Relationship between Return, Volume and Volatility in the Ghana Stock Market

Transcription

1 Relationship between Return, Volume and Volatility in the Ghana Stock Market Eugene Osei-Wusu Department of Finance and Statistics Hanken School of Economics Vasa 2011

2 HANKEN SCHOOL OF ECONOMICS Department of: Finance and Statistics Type of work:thesis Author: Eugene Osei-Wusu Date: Title of thesis: Relationship between Return, Volume and Volatility in the Ghana Stock Market Abstract: This study investigates the relationship between return, volume and volatility by using data from the Ghana stock exchange (GSE). The data set comprise of daily closing prices and trading volume collated from 1 st August 2005 to 31 st December The empirical examination is conducted by fitting the simple GARCH, GJR and EGARCH models to the trading volume and thinly corrected return series over the sample period. The results of the study show that contemporaneous or lag trading volume do not significantly impact on the raw return, as well as the thinly corrected returns series. This implies that knowledge of any of the variables cannot be utilized to improve the forecast of the other. On the other hand, the study found significant impact of volume on the volatility of both the raw return and the adjusted return, using the GARCH (2,1) model. Moreover, the EGARCH model shows that trading volume has asymmetric impact on the volatility of both the raw and adjusted return; even though, this was rejected in the GJR model. However, both the GJR and the EGARCH conclusively accept the presence of asymmetry in the response to volatility of both the raw and adjusted return series. The results of the study also reject the presence of the mixture of distribution hypothesis (MDH) in the Ghana stock market, when trading volume is used as a proxy for the rate of informational arrival to the market. The study finally reveals that the devaluation of the Ghanaian currency on July possibly has increasing impact on the volatility of stock returns on the GSE. These empirical findings provide useful information to investors, with regards to the microstructure of the GSE. Keywords: Return, Volume, Volatility, GARCH

3 1 CONTENTS 1 Introduction 4 2 Theory and previous research Brief overview of the ghana stock exchange (gse) 9 3 Methodology Thin trading and return calculation Unit root test Autoregressive conditional heteroscedasticity (arch) Generalised autoregressive conditional heteroscedasticity (garch) Asymmetric garch models The gjr-tarch (2,1) model The egarch model 16 4 Data 18 5 Descriptive statistics and diagnostic tests Descriptive statistics and arch test Unit root test Autocorrelation test 23 6 Empirical results Contemporaneous and lag trading volume Trading volume and garch effect Test asymmetries in volatility Gjr estimate Egarch estimate 35

4 2 7 Robustness tests 38 8 Conclusion 39 References 41 APPENDICES Appendix 1 Ljung-Box test for autocorrelation in standardized residuals 44 Appendix 2 Country profile macroeconomic indicators, ghana 50 TABLES Table 1 Market development statistics on the ghana stock exchange 10 Table 2 Descriptive statistics and arch test 20 Table 3 Summary of unit root test 22 Table 4 Autocorrelation test 24 Table 5 Garch (2,1) contemporaneous trading volume 26 Table 6 Garch (2,1) lag trading volume 27 Table 7 Restricted garch (2,1) estimate 29 Table 8 Unrestricted garch (2,1) estimate 30 Table 9 Negative size bias test 31 Table 10 Restricted gjr (2,1) estimate 33 Table 11 Unrestricted gjr (2,1) estimate 34 Table 12 Restricted egarch (2,1) estimate 36 Table 13 Unrestricted egarch (2,1) estimate 37

5 3 FIGURES Figure 1 General economy indicators (millions) ghana 10 Figure 2 Daily return - gse all-share index 21 Figure 3 Daily adjusted returns - gse all-share index 21 Figure 4 Daily trading volume - gse all-share index 21

6 4 1 Introduction Financial theory reveals that information flow is usually the result of fluctuations in stock market and trading volume. Stock prices are usually influenced by positive trading volume through the available set of relevant information in the market and researchers have over the years investigated the effect of previous day returns and volume on current market returns. In an efficient market, investors cannot make excess profit just by trading on past information since all information is immediately incorporated by the market. This theory is known as the Efficient Market Hypothesis (EMH). Following studies such as Clark (1973), Epps and Epps (1976) and Copeland (1976), several financial researchers have investigated the relationship between return, volume and volatility on different markets and interesting results have been reported. In his study of financial markets, Karpoff (1987) outlined four key reasons why the price-volume relation is important: First, it provides insight into the operations of financial markets; Second, it is important for event studies that use a combination of price and volume data to draw inferences; Third, it provides insight into the debate over the empirical distribution of speculative assets; and finally, it has significant implications for research into futures markets as price variability affects volume of trade in futures contract. In the case of the Ghana stock exchange (GSE), very little literature is available that explores the link between stock return and trading volume. This study fills this gap by examining the daily returns and trading volume of the Ghana stock market from 2005 to 2010 for evidence of significant possible relationship between the variables. That is, the main focus of the study is to investigate whether trading volume has an explanatory power on the return volatility of the GSE. However, studies have shown that emerging markets are typically characterized by thin trading. The effect of thin trading is that prices recorded at the end of a time period have a tendency to be positively autocorrelated (Siriopoulos, Tsotsos and Karagianni 2001). Thus, thin (infrequent) trading introduces autocorrelation in the time series of returns for a series which would otherwise exhibit serial independence. Therefore, an analysis is performed to correct for thin or infrequent trading in the second stage. In the third and final stage the volatility behaviour of stock returns is examined where trading volume, past residual error and past volatility are used as information set. The study is organized as follows: Section 2 discusses the theoretical framework of the study and previous research. A brief overview of the Ghana stock exchange is also provided in section 2. Section 3 discusses methodology and a description of the time series data used is provided in section 4. Descriptive features and some diagnostic

7 5 testing on the time series data employed are also presented in section 5. The empirical results are discussed in Section 6 and the last Section presents conclusion.

8 6 2 Theory and previous research The theoretical framework of this study is set on two different hypotheses regarding the link between return, volatility and volume. The mixture of distribution hypothesis (MDH) derived by Clark (1973) and Epps and Epps (1976), is based on the assumption that the change in return and volume is due to the arrival of news or information. This news or information is often interpreted as negative or positive shocks. If the shock is unexpectedly negative, the price of the securities decreases and if it is unexpectedly positive, then the effect on price change will be positive. These movements are supposed to be influenced by the above-average trading activity in the market as it adjusts to a new equilibrium. The MDH further posits that since changes in the volumevolatility variables are always simultaneous in response to the latent news or information arrival, it is logical to conclude that no information in the previous volatility data can be utilized to predict volume. The second theory is the sequential information arrival hypothesis (SIAH) proposed by Copeland (1976). Contrary to the MDH, the SIAH examines the relationship between volume and volatility by explaining the function of previous values of volatility in present and future forecast of volume. The underlying assumption is that, traders do not receive the information at the same time which creates incomplete equilibrium. Therefore, the final equilibrium is attained when all traders tend to react to new information or news concurrently. This makes it possible to predict trading volume. The return volume relationship has been broadly examined in the developed markets since the early 1970s (example: Clark (1973) Karpoff (1987); Lamoureux and Landstrapes, (1990)). By using the GARCH model, Lamoureux and Landstrapes (1990) concludes that the persistence in the volatility of the US market diminishes when volume is introduced in the conditional variance equation. In recent years, Fenghua and Xiaoguang (2009) used the composite index of several developed and developing markets, including the CAC40 (CAC), Xetra DAX (DAX), NIKKEI 225, S&P 500, SWISS market index, Strait Times Index (STI) in Singapore, Shanghai Security Composite Index (SSE) and Shenzhen Component Index (SZE) in China to examine the variability in returns, unexpected trading volume (volume without time trend and autocorrelation) and persistence-free trading volume (unexpected trading volume without heteroscedasticity). Their results indicate significant trading volume in all the observed markets. They conclude that both unexpected trading volume and persistence-free volume have strong explanatory power to the return volatilities. However, the persistence-free volume explained the heteroscedasticity of the return better than the unexpected volume. They used the simple GARCH model for the

9 7 empirical tests. Similarly, Hussain (2011) studied the intraday behavior of bid-ask spread, trading volume and volatility using an aggregate data on the DAX30 constituents. The study found that contemporaneous and lagged trading volume, and bid-ask spread have statistically significant effect on return volatility. His results further indicate that there is asymmetric effect of trading volume on conditional volatility. Moreover, Louhichi (2011) reports a consistent result using the CAC40 index. His results indicate positive relationship between volume and return, and significant reduction in volatility persistence by including volume in the variance equation of the GARCH model. On the contrary however, Bong-Soo and Rui (2002) employed the Grangercausality test to show that trading volume does not Granger-cause returns on the New York, Tokyo and London stock markets. Regarding the cross country relationships, the study found that the US financial market variables contain an extensive predictive power for UK, and Japanese financial market variables. It is observed from the previous literature that the results on the developed markets vary according to the models and techniques employed by the researchers. A wide body of the literature using the GARCH model often shows results consistent with the concept. As is the case with the developed markets, studies from the emerging market view point also show variable results. Whereas, some indicate positive relationship, others indicate no positive association between the variables. For example, Mubarik and Javid (2009) studied the Pakistani stock market and found that there exist significant interaction between trading volume and return volatility when volume is entered into variance equation of GARCH-M model. They used daily returns and volume series of seventy stocks traded at the Karachi Stock Exchange from July 1998 to October They tested the existence of the Sequential Information Arrival Hypothesis (SIAH) and the mixture of distribution hypothesis (MDH). De Medeiros and Doornik (2006) conducted a similar study on the Brazilian stock market and concluded that there exist contemporaneous, as well as dynamic relationship between stock returns and volume. They further show that return volatility contains information about upcoming trading volumes. The empirical methods they adopted include the cross-correlation analysis, bivariate simultaneous equations, regression analysis, GARCH modeling, VAR modeling, and Granger causality tests. In the case of Thailand, Thammasiri and Pattarathammas (2010) used the SET50 index futures market return and volume from 2006 to 2008 and concluded that there exist significant contemporaneous and dynamic relationships between volume and return, thereby, providing support for the SIAH in the Thai Futures market.

10 8 In the African context, however, Nowbutsing and Naregadu (2009) examined the Mauritius stock market using thirty-six stocks, six constructed indices and the SEMDEX and reported no positive relationship between trading volume, volatility and returns. They employed the simple GARCH and and the asymmetric GJR-TARCH to test the MDH. Similarly, Girard and Omran (2009) show that volatility persistence is not eliminated in the Cairo and Alaxandria (CASE) stock exchange when lagged or contemporaneous volume is introduced into the GARCH model. They collected data on 79 stocks from 1998 to Other similar research on emerging markets include; a study by Naliniprava (2010), on the Indian stock market. The study employed ARCH, GARCH, EGARCH, TARCH, PGARCH and Component ARCH models. They collected data based on the daily closing price of actively traded 30 scripts and trading volume from the Bombay Stock Exchange spanning January 2005 to January The results showed that recent news of trading volume may be used to improve the prediction of stock price volatility. Srinivasan, Devanadhen and Malabika (2010) investigated the price changes, trading volume and time-varying conditional volatility for selected Asia Pacific stock markets by using daily data set from 1 st January 2005 to 31st December The results of the study demonstrate that for some countries, return causes volume and volume causes returns. Moreover, the results show a positive correlation between stock return and trading volume series for most of the stock markets, that is, Australia, India, Japan, New Zealand and Taiwan using the Granger casuality test and the Variance Decomposition (VDC) test.

11 Brief overview of the Ghana stock exchange (GSE) The Ghana stock exchange was incorporated in July 1989 with trading commencing in November It currently has 34 listed companies and 2 corporate bonds. The main indices are the GSE All-Share Index and the Databank Stock Index (DSI). Three other indices comprising the SAS Index (SASI), SAS Manufacturing Index (SAS-MI) and the SAS Financial Index (SAS-FI) have also been published by the Strategic African Securities Limited. Trading activities of the exchange always take place daily (5 days of the week) on the floor of the exchange. The Ashanti Gold shares however, can be traded both through the exchange and over-the-counter after the close of the day s trading activities. All over-the-counter trades are subsequently reported at the next trading session. The exchange has two sessions; the pre-market sessions, which start from 9:30am to 10:00am and the normal trading sessions, which commence at 10:00am to 12:00noon on all trading days. Trading does not take place on Saturdays, Sundays and holidays declared by the exchange in advance. Table 1 shows some market development statistics on the GSE from 2000 to 2008 As can be seen from the table, there have been some improvements in the market from 2000 to It shows that the number of listed firms, market capitalization, the All Share Index (ASI), trading volume and value of shares traded, have all witnessed consistent improvements. For instance, the number of listed companies had increased from 24 in 2000 to 35 in Moreover, the table shows that total market capitalization of the GSE recorded a phenomenal growth of more than 3000% over the eight year period. Other improvements are seen in the volume of shares traded which climbed as high as million in Since the performance of financial market has effect on the general performance of the economy of a nation, the study reports some macroeconomic statistics on Ghana from 2000 to Similar to the movements observed in the stock market, there has been consistent expansion in the general economy since According to figure 1, the country s gross domestic product (GDP) growth in 2008 and 2009 was about sixteen and fifteen dollars respectively, as compared to about five million dollars that was recorded in the year Even though, imports of goods and services beat exports in all the years observed, it is evident that the nation s exports have also increased consistently over the years. Comprehensive accounts of the macroeconomic statistics are shown in table 20.

12 10 Table 1 Market development statistics on the Ghana stock exchange Year Volume traded (m) Value traded GH(m) GSE Allshare index ( % change) Firms Market Cap. GH(M) , , ,185 11,249 12,368 17,895.1 Source: Ghana Securities and Exchange Commission report (2008), p 31 Source: African Development Bank Online Data Portal , , , , ,0 Exports of goods & services, Value (WEO, cur. US$) Imports of goods & services, Value (WEO, cur. US$) GDP (current US$) 8 000, , , ,0 0, Figure 1 General economy indicators (millions), Ghana 1 Table 2 is located in the appendix

13 11 3 Methodology This study investigates the relationship between return, volume and volatility by following the Heteroscedasticity model contained in most financial literature. The empirical examination is conducted by fitting the GARCH model proposed by Bollerslev (1986) first, to the returns series, and subsequently, to the thinly corrected returns series. Specifically, the GARCH (2,1) model is employed by the study. Studies have shown that thin trading is a common feature of most emerging markets. For example, in his study of the efficiency of the Vietnamese stock market, Loc, Lanjouw and Lensink (2010) reported that the non-parametric runs test rejected the null of random walk in the observed time series. However, the same method failed to reject the random walk in the returns of four stocks when the series were corrected for thin trading. Similarly, Al-Khazali, Ding and Chong Soo (2007) conclude that the correction for thin trading makes all of the MENA markets: Bahrain, Egypt, Jordan, Kuwait, Morocco, Oman, Saudi Arabia, and Tunisia efficient in the weak form; even though, all the series, in their raw state rejected the random walk. Stationarity of the series are examined by employing two unit root testing methodologies; the Augmented Dickey- Fuller unit root test proposed by Dickey and Fuller (1979) and Kwaitkowski, Phillips, Schmidt and Shin (KPSS, 1992) test. Finally, asymmetries in return volatility and volume are investigated using the Exponential GARCH (EGARCH) and the GJR models Thin trading and return calculation Studies have shown that thin (infrequent) trading can induce autocorrelation in the return series and in recent years, it has been reported as a common feature of most emerging markets. Some of the earliest studies on the subject include; Fisher (1966) and Dimson (1979). Thin trading can occur in two different instances. First, it results when stocks trade every consecutive interval, but not necessarily at the close of each interval and this is often termed as nonsynchronous trading. The second occurs when stocks do not trade every consecutive interval and is often referred to as non trading. In this study, the method employed by Miller, Muthuswamy, and Whaley (1994) to model the effects of both forms of thin trading of index portfolio stocks on the observed changes in the index level, have been followed. They employed a modified AR(1) process to represent the observed index price change process. This is shown by equation (1):

14 12 = + 1(1 ), (1) where is the true index level innovation, is the observed index level change, and the parameter measures the degree of trading infrequency. In this specification, is taken to lie between zero and one, and as approaches zero, trading becomes perfectly continuous. They explain that the observed change in the index level then fully captures the contemporaneous true index innovation, which is assumed to be mean zero serially uncorrelated shock variable with a homoscedastic variance,. On the other hand, as approaches one it implies that the last trade for a stock in the index may have taken place in some previous period. Miller et, al (1994) indicate that the observed price changes can be adjusted by (1) to remove the thin trading effects from the measurement of returns. By estimating the observed index price change process as a modified AR (1) process, they show that the residuals from the model can be used to adjust the return calculation using the formula: = /(1 ), (2) where is the return at time t adjusted for thin trading. Thus, the correction model assumes a constant thin trading adjustment throughout the estimation period Unit root test Theoretically, a time series that contains a unit root are often characterized as nonstationary processes that have no tendency to return to a long-run deterministic path. The variance of the series is said to be time-dependent and goes to infinity as time evolves. In this study, the Augmented Dickey Fuller (1979) and Kwaitkowski, Phillips, Schmidt and Shin (KPSS, 1992) unit root tests are applied to all variables to verify stationarity. The ADF test equation is specified below. The dependent variable x is the trading volume or the return. The null hypothesis for the test is that the variables are non-stationary or have a unit root. (3) = + P + + The KPSS (1992) tests differs from the ADF test already described and it is often used for confirmatory purposes of the presence of a unit root in time series after conducting

15 13 the ADF test. The test assumes that the observed time series is stationary around a deterministic trend under the null hypothesis. The KPSS statistic is based on the residuals from the OLS regression of on the exogenous variables : = + (4) The LM statistic is defined as: = () /(²), (5) where, is an estimator of the residual spectrum at frequency zero and () is a cumulative residual function Autoregressive conditional heteroscedasticity (ARCH) The series is examined for ARCH effect at lag 1. The ARCH model was developed independently by Engle (1982) and it was a major breakthrough in econometric modelling. This is because the ARCH model provides explanation to several of the important features of financial asset returns, such as; volatility clustering, and leptokurtosis. It is suggested that before estimating a GARCH-type model, it is ideal first, to compute a test for ARCH effects to make sure this class of models is appropriate for the data. Thus, the ARCH test serves as a purely diagnostic test to justify the application of GARCH-type models. An important support for the use of ARCH family models is given by Lamoureux and Landstrapes, (1990) who explain that the presence of ARCH is based upon the hypothesis that daily returns are generated by a mixture of distributions, in which the rate of information arrival is the stochastic mixing variable. Thus, the presence of ARCH in returns is due to MDH. The ARCH model up to order is of the form: = ( ) +, (6) = = +, = 1, 2,3,. (7) Notice that equation (6) is the conditional mean equation, where represents the conditional mean given the available information at time 1; denotes a sequence of random variables with zero mean and constant variance. In equation 7, the following conditions must always exist to ensure that the conditional variance is always positive: 1, and, 0(= 1,2,3,.).

16 Generalised autoregressive conditional heteroscedasticity (GARCH) The GARCH model derived by Bollerslev (1986) was an extension to the ARCH model. It is discovered to provide a good fit for financial time series and offers explanation to most of the distributional features of asset returns. For instance, the GARCH is said to be less likely to breach non-negativity constraints and needs fewer lags to be included in the model. This study employs a GARCH (2,1) model, modified to include a dummy variable, accounting for the possible effects on market volatility of the July 2007 Ghanaian currency devaluation. By viewing the stochastic process of stock returns as a GARCH (2,1) process, the mean equation can be written as an AR(1) model: = + + ~ (0, ) (8) where represents the return or the adjusted return at time t and is the lagged return or adjusted return. is the residual error term for the day t and is treated as a collective measure of news at times t. Equation (8) is an AR(1) model, which describes returns as been dependent on its own lagged values. In order to investigate whether contemporaneous or lag trading volume has impact on returns, the volume parameter is included in the mean equation as shown below: = (9) = (10) The second part of the GARCH (2,1) model is the variance equation. Here, the volume parameter is entered into the conditional variance equation to investigate whether trading volume explains the GARCH effects for returns on the GSE. The model with or without the volume parameter is shown below. In order to account for the possible effects on stock market volatility of the July 2007 currency devaluation, a dummy variable is added to the conditional variance equation: = (11) = , (12) where represents the conditional variance term at period t and is mean. and represents the news coefficient and news about volatility from the previous period,

17 15 measured as the lag of the squared residual from the mean equation,. represents a persistence coefficient and is the forecast variance at period 1 which is the GARCH term. The parameter is the coefficient of the dummy that takes the value of 1 for the period after July 3, 2007 (when the new currency was introduced) and 0 or otherwise. A statistically significant value for the dummy variable will mean that the devaluation of the currency has an impact on the market volatility. Positive suggests that the introduction of the new currency possibly increases the market volatility. Whereas, negative will suggest that the introduction causes a reduction in volatility. is the trading volume on day t. The GARCH (2,1) refers to the presence of first-order GARCH term, and first and second-order ARCH terms Asymmetric GARCH models The deficiency of the simple GARCH model often prompts the use of models that can capture the possible asymmetries associated with stock market volatility. The GARCH model is argued to enforce a symmetric response of volatility to both positive and negative shocks therefore, its inability to fully explain the impact of negative and positive shocks on volatility. Currently, there are many asymmetric GARCH models that can be employed in empirical financial study. This study however, employs two of the most popular formulations: the GJR (TARCH) model and the EGARCH model. Similarly, both the GJR and EGARCH models are modified to include the currency devaluation dummy variable. In order to verify whether these asymmetric models will provide a better fit for the data, the negative size bias diagnostic test proposed by Engle and Ng (1993) is conducted. This test is purely a diagnostic measure that examines the returns series for possible asymmetries in volatility. Specifically, the negative size bias test investigates whether the size of the shock has symmetric response to volatility or not. In empirical study, the Engel and Ng (1993) test is usually applied to the residuals of a GARCH fit to the returns data. The size of the shock is interpreted to have asymmetric impact if is significant in the regression: where S, Z, = + S,, +, (13) is a dummy = 1 if Z <0 and is an iid error term. Z, standardized residuals from the GARCH (2,1) estimate. is the square of the

18 The GJR-TARCH (2,1) model The GJR model was developed and named after the authors; Glosten, Jagannathan and Runkle (1993). This model is very similar to the GARCH with an additional parameter accounting for the possible asymmetries. The model with the trading volume parameter is shown below. The objective is to investigate whether response to volatility is asymmetric and moreover, whether trading volume has asymmetric impact on volatility. Similar to the test approach under the GARCH (2,1) model, the study first estimates a standard GJR without the trading volume and finally estimate by including trading volume in the conditional variance equation. These are shown below: = (14) = (15) Equation 14 is the standard GJR model including the currency devaluation dummy that account for the possible impact on market volatility of the period after the devaluation. In equation 15, is the volume parameter that measures whether trading volume has a significant asymmetric impact on return volatility. For asymmetric effect, the parameter must be significantly different from zero. is a dummy variable equal to one, if <0. Here, the condition for non-negativity will be: >0, + >0, > The EGARCH model The Exponential GARCH (EGARCH) was developed independently by Nelson (1991). Since the model imposes a log on the conditional variance, forecasts of the conditional variance are always non-negative even if the parameters are negative. This contributes to a clear advantage over the pure GARCH model. The model with or without trading volume is shown below. The significance of the trading volume parameter will be shown by its impact on volatility. Here also, the study incorporates the currency devaluation dummy that takes the value 1 to represent the period after July 3, 2007 and 0 or otherwise. log = + log (16) +

19 17 log = + log (17) + + Note that is the GARCH term that measures the impact of last periods forecast variance. A positive indicates volatility clustering, implying that positive stock price changes are associated with further positive changes and vice versa. is the ARCH term that measures the effect of news about volatility from the previous period on current period volatility. The presence of asymmetry is determined by the hypothesis <0. The impact is asymmetric if 0. A negative implies that negative shocks have greater impact on volatility than positive shocks of the same size.

20 18 4 Data The time series data used in this study includes daily closing prices and trading volume of the main market index referred to as the GSE All Share Index. The sample period is from 1 st August 2005 to 31 st December Two data sources have been utilized, and these include; the datastream and the commercial database of Business Ghana. These data sources are believed to be credible since they have been the source of numerous empirical studies in the past. Since returns rather than prices have been employed in this study, the first approach had been to generate daily returns from the price series. The continuously compounded returns are calculated as: = 100 ln ( / ), (18) where and represents the closing price at day and 1 respectively. Similarly, the trading volume parameter is measured by the log difference change in the trading volume at day and 1 and computed as: = ln ( ), (19) where is day trading volume and is the previous day s trading volume.

21 19 5 Descriptive statistics and diagnostic tests In this section, the basic descriptive features of the return and trading volume series are presented. The unit root test is conducted to verify stationarity in the series and ARCH is investigated at lag 1 to confirm the appropriateness of the GARCH model for the data. It must be emphasized again that the empirical examination is conducted in the return, as well as the adjusted returns series Descriptive statistics and ARCH test Table 2 summarizes the descriptive features of the daily return and volume on the GSE. It shows that the returns have negative mean and negative skewness indicating that the distribution is skewed to the left. Moreover, the high kurtosis and Jarque-Bera (JB) statistic indicate that the return distribution is fat tailed. However, the adjusted returns have positive mean, although it has similar skewness, kurtosis and JB statistic as the returns. Nonetheless, the null of normality is conclusively rejected in both the returns and adjusted returns series. Daily trading volume, unlike the returns, has positive skewness meaning that the distribution is skewed to the right. Again, the Jarque-bera statistic is very high and the distribution has high kurtosis. Again, the null of normally distributed trading volume series is conclusively rejected. Table 2, further presents the test for autoregressive conditional heteroscedasticity (ARCH) in the residuals. It is seen that the coefficient of the lagged squared residuals is positive and significant for both the actual returns and the thinly corrected returns, which agrees fully with an ARCH process. Figures 1, 2 and 3 respectively, show the volatility behaviour of the return, adjusted return and the volume series over the sample period. As can be seen, the behaviour of figures 1 and 2 are very similar. The significant point to note from both figures is that volatility occurs in bursts, or clustering. It is seen that, there have been a prolonged period of relative serenity in the market during the last quarter of 2005 through to early 2007, evidence by only comparatively small positive and negative spikes. However, during mid-2007 to early 2009, the market witnessed relatively high volatility. On the other hand, the market s trading volume (Figure 2) was far more volatile over the sampling period. This is shown by the large positive and large negative spikes observed from 2005 through to 2010.

22 20 Table 2 Descriptive Statistics and ARCH Test Variable Mean Std. Dev Skewness Kurtosis JB Prob Returns Adj. Returns 2.46E Trading Volume ARCH Effect at Lag 1 Variable Coefficient Std. Error t-statistic Probability C Rt. RESID^2(-1) C E Adj. Rt. RESID^2(-1) The hypotheses for the JB-test are: H0 = normal distribution H1 = no normal distribution ARCH Diagnostic statistics for - R-squared ( ), Adjusted R-squared ( ), Log likelihood ( ), Durbin-Watson stat ( ), Akaike info criterion ( ), Schwarz criterion ( ) ARCH Diagnostic statistics for - R-squared ( ), Adjusted R-squared ( ), Log likelihood ( ), Durbin-Watson stat ( ), Akaike info criterion ( ), Schwarz criterion ( ), F-statistic ( ), Prob(F-statistic( )

23 21 Figure 2 Daily Return - GSE All-Share Index Figure 3 Daily Adjusted Returns - GSE All-Share Index Figure 4 Daily Trading Volume - GSE All-Share Index

24 Unit root test The presence or absence of a unit root in time series have diverse implication on the application of such a series in any empirical study. Financial theory suggests that any data used for a study must be stationary. In this study, the stationarity of the trading volume and adjusted return series have been verified by employing the Augmented Dickey-Fuller unit root test and the KPSS test. The test results summarized in Table 3 reveals that both the ADF and KPSS tests conclusively, reject the presence of a unit root in the volume, returns and the adjusted returns series at the 1%, 5% and 10% significant levels. More specifically, the ADF test statistics and the KPSS LM statistics of the volume and returns; respectively, are all smaller than the critical values. This implies that the series are stationary. Table 3 Summary of unit root test Variable ADF (Test Statistics) KPSS Test (LM Stats) P-values Returns Adj. Returns Volume Test type Critical values ADF 1% 5% 10% Returns Adj. Return Volume KPSS 1% 5% 10% Returns Adj. Return Volume ADF and KPSS tests have been computed with 10 lags, and in the level of the series

25 Autocorrelation test A significant effect of thin trading is that it can induce autocorrelation in a series which ordinarily would have been serially independent. Proponents of the concept believe that thin trading often lead to the false conclusion of inefficiency of emerging markets (Loc, Lanjouw and Lensink (2010); Al-Khazali, Ding and Chong Soo (2007)). Moreover, the use of data from thin markets in any empirical study has the potential of negatively affecting the econometrician s estimates or results. This study investigates the effect of thin trading by conducting autocorrelation test in both the returns and adjusted returns series. The test results shown in table 4 reveal that there is significant dependence in both the returns and the adjusted returns series from lag 4 to 10. However, the Q-Statistics in the adjusted returns have slightly smaller values from the significant lags as compared to the raw returns series. This suggests that the return series is comparatively, highly autocorrelated than the adjusted returns series and therefore, may be the effect of infrequent trading. 2 The autocorrelation of a series Y at lag k is estimated by: = ( )( )/ ( ), where is the serial correlation coefficient of stock returns at lag; N is the number of observations; is the stock return over the period t; is the stock return over the period t+k; is the sample mean of stock returns; and k is the lag of the period.

26 24 Table 4 Autocorrelation test Returns LAG AC PAC Q-Stat Probability Adj. Returns

27 25 6 Empirical results This section presents the empirical results of the study. First, the data series is examined for contemporaneous or lag relationship by introducing the volume parameter in the mean equation of GARCH (2,1). Second, the impact of trading volume on volatility is examined under two separate assumptions: restricted and unrestricted variance equation of the GARCH (2,1) model. Finally, asymmetries in volatility is investigated using the GJR-TARCH (2,1) and the EGARCH (2,1) models Contemporaneous and lag trading volume In this section, the study examines whether contemporaneous or lag trading volume has a statistically significant relationship with the return or adjusted return of the GSE. The examination is initially conducted in the returns, and subsequently, in the thinly adjusted returns. Table 5, shows the result using contemporaneous volume; and it is observed that the parameter of the trading volume is positive, however, not statistically significant in both the raw return and the adjusted return series. Similarly, in table 6, the one day lag trading volume is not statistically significant in the returns, as well as the adjusted returns series. This implies that contemporaneous, as well as lag trading volume have no statistically significant effect on the raw returns and/or the adjusted returns series of the GSE. This result is consistent with Girard and Omran (2009). With regards to the conditional variance equation, it observed from both tables 5 and 6 that all the estimated parameters are significant at the 1% level. Specifically, volatility is seen to be persistent and the conditional variance is stationary. Further, the ARCH terms of, and the GARCH coefficient are all statistically significant, suggesting that the conditional variance is greatly influenced by previous and current variance. This also implies that both previous and current shocks have impact on current return. This result seems to suggest that the Ghana stock market is weak form inefficient, and consistent with the findings of Appiah-Kusi, Kojo and Menyah (2003), Frimpong (2008), and Smith (2008).

28 26 Table 5 GARCH (2,1) Contemporaneous trading volume Dependent Variable: Mean Equation Coefficient z-statistic Probability R Variance Equation *** *** *** *** *** Dependent Variable: Mean Equation Coefficient z-statistic Probability R * Variance Equation *** *** *** *** *** (***), (**) and (*) denote significance at 1%, 5% and 10% levels respectively

29 27 Table 6 GARCH (2,1) Lag trading volume Dependent Variable: Mean Equation Coefficient z-statistic Probability R (-1) Variance Equation *** *** *** *** *** Dependent Variable: Mean Equation Coefficient z-statistic Probability R *** (-1) Variance Equation *** *** *** *** *** (***), (**) and (*) denote significance at 1%, 5% and 10% levels respectively

30 Trading volume and GARCH effect This section, presents the empirical investigation of the impact of volume on stock return volatility using the GARCH (2,1) model. This examination is conducted in two fold; first, the variance equation is restricted under the assumption that the volume parameter is equal to zero ( = 0). The second instance is the unrestricted case where is included in the variance equation. This approach has been adopted in order to compare the outputs after introducing volume in the analysis. Note that, as a result of the devaluation of the Ghanaian currency in July 2007, the study incorporates a dummy variable into the conditional variance model to investigate the effect of the policy on the market volatility. The test results under the two separate assumptions are summarized in tables 7 and 8. As shown in Table 7 (restricted variance equation) the coefficients on both the lagged squared residual and lagged conditional variance terms are positive and significant in the returns as well as the adjusted returns series at the 1% level. Typically, the value of is high and the sum of the coefficients, ( + )+ = 0.99 in both series. Since a large sum of these parameters theoretically implies that a large positive or negative return will lead future forecast of the variance to be high for protracted period, the study concludes that shocks to the conditional variance will be very persistent. It also follows that, the half-lives of shocks to the volatility of the GSE, measured as (0.5) /( + + ) is 68days for both the raw return and the adjusted return. On the other hand, the coefficient is positive and highly significant, implying that the GSE has possibly been far more volatile since the devaluation of the currency. The above results hold for both the raw return and the adjusted return series. In Table 8, the focus is on the trading volume parameter, and it is seen that the parameter is positive and highly significant at the 1% level in the thinly adjusted return series. In the case of the raw return series, the volume parameter is only significant at the 10% level. Therefore, it can be concluded that the correction for thin trading has been necessary. Moreover, it is observed that the introduction of volume into the analysis did not significantly alter the volatility persistence. Therefore, with regards to the theory of MDH, it can be concluded that the ARCH effects in stock returns of the GSE is less likely to be due to the MDH, as it was observed by Lamoureux and Landstrapes, (1990) in the US market. Thus, the results indicate that the MDH does not exist in the Ghana stock market, and consistent with findings of a number of studies on emerging markets (Naliniprava, (2010), in the Indian stock market and Mubarik and Javi (2009), in Pakistan have found similar results). It is necessary to note again that, the parameter remains statistically significant at the 1% level, even, after introducing volume into the analysis.

31 29 Table 7 Restricted GARCH (2,1) estimate Dependent Variable: Mean Equation Coefficient z-statistic Probability Variance Equation *** *** *** *** *** Dependent Variable: Mean Equation Coefficient z-statistic Probability Variance Equation *** *** *** *** *** (***), (**) and (*) denote significance at 1%, 5% and 10% levels respectively.

32 30 Table 8 Unrestricted GARCH (2,1) estimate Dependent Variable: Mean Equation Coefficient z-statistics Probability Variance Equation *** *** *** *** * Dependent Variable: Mean Equation Coefficient z-statistics Probability Variance Equation 8.43E *** *** *** *** *** (***), (**) and (*) denote significance at 1%, 5% and 10% levels respectively.

33 Test asymmetries in volatility In order to investigate whether the asymmetric GJR and EGARCH will provide a better fit to the series as compared to the simple GARCH model, the study conducted the Engle and Ng (1993) negative size bias test. This test is purely a diagnostic measure that determines whether the size of the shocks to the conditional variance have different impact. The test is computed from the residuals of the GARCH (2,1) model fit to the returns and adjusted returns data. The results summarized in table 9 shows that the coefficient is negative and significant at the 1% level in both the raw return and the adjusted return. This implies that response of volatility to shocks in the raw returns and the thinly corrected returns series is not symmetric. Thus, negative and positive shocks to the lagged residual, impact differently upon the conditional variance. This result makes it appropriate to use models that can capture such possible asymmetries in the volatility. Table 9 Negative size bias test Panel A: GARCH (2,1) residual_ Variable Coefficient t-statistics Probability Panel B: GARCH (2,1) residual_ Variable Coefficient t-statistics Probability The negative size bias test is computed from the regression;,,, +, where, is a dummy = 1 if <0 and is an error term., is the standardized squared residuals from the GARCH (1,1) estimate

34 GJR estimate In this section, the results of the GJR asymmetry tests are presented. Table 9 presents the results of the test without trading volume, and table 10 shows the results that includes volume in the analysis. As can be seen from table 8, the coefficients, is positive and highly statistically significant, implying that there is asymmetric response of volatility to shocks in both the actual returns and the thinly adjusted returns series. Specifically, the result shows that the downside of the GSE is more volatile than the up side. Moreover, the coefficients, and ; are all statistically significant at the 1% level. This imply that both old and recent news have significant impact on volatility. Asymmetry measured as [( + + )/( + )], is approximately 3 and 2 respectively for the raw return and the adjusted return series. This means that the impact of negative shocks is three times higher than the impact of same positive shocks in the raw returns and two times higher in the adjusted return. This result is consistent with the normal application of a GARCH type model to index return series. Moreover, the coefficient is positive and highly significant, meaning that the devaluation policy has causes increased volatility of stock returns of the GSE. In table 10, the focus is on the trading volume parameter. It is seen that the parameters,,,, and remains statistically significant at the 1% level in both series. However, the parameter which measures whether trading volume has asymmetric impact on volatility is positive but not statistically significant. This means that volume has no asymmetric impact on volatility, and that asymmetry is only observed through shocks to the conditional variance, such as the announcement of a new government policy. This result is consistent in both the actual returns and the adjusted returns series. Here also, asymmetry is approximately 2 in the raw and adjusted returns series, meaning that the increase in volatility is two times higher when the shock is negative than same positive shock.