 .95104

.52116 .85503 .93659 .84366 .88770 .77306

Ghana .03133 .20768 .16836 .60827 .92056 .99296

Ivory Coast Kenya .05008 .31223 .34064 .05199 .19913 .20488

.39559 .51274 .78255 .42153 .34926 .51688

Mauritius Morocco .65043 .33940 .37342 .53648 .36502 .61897

.82999 .23746 .00597 .46097 .16233 .00170

Nigeria .32304 .39415 .26263 .98663 .91680 .93500

South Africa Swaziland Zimbabwe .15735 .29529 .28026 .72738 .84796 .06839

.85309 .97870 .99910 1.0000 1.0000 1.0000

.02485 .07534 .16430 .50850 .50542 .45278

P values of the Engle and Ng (1993) diagnostic tests on the residuals from the estimates of Eqs. (5) and (6) Sign Bias Test .30536 .20462 .25463 .63055 .85721 .67737 .84878 .37277 .75300 Negative Size Bias Test .91639 .32279 .95369 .91305 .46735 .61329 .39940 .51949 .17957 Positive Size Bias Test .70982 .72453 .24360 .24687 .73950 .97797 .53125 .86867 .18188 Joint Test of Three Effects .66317 .55132 .56348 .47257 .84280 .75988 .75129 .81301 .21838 d 1.6741 2.000 1.1050 0.6851 2.000 1.9996 201.02 0.9882 2.1490

.21373 .99905 .64441 .66460 0.2460

.07679 .07033 .93340 .20167 2.097

d is the scale parameter of the distribution of the error term. When d < 2, the distribution of the error term has thicker tails than the normal distribution. On the other hand, when d>2, the distribution of the error term has thinner tails than the normal distribution.

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Table 5 Diagnostic tests. P values of Ljung-Box Test Statistics on the residuals from the estimates of Eqs. (5) and (6) below

263

264

Table 6 EGARCH-M ( p, q) tests of linearity and weak-form efficiency of African stock markets based on Eqs. (5) and (6) a0 a1 a2 l b0 g1

Egypt

Ghana

Ivory Coast Kenya

0.00409 (.0538) 0.0110 * (.8760) 269.8 (.0000) 0.1057 (.6706) 0.0344 (.0513) 1.9245 (.0000) 0.9283 (.0000)

0.04525 (.0117) 0.01212 (.0000) 149.5 (.0000) 3.7327 (.0075) 0.01815 (.0012) 0.01474 (.0000) 0.83183 (.0000)

0.00006 (.8563) 0.61075 (.0000) 3.46111 (.0000) 0.19713 (.0000) 3.87588 (.0000) 0.16932 (.0000) 0.72653 (.0000)

0.05970 0.000001 (.32464) (.0031) 0.118962 (.24227)

0.01637 (.3442) 0.00999 (.3511)

1.77241 (.0000) 0.76586 (.0024) 0.59366 (.0006)

1.8273 0.86594

6.303 0.84657

0.2725 0.55721

0.00905 (.0184) 0.22803 (.0000) 967.7 (.0000) 0.71902 (.1720) 1.31940 (.0779) 0.86594 (.0000)

g2 g3 f1 f2 f3

Nigeria

South Africa Swaziland

0.00442 (.6436) 0.13649 * (.1055) 194.96 (.0000) 0.38638 (.47217) 0.34685 (.7630) 0.47532 (.4486) 0.13762 (.8143) 0.36382 (.4915) 0.00003 0.13788 0.70090 (.1711) (.2553) (.3989) 0.00001 0.32079 1.40965 (.3219) (.0168) (.1531)

0.01910 (.0000) 0.09040 (.0777) 136.7 (.0000) 1.87769 (.0004) 1.12292 (.0000) 0.88376 (.0000)

5947 0.98988

1.3757 0.88376

0.00119 (.8693) 0.08655 (.0218) 372.1 (.0000) 0.03014 (.9603) 0.15668 (.5809) 0.58368 (.1967) 0.76499 (.6567) 0.36655 (.7759) 0.21907 (.3066) 0.16548 (.4167) 0.20077 (.6079) 0.12019 (.6686) 0.2963 0.98212

0.00478 (.0456) 0.07801 * (.1498) 32.04 (.0000) 0.27031 (.1212) 0.08511 (.1711) 0.98988 (.0000)

Mauritius

Morocco

0.00490 (.0912) 0.05153 * (.1188) 437.6 (.0000) 0.49871 (.0834) 0.45541 (.3280) 0.27017 (.2947) 0.67953 (.0098)

0.08694 (.0158) 0.06446 (.1041)

f4 qP gi

8984 0.9962

P values are in parentheses. * Indicates that the market is weak-form efficient.

0.5578 0.94970

0.0122 0.97676

Zimbabwe

0.00006 (.0000) 0.01613 (.0000) 379.3 (.0000) 0.00827 (.0000) 1.59206 (.0000) 0.36749 (.0000) 0.45473 (.0000)

0.00376 (.0240) 0.02810 * (.7248) 7.6690 (.0000) 0.02056 (.8044) 0.01902 (.0000) 1.79529 (.0000) 0.79832 (.0000)

1.87220 (.0000) 0.24908 (.0148)

0.66093 (.0000) 0.71992 (.0000)

0.08710 0.0013 0.82222 0.99697

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Statistic Botswana

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stock markets. The estimates for the markets in Botswana, Egypt, Kenya, Morocco, South Africa, and Zimbabwe are, however, not significantly different from zero. The estimate for Mauritius is negative and significantly different from zero at 10%. This finding is similar to that reported by Nelson (1991). The variety of results for l is not surprising since the literature is replete with mixed results (see, for example, Glosten, Jagannathan, & Runkle, 1993; Whitelaw, 1994). This means that each market must be analysed with a model specification, which is consistent with its underlying return generation process rather than being forced to conform to a specific dynamic pattern. Hence, the inclusion of the conditional standard deviation in the mean equation has enabled us to identify those markets where conditional volatility impacts the return generation process. Tests for evidence of nonlinearity in the return generation process are confirmed by the statistically significant coefficient estimates for a2 for all 11 markets. These results are consistent with markets where investors may not react quickly to new information because of high transaction costs and taxes that were prevalent during the sample period as reported in Table 2. The findings are also consistent with markets that overreact to bad news and underreact to good news such that the adjustment required to restore equilibrium might not be proportional to the amount by which the price deviates from the asset’s real value. These results are therefore consistent with those of Scheinkman and LeBaron (1989), who also found evidence that stock returns follow a nonlinear dynamic process. 5.2.3. The inefficient markets The efficiency tests results are discussed in two parts. This section focuses on the inefficient markets, while the next section concentrates on the efficient markets. The coefficients of the weak-form efficiency parameter in the mean equation, a1, reported in Table 6 are significantly different from zero in the markets of Botswana, Ghana, Ivory Coast, Nigeria, South Africa, and Swaziland. These results indicate that stock market prices do not adjust rapidly to the arrival of new information, hence, future prices could be predicted from lagged prices. Stock price predictability can arise as a consequence of market inefficiency or the risk-averse behaviour of investors and time-varying risk premium. Since our results are based on the EGARCH-M model, which accounts for time-varying risk premium, they imply that the inefficiency in these markets cannot be attributed the risk-averse behaviour of investors. The finding for South Africa confirms earlier result by Roux and Gilberston (1978) and is reinforced by the anecdotal evidence in the Financial Times of London on 31st August 2000 of inadequate disclosure and insider trading on the Johannesburg market. The result for the Nigerian exchange is contrary to previous findings by Olowe (1999) and Samuels and Yacout (1981). The new result may reflect the fact that prior studies used inappropriate data measurement techniques and empirical models. They are, however, consistent with claims by practitioners such as Alile and Anao (1986) that the Nigerian stock market is inefficient. The results for the other four inefficient markets establish the benchmark with which future studies may be compared. These four markets are the smallest in terms of number of listed companies as well as by market capitalisation at the end of 1995 (see Table 2). However, the fact that two of the inefficient markets in Nigeria and South Africa are relatively large markets, in the context of the continent, suggests that market size is not an important

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determinant of a market’s weak-form efficiency. This is reinforced by the fact that the Mauritius market is efficient even though it is one of the smallest in our sample.10 We next investigate the extent to which trading volume may be related to weak-form efficiency. Using the turnover ratio as a broad measure of trading activity, it is noted that with the exception Botswana, the markets in Ghana, Ivory Coast, and Swaziland have the lowest three ratios ranging from 0.1 to 2.2. This observation is reinforced by the fact that a rank correlation of the efficiency coefficient against trading volume produced a statistically insignificant relationship. Additionally, it also appears that trading has not been inhibited by transfer or capital gain taxes since such costs do not differ significantly across the markets.11 Trading commissions also do not exert a significant impact on the efficiency or otherwise of a market since a rank correlation of the magnitude of the efficiency coefficient and the highest commission rates12 (in Table 2) produced a coefficient of .078 ( P value .820). This is evident from the raw data that with the exception of very small transactions, commission rates for all the markets do not exceed 1%. In the case of Kenya where the normal commission rate marginally exceeds 1%, the market is nevertheless efficient. On the basis of the rank correlation analysis, it appears that the weak-form inefficiency of six African markets is not likely to be associated with trading volume, number of firms, market capitalisation, transfer taxes, or trading commissions. It may well be that market participants do not exploit potentially profitable opportunities because total transaction costs would invariably wipe out any potential gains.13 5.2.4. The efficient markets The estimated coefficients of the efficiency parameter in the mean equation for Egypt, Kenya, Mauritius, Morocco, and Zimbabwe were not significantly different from zero. This implies that the price dynamics in these markets are consistent with weak-form efficiency. With the exception of Mauritius, these markets are among the oldest on the continent. However, a rank correlation of age and magnitude of the efficiency parameter produced a value of .263 ( P value .434), which implies that age does not determine the efficiency or otherwise of a market. The results for Egypt, Kenya, and Zimbabwe are consistent with those of earlier studies by Claessens et al. (1995), Cooper (1982), and Dickinson and Muragu (1994), respectively. The results for Morocco and Mauritius extend our understanding of the behaviour of prices in those markets given the lack of prior studies in such markets.

10

A Spearman rank correlation of the magnitude of the market efficiency coefficient against the number of listed companies and total market capitalisation in turn produced a statistically insignificant coefficient. In performing the rank correlation tests, efficiency coefficients that were statistically insignificant from zero were assigned a value of zero while those that statistically differ from zero were assigned their estimated values. 11 Among the inefficient markets, only Ghana had transfer taxes during the sample period. Similarly, only Ivory Coast had a significant capital gains tax rate during the sample period. 12 A commission rate of 3% was assumed for Ivory Coast. 13 A more rigorous analysis of the potential correlates of efficiency is not feasible due to the relatively small number of markets studied.

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The coefficients of past volatility shocks (fi) and past conditional variance (gi) are statistically significant for Egypt and Zimbabwe, indicating that the volatility terms are predictable using past information. On the other hand, the results for Kenya and Mauritius are mixed, suggesting difficulties in forecasting volatility. The finding that the conditional volatility coefficients for Morocco are not significant is probably due to our use of monthly return that may be less informative P than weekly returns.14 The estimated degree of volatility persistence is measured by gi. The gi values in Table 6 are less than 1 for both inefficient and efficient markets—results necessary for the unconditional variance to be finite. With the exception of the Ivory Coast, there is strong volatility persistence in all the other markets. The asymmetry coefficient q in Table 6 is negative for all the markets except those in Morocco, Mauritius, and South Africa. This suggests that for eight markets, negative shocks have a larger impact of future volatility than positive shocks. This reinforces the earlier finding that the return generation process in these markets is nonlinear—hence, the price adjustment process towards equilibrium after a shock is not proportional to the amount by which the shock induced deviation from the asset’s real value.

6. Conclusion The paper focussed on testing the weak-form efficiency of 11 African stock markets, six of which had no previous academic studies. In contrast to most previous studies, we acknowledge the possibility of nonlinearity in the return generating process and account for this in the design of a test method that accommodates both linear and nonlinear specifications. Secondly, the problem of thin trading that usually characterises small equity markets was addressed by computing returns with a procedure that recognises such a problem. Thirdly, we used an EGARCH-M model to control for changes in risk and return over time. A number of new results emerge from our empirical work. Firstly, we find that the return generation process is nonlinear in all the 11 markets in our sample, and in five of the markets, investors demand a time-varying risk premium for the risks they bear. Such results will help portfolio managers to deepen their understanding of the risk–return relationship as well as the evolution of prices in African stock markets. For example, markets with changing risk premium are likely to be seen as being more volatile than where the conditional standard deviation coefficient was not significant. Secondly, our tests show that the majority of the markets in our sample do not exhibit weak-form efficiency. In particular, our finding that the Nigerian market is not efficient despite prior evidence to the contrary, reinforces the appropriateness of our modelling approach, which produces a significant time-varying risk premium for the Nigerian market which linear models would not have been able to capture. For the markets in Egypt, Kenya, South Africa, and Zimbabwe, where the time-varying risk 14

These results are similar to those for the inefficient markets where the coefficients for Ivory Coast and Swaziland are significant, and those for Botswana, Ghana, and Nigeria are mixed. The results for South Africa are insignificant.

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premium was not significant, we find that the results of our efficiency tests are also consistent with those of prior studies. This suggests that efficiency test models that do not control for time-varying risk premium are likely to be using inappropriate models. Thirdly, we provide efficiency test results for six markets that lack such studies. Of these six markets, we find that the markets in Mauritius and Morocco are weak-form efficient while those in Botswana, Ghana, Ivory Coast, and Swaziland are inefficient. Fourthly, the preliminary investigation of some potential causes of inefficiency suggests that high transaction taxes, trading commissions, and trading volume, among others, do not determine whether or not a market is efficient. It is, however, plausible that investors recognise that after accounting for all transaction costs, trades to exploit inefficiencies are not likely to be profitable. The additional empirical work required to estimate the profitability of trading strategies in the inefficient markets lies outside the scope of this paper. Future research should also explore in detail the microstructure and other factors that account for the inefficiency in some of the markets.

Acknowledgements We would like to thank the numerous officials of African stock exchanges who promptly responded to our requests for data. We also thank Antonios Antoniou for his comments on the initial research on which this paper is based as well as two anonymous referees for their insightful comments. We accept responsibility for any remaining errors.

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