Empirical Evidence from Sudanese Stock Market

Middle Eastern Finance and Economics ISSN: 1450-2889 Issue 16 (2012) © EuroJournals Publishing, Inc. 2012 http://www.middleeasterneconomicsandfinance.com

Day-of-the-Week Effect on Returns and Conditional Volatility: Empirical Evidence from Sudanese Stock Market Suliman Zakaria Suliman Abdalla Assistant Professor (Financial Econometrics) Department of Quantitative Analysis, College of Business Administration King Saud University, Riyadh, Kingdom of Saudi Arabia E-mail: [email protected]; [email protected] Tel: +966560847037; Fax: +9664678648 Abstract This paper investigates the day of the week effect anomaly on stock market returns and the conditional volatility of the Khartoum stock exchange (KSE) from Sudan over the period of 2nd January 2006 to 30th October 2011 using daily observations on the general market index. The paper tests for possible existence of the day of the week variation by employing Ordinary Least Squares (OLS) technique as well as two different univariate specifications of the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model. Empirical results based on using OLS and GARCH models find; in general, negative and insignificant estimated parameters for all days of the week in both returns and conditional volatility equations. Also, the results indicate that the day of the week effect is not influenced by the stock market risk based on using GARCH-M(1,1) model. Furthermore, results show that the null hypothesis that the day of the week dummy variables are jointly equal to zero is accepted. Hence, day of the week effect is not present in the KSE index returns during the period of the study, a finding which contradicts most of the empirical finance literature investigating the phenomena in financial markets across different regions and countries. Keywords: Day of the week effect, Mean returns, Dummy variable regression, Volatility, GARCH, Khartoum Stock Exchange

Acknowledgment The author is gratefully acknowledges the financial support provided by the Research Center at the College of Business Administration (King Saud University).

1. Introduction Over the last few decades, calendar anomalies in financial markets have become a fertile area for research in empirical finance literature, and have been receiving considerable attention from academics as well as practitioners. A well-known and most important anomalies can be listed briefly as: (i) the day of the week effect1 (significantly lower/higher returns on some day of the week; usually higher Friday returns and lower Monday returns); (ii) the holiday effect (returns higher on the days before 1

The studies on the day-of-the-week effect have been ongoing since 1930 when Kelly revealed the existence of a Monday effect on the US markets, where the returns turned out to be negative.

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some festivals or vacations); and (iii) the monthly or January effect (relatively higher January returns compare with other months of the year). The day of the week effect is a phenomenon that develops a form of anomaly of the efficient capital markets theory. According to this phenomenon, the average daily returns of the market are not the same for all the days of the week, as we would expect on the basis of the efficient market theory. The presence or absence of this effect has important implications for investors. Their investment strategies, portfolio selection and management will vary according to different effects, to reap maximum profits. There is a large and extensive empirical literature2 in different financial markets which focuses on the issue of the day of the week effect. The issue appears in various forms in international literature such as market efficiency, calendar effects, non-randomness of stock market returns, Monday effect and others. The earliest empirical examinations of the day of the week effect seem to go back to the studies by Cross (1973), French (1980), and around the same period; Gibbons and Hess (1981), Lakonishok and Levi (1982), Gultekin and Gultekin (1983), Keim (1983), Keim and Stambaugh (1984), Rogalski (1984), Theobald and Price (1984), Jaffe & Westerfield (1985), Harris (1986) and Simrlock & Starts (1986) have also investigated this effect across different markets. These studies provide evidence that there are differences in distribution of stock returns for each day of the week and come to the conclusion that Mondays’ average returns are negative and Fridays’ are positive, which means the stock exchange market starts downwards and ends upwards. However, there are many other studies such as Condoyanni, O’Hanlon and Ward (1987), Solnic and Bousqet (1990), in the French stock market, Athanassakos and Robinson (1994), in the stock markets of Australia and Japan, Kim (1988) in the stock markets of Japan and Korea, Dubois and Louvet (1996) in the stock markets of Japan and Australia,, Balaban (1995) in the stock market of Turkey, which supported that the negative average returns are observed on Tuesdays. More recently, the issue of day of the week effect has also investigated extensively. For example: Chusanachoti and Ravindra (2002), Kiymaz and Berument (2003), Kohers et al. (2004), Lian and Chen (2004), Brusa, Liu, and Schulman (2005), Cai et al. (2006), Chukwuogor (2007), Kenourgios and Samitas (2008), Marrett, and Worthington, (2008), Anwar, and Mulyadi, (2009), Blau, et al. (2009), Christophe et al. (2009), Naliniprava (2010), Phaisarn and Wichian (2010), Worthington, (2010), Faryad et al (2011), Mine and Ikram (2011), Raja et al. (2011) and Talat and Ibrahim (2011). Their results confirm the findings of previous studies in the sense that the patterns of the effect are mixed with majority of them suggested a negative Monday and a positive Friday3. On the other hand, some researchers found no evidence of day of the week effect. For instance, Santemases (1986), Pena (1995) and Gardeazabal and Regulez (2002) have documented on insignificant week day effects on the Spanish stock market. Brooks and Persand (2001) found no day of the week effect for the Philippines. Marashdeh (1994) and Davidson and Peker (1996) conclude that there is no day of the week effect in the Malaysian stock market. The Demirer and Karan (2002) study of the Turkish stock market did not find clear evidence of “the effect” even though they noted that the Friday returns were “consistently high”. Aly et al (2004) study the Egyptian market and show that there is no significant difference among daily mean returns. In a study for the small off-shore market of Mauritius, Agathee (2008) suggests no significant existence of a calendar effect. Despite the large number of studies in market anomalies, there is no consensus about underlying reasoning; some of the anomalies quickly disappear after being reported. However, some of the anomalies (such as the day of the week effect) are persistent; the most usual days where the day of the week effect appears in the various stock markets over the world are Mondays, Tuesdays, and Fridays. In addition to that, findings are contradictory in the sense that equity markets report different 2

3

Most studies dealing with this anomaly use a simple dummy variable approach based on a linear regression with 5 dummy variables referring to the days of the week. The most satisfactory explanation that has been given for the negative returns on Mondays is that usually the most unfavorable news appears during the weekends. These unfavorable news influence the majority of the investors negatively, causing them to sell on the following Monday.

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results due to their individual characteristics. Researchers have found the day of the week effect sensitive to the level of the markets’ maturity and size, the economic cycle and the organizational structure. Although calendar anomalies in developed equity markets have been investigated extensively, little attention has been paid in developing markets, and to the best of my knowledge, empirical research on the topic of these calendar anomalies is fragmented as there is no work in the Sudanese stock market, so the current study attempts to fill this gap. The main objective of this paper is to investigate the existence of the day of the week effect in the Sudanese stock market for both the returns and conditional variance (volatility) using daily observations of the general price index series from Khartoum Stock Exchmange (KSE), the main stock market in Sudan for the period 2nd January 2006 to 30th October 2011 by applying the usual OLS regression and two different GARCH specifications. The remainder of this paper is organized as follows: Section 2 provides a general overview of the Khartoum Stock Exchange. Section 3 describes the data and provides summary statistics. In the fourth section the methodology is presented, while the results of the estimation are discussed in section 5. Finally, section 6 concludes the paper.

2. An Overview of the Sudanese Stock Market The Khartoum Stock Exchange (KSE) is the principal stock exchange of Sudan located in Khartoum. KSE started its activities officially in January 1995 with the assistance of the Common Market for Eastern and Southern Africa (CoMESA)4, with the objective of regulating and controlling the issuance of securities, and mobilizing private savings for investment in securities. Securities traded in the KSE are ordinary shares and investment units. Furthermore, a substantial number of mutual funds and Government Investment Certificates (GISs) are also traded, (KSE Annual report, 2010). Orders are handled through brokers during trading hours and share prices are quoted in Sudanese Pound (SDG). Trading is processed manually by continuous auction from Sunday to Thursday for one hour from 10.00 am to 11.00 am. Thereby, buy and sells orders are passed on to floor-based representatives of registered brokers for execution. Trading in securities is taking place in two markets: the so called primary and secondary markets5. As a part of the financial system in Sudan, KSE operates on the basis of Islamic Shariaa and is supervised and regulated by the Central Bank of Sudan. The key feature of Islamic Shariaa practices in Khartoum stock exchange is that it is aimed to offer investment portfolios from common stocks of listed companies. These ideally satisfy three basic criteria: (i) legitimate field of economic activity; (ii) interest-free dealings in both assets and liabilities; and (iii) the dominance of real assets. Thus, e.g., a company must not be engaged in the production of illegitimate goods like alcoholic drinks; it must not deal with interest rate financing as a means to leverage its capital structure through fixed debt liabilities, or generate interest income from investment securities. Since a company’s shares represent equity rights in its assets, the latter should be real assets, not liquid money or receivable debt as they cannot be sold freely at a profit, like real goods, real estate and machinery (Hassan and Lewis, 2007). As a consequence of this rules, the composition of assets traded at the KSE differs substantially from other stock markets. In particular, due to the regulations imposed by Islamic Shariaa practices a separate class of investment vehicles on the KSE is provided by the so called Government 4

Member states are: Burundi, Comoros, Democratic Republic of Congo, Djibouti, Egypt, Eritrea, Ethiopia, Kenya, Libya, Madagascar, Malawi, Mauritius, Rwanda, Seychelles, Sudan, Swaziland, Uganda, Zambia and Zimbabwe. 5 The Primary Market deals with the trading of new securities. When a company issues securities for the first time (i.e. IPO) , they are traded in the Primary Market through the help of issuing houses, Dealing /Brokerage Firms, Investment Bankers and or Underwriters. The acronym IPO stands for Initial Public Offering, which means the first time a company is offering securities to the general public for subscription. Once the securities (shares) of a company are in the hands the general public, they can be traded in the Secondary Market to enhance liquidity amongst holders of such financial securities. Thus, the Secondary Market facilitates the buying and selling of securities that are already in the hands of the general public (investors).


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Musharakah6 Certificates (GMCs), which represents an Islamic equivalent to conventional bonds (also known as Shahama bonds)7. Shahama bonds offer a way for the government to borrow money in the domestic market instead of printing more banknotes. After one year, holders of GMCs can either liquidate them or extend their duration. These bonds are backed by the stocks of various companies owned by the Ministry of Finance. Consequently, they might be considered as asset-backed securities. The profitability of GMCs depends on the financial results of the companies in the underlying portfolio. It can reach up to 33 per cent per annum. Hence, the profit of GMCs is variable rather than fixed. The government issues these bonds on a quarterly basis and their placement on the market is done usually very fast- in just six days. KSE is relatively small market as compared to the stock markets of the developed countries or even to some countries in the Arab region (see Table 1); the number of listed companies of the market is few and most stocks are infrequently traded, market capitalization and traded value are very low. Banks, Communications and Certificates sectors dominate the trading activity of the market in terms of volume of trading and number of shares. KSE currently lists 53 companies with a total market capitalization of $ 3,166.89 million (KSE Annual report, 2010)8 (See Table 2 for more details and summary statistics representing the trading activity in Khartoum stock exchange over the period of the study). The overall performance of the Khartoum stock market is measured by the KSE index, which is a market capitalization-weighted index. In September 2003, the KSE index was established and listed in the Arab Monetary Fund database. At the end of the first month the index closed at 961.74 points. At December 2005, the index closed at the highest level of 3259.17 points. In October 2011 it was fluctuating around average value of 2369.23. Table 1:

Trading Activity in Some Arab Stock markets (2010)

Value Traded Shares Traded Market Capitalization No. of (U.S.$) (Million) (U.S.$) Transactions Abu Dhabi 9,115.70 17,111.97 71,268.62 352879 Amman 9,349.25 6,912.23 30,995.34 1859611 Bahrain 283.26 610.12 19,902.66 19375 Beirut 1,693.10 150.70 18,210.20 18631 Casablanca 14,249.58 354.66 69,058.36 329129 Khartoum 972.69 166.55 3,166.89 8266 Doha 17,726.54 2,012.25 123,316.64 1017570 Dubai 18,473.25 37,578.17 54,722.23 777326 Egypt 36,967.80 27,336.99 85,725.96 9606668 Kuwait 42,772.42 73,682.50 124,919.97 1237908 Muscat 3,365.40 2,990.60 21,712.05 536135 Palestine 586.63 217.20 3,460.80 79727 Saudi 192,445.39 31,555.34 353,419.01 16108992 Tunis 1,913.30 245.04 11,750.70 574461 Source: Compiled by the author based on data from Arab Monetary Fund website and KSE annual report. Market

6

7

8

No. of Listed Companies 64 277 49 26 75 53 43 65 212 214 119 40 146 56

“Musharakah” is a word of Arabic origin which literally means sharing. In the context of business and trade it means a joint enterprise in which all the partners share the profit or loss of the joint venture. It is an ideal alternative for the interest-based financing with far reaching effects on both production and distribution (Usmani, 1998). For a detailed discussion of the Islamic Shariaa principles and its practices on stock exchange see for example: El-Gamal (2006) and Ayub (2007). Out of this listed number there are 20 banks, 8 Insurance companies, 6 commercial companies, 2 in the industrial sector and 3 companies in the agricultural sector, 4 in the communication sector, 5 in services sector and 5 other companies with various activities.

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Table 2:

Summary of Trading Activity in Khartoum Stock Exchange (Secondary market)

Market No. of traded Volume of No. of Capitalization Shares (In trading ($ Transactions ($ millions) Million) millions) 2006 52 7,567.78 833.89 3,912.61 5842 2007 53 9,411.56 749.58 4,048.64 7195 2008 53 289.00 751.60 3,416.60 8177 2009 53 164.71 891.27 2,784.76 8069 2010 53 166.55 972.69 3,166.89 8266 Notes: * The number of listed companies does not include Funds & Certificates. Source: Compiled by the author based on data from KSE and Central Bank of Sudan annual reports. No. of Listed Companies*

Year

Certificates Traded (In thousands) 1,472.4 2,016.5 2,421.1 3,417.7 3,452.4

3. The Data and Basic Statistics 3.1. Data for Analysis The time series data used for investigating the day-of-the-week effect in this paper are the daily closing prices of Khartoum Stock Exchange (KSE) index over the period from 2nd January 2006 to 30th October 2011, resulting in total observations of 1548, excluding public holidays. During this period trading is conducting Sunday to Thursday9. These closing prices have been taken from the KSE website (http://www.kse.com.sd). Daily returns rt were calculated as the continuously compounded returns corresponding to the first difference in logarithms of closing prices of KSE-Index of successive days:  P  rt = log  t   Pt −1 

(1)

where Pt and Pt −1 denote the closing market index of KSE at the current (t) and previous day (t-1), respectively. 3.2. Summary Statistics To specify the distributional properties of the daily KSE returns series rt for each day of the week as well as for the entire study period, various descriptive statistics were calculated, the results are reported in Table 3. Table 3:

Descriptive Statistics of the KSE Return Series

Statistic Sunday Monday Mean -0.00899 -0.000811 Median 0.00000 0.000000 Maximum 0.211228 0.036939 Minimum -0.116074 -0.113392 Standard deviation 0.020541 0.009303 Skewness 1.972633 7.353670 Kurtosis 48.46297 82.32316 Jarque- Bera 26464.43* 83525.36* No. of observations 306 309 Notes: * denotes statistical significance at 1% level.

Tuesday -0.000423 0.000000 0.088654 -0.119453 0.014141 2.328377 34.52679 13076.16* 310

Wednesday -0.000511 0.000000 0.111581 -0.111711 0.015050 0.244184 44.26296 21782.55* 308

Thursday -0.000478 0.000000 0.131066 -0.142914 0.014676 0.213310 56.79345 37862.09* 315

All Days -0.000160 0.000000 0.211228 -0.116074 0.012708 1.896395 86.11071 44616.1* 1548

Table 3 reports the preliminary statistics for the returns for each day of the week as well as for the returns of the entire period. According to the results in Table 3, four important points are be observed: First, Khartoum stock exchange has negatively mean returns for all days of the week, a result which is not consistent with empirical finance literature behind the day of the week effect. Second, the 9

The work week in Sudan is Sunday through Thursday with Friday and Saturday being the weekend.


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standard deviation on Sunday (the starting day of the week) is (0.0205) which is more than the standard deviations on other days of the week. It shows that Sunday returns are more volatile. Third, by examining the skewness for the returns series of each day, the results in Table 3 also show that all sample distributions are positively skewed, indicating that they are nonsymmetric. Furthermore, they all exhibit high levels of kurtosis (distributions have thicker tails than normal distributions). Finally, the return distributions for all days are non-normal. All Jarque-Bera statistics for normality test are significant at the 1% level, suggesting the rejection of the null hypothesis.

4. Methodology Most of the studies reported in the empirical finance literature investigated the day of the week effect phenomena in mean returns by employing the Ordinary Least Squares (OLS) methodology in which returns are regressed on five daily dummy variables, as done, for instance in Cross (1973), French (1980), Lakonishok and Levi (1982), Gibbons and Hess (1981), Keim and Stambough (1984), Jaffe and Westerfield (1985), Smirlock and Starks (1986), Abraham and Ikenberry (1994), and Agrawal and Tandon (1994). The OLS specification can be written as follows: (2) rt = β1SUNt + β 2 MONt + β3TUEt + β 4WEDt + β5THU t + ε t where: rt : the index returns on day t; SUNt : dummy variable equal to 1 if t is a Sunday and 0 otherwise; MON t : dummy variable equal to 1 if t is a Monday and 0 otherwise; TUEt : dummy variable equal to 1 if t is a Tuesday and 0 otherwise; WEDt : dummy variable equal to 1 if t is a Wednesday and 0 otherwise; THU t : dummy variable equal to 1 if t is a Thursday and 0 otherwise;

ε t : error term; β1 , β 2 , β3 , β 4 , and β5 are the coefficients to be estimated. However, as Connolly (1989, 1991) claim, several specific problems may arise while using this approach: (i) the returns are likely to be autocorrelated; (ii) the residuals are possibly non-normal; (iii) the issue of heteroscedasticity may arise; and (iv) outliers with high/low value of return may distort the overall picture. To eliminate the possibility of having autocorrelated errors, lagged values of the return variable must be included in model (2). The resulting equation has the following specification10: P

rt = β1SUNt + β 2 MONt + β3TUEt + β 4WEDt + β5THU t + ∑ rt −i + ε t

(3)

i =1

where the variables and their coefficients are explained as in Eq. (2). And, in order to address the problem of heteroscedasticity, we allow variances of the errors to be time dependent to include a conditional Heteroscedasticity11 that captures time variation of variance in stock returns. Thus, error terms now have a mean of zero and a time changing variance of ht2 that is,

ε ~ (0, ht2 ) . To do so, the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model, proposed initially by Engle (1982) and further developed by Bollerslev (1986) is used.

10

In the equation, the intercept term is excluded, in order to avoid the problem dummy variable trap (Damodar and Dawn (2009) for more details). 11 Because the data are daily and so are of high frequency we expect that ARCH effects exist. It is a well documented fact that financial market returns suffer time-dependent changes in volatility (Fama, 1965, Lau et al., 1990, Kim and Kon, 1994). Applying ordinary least squares we confirm this assumption.

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In presenting GARCH models, there are two distinct equations, the first for the conditional mean and the second one for the conditional variance12. In this model, the conditional variance is represented as a linear function of a long term mean of the variance, its own lags and the previous realized variance. The general specification of GARCH, GARCH (p, q) is given by: Mean equation rt = µ + ε t (4) q p Variance equation σ 2 = ω + α ε 2 + β σ 2 (5) t

∑

j t −1

j =1

∑

i

t −1

i =1

where ω > 0 . And α1 ≥ 0 and β1 ≥ 0 , and: rt = return of the asset at time t. µ = average return. ε t = residual returns, defined as: (6) where zt is standardized residual returns (i.e. iid random variable with zero mean and variance 1), and σt2 is conditional variance. The constraints α1 ≥ 0 and β1 ≥ 0 are needed to ensure σ t2 is strictly positive (Poon, 2005). ε t = σ t zt

Models to be Estimated Considering the discussion in the previous section, the paper investigates the day of the week effect for the Khartoum stock exchange in both returns and conditional variance equations, by using the usual OLS regression and two different Generalized Autoregressive Conditional Heteroscedastic (GARCH) specifications. The parameters of the two different GARCH types of specifications for the return and volatility equations are estimated following the quasi-maximum likelihood (QML) estimation introduced by Bollerslev and Wooldridge (1992) under the assumption of Gaussian distributed error terms. The log likelihood function is maximized using Marquardt’s numerical iterative algorithm to search for optimal parameters.13 Model 1: Day of the Week Effect in Return Using OLS Regression In the first model, the paper employs a dummy variable approach based on a linear regression with 5 dummy variables referring to the days of the week, we include in this model lagged values of the return variable to eliminate the possibility of having autocorrelated errors, accordingly, the first model can be written as follows: P (7) rt = β1SUNt + β 2 MON t + β3TUEt + β 4WEDt + β5THU t + ∑ rt −i + ε t i =1

Model 2: Day of the Week Effect in Return Using GARCH Model The second model is the GARCH (1,1), which will be used to address the possibility of having heteroscedasticity problem, the model has the following form: P (8) rt = β1SUNt + β 2 MON t + β3TUEt + β 4WEDt + β5THU t + ∑ rt −i + ε t i =1

(9)

σ t2 = ω + α1ε t2−1 + β1σ t2−1

Model 3: Day of the Week Effect in Return and Volatility Using GARCH-M Model 12

In the GARCH model, the mean equation is written as a function of a constant with an error term. Since σ t2 is the one – period ahead forecast variance based on past information, it is called the conditional variance. The conditional variance equation is specified as a function of three terms: (i) A constant term : ω , (ii) News about volatility from the previous period, measured as the lag of the squared residual from the mean equation: forecast variance:

13

2 σ t −1

ε t2−1

(the ARCH term), and (iii) Last period

(the GARCH term).

For potential issues regarding the numerical solution of the maximum likelihood estimators for GARCH models, the interested reader might consult Maringer and Winker (2009).


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In the third model, the paper make use of the Generalized Autoregressive Conditional Heteroscedasticity in Mean (GARCH-M)14 model. In which, we include some exogenous variable into the variance equation to allows one to incorporate volatility effect as well as risk premium, therefore, the third model of the following form: P (10) rt = β1SUN t + β 2 MON t + β 3TUEt + β 4WEDt + β 5THU t + ∑ rt −i + λσ t2 + ε t i =1

σ

2 t −1

= β1SUN t + β 2 MONt + β 3TUEt + β 4WEDt + β 5THU t + α1ε t2−1 + β1σ t2−1

(11)

σ : The variance of the error term; 2 t

ε t2−1 : Last period’s volatility (the ARCH term); σ t2−1 :

Last period’s variance (the GARCH term). and λ is called the risk premium parameter. A positive λπ indicates that the return is positively related to its volatility. In other words, a rise in mean return is caused by an increase in conditional variance as a proxy of increased risk. ε t is an error term with zero mean and conditional variance σ t2 (see Engle, Lilien, and Robins 1987 for more details);

Testing for Heteroscedasticity One of the most important issues before applying the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) methodology is to first examine the residuals for evidence of heteroscedasticity. To test for heteroscedasticity in residuals of the KSE index returns series, the Lagrange Multiplier (LM) test proposed by Engle (1982) is applied. In summary, the test procedure is performed by first obtaining the residuals et from an ordinary least squares regression of the conditional mean equation, which might be an autoregressive (AR) process, moving average (MA) process or a combination of AR and MA processes; i.e., an ARMA process. For example, in ARMA (1,1) process the conditional mean equation will be: rt = ϕ1rt −1 + ε t + θ1ε t −1 (12) After obtaining the residuals et , the next step consists in regressing the squared residuals on a constant and q lags as in the following equation: (13) et2 = α 0 + α1et2−1 + α 2et2−2 + ... + α q et2−q +ν t The null hypothesis that there is no autoregressive conditional heteroscedasticity (ARCH) up to order q can be formulated as: H 0 : α1 = α 2 .. = α q = 0

against an alternative: H1 : α i > 0

for at least one i = 1, 2, …, q. The test statistic for the joint significance of the q-lagged squared residuals is given by the number of observations times the R-squared ( TR 2 ) of the regression (13). TR 2 is evaluated against the χ 2 ( q) distribution. This represents an asymptotically locally most powerful test (Rachev et al., 2007)

5. Empirical Results OLS regression The results of OLS regression for each day of the week using model (1) are presented in Table 4.

14

This model is an extension of the basic GARCH framework which allows the conditional mean of a sequence to depend on its conditional variance or standard deviation. It was developed by Engle, Lilien, and Robins (1987)

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Table 4:

OLS Results for the Day of the Week Effect

Variable SUN MON TUS WED THU

Coefficient -0.000387 -0.000453 -1.22E-05 0.000431 -1.73E-07 -0.107872

rt −1

Statistics F-Statistic Chi-Square Lags 5 10 15

Panel A: OLS Results Std. Error 0.008980 0.017901 0.012658 0.015503 5.34E-06 0.025334

t-Statistic -0.043062 -0.025313 -0.000964 0.027782 -0.032474 -4.258035

Panel B: Diagnostic Checking: Wald Test Value 0.067889 0.339443 Panel C: Diagnostic Checking: ARCH-LM Test ARCH-LM test statistic 75.77530 236.6096 236.6096

Probability 0.9657 0.9798 0.9992 0.9778 0.9741 0.0000 Probability 0.996828 0.996835

Prob. Chi-square 0.0000 0.0000 0.0000

The results in Panel A of Table 4 show that all t-statistics of the estimated parameters are negative and statistically insignificant for all days of the week. This result indicates that the average daily returns for Khartoum stock exchange is independent of the days of the week. The Wald test results in Panel B of the Table indicate that the null hypothesis that the day of the week dummy variables are jointly equal to zero is accepted. Hence, day-of-the-week effect is not present in the KSE returns series during the period of the study, confirming the results of panel A of Table 4. To confirm the use of the GARCH methodology we have to test for heteroscedasticity, to do so, the study employs ARCH-LM test to the previous equation to test the null hypothesis that there are no ARCH effects in the residuals series up to lag 15. The ARCH-LM test results in Panel C of Table 4 provide strong evidence for rejecting the null hypothesis of no ARCH effects. Rejecting this null hypothesis is an indication of the existence of ARCH effects in the residuals series and therefore the variance of the returns series of KSE index is non-constant.

Estimation Results of the GARCH (1,1) Model Table 5 summarizes the results from the reexamination of the day of the week effect on the Khartoum index returns with the GARCH (1,1) model. Table 5:

Variable SUN MON TUS WED THU rt −1

ω α β

The Day of the Week Effect in Returns Equation Panel A: Coefficient Estimates Mean Equation Coefficient Std. Error 0.006579 0.006637 0.001165 0.019164 0.005197 0.013075 -0.010608 0.010497 -3.68E-07 1.57E-05 0.153168 0.040262 2.11E-05 0.899545 0.428629

Variance Equation 4.73E-07 0.055589 0.012860

Z-Statistic 0.991399 0.060803 0.397441 -1.010615 -0.023503 3.804278

Probability 0.3215 0.9515 0.6910 0.3122 0.9812 0.0001

44.61720 16.18209 33.32965

0.0000 0.0000 0.0000

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Middle Eastern Finance and Economics - Issue 16 (2012) Table 5:

The Day of the Week Effect in Returns Equation - continued

Statistics F-Statistic Chi-Square Lags 5 10 15

Panel B: Diagnostic Checking: Wald Test Value 0.096744 0.878643 Panel C: Diagnostic Checking: ARCH-LM Test ARCH-LM test statistic 0.052995 0.587797 0.785110

Probability 0.934768 0.934815 Prob. Chi-square 0.999966 0.999986 1.000000

The estimated coefficients of the five days of the week reported in Panel A of Table 5 provide evidence that the GARCH (1,1) results are similar to the OLS results of being statistically insignificant. In the variance equation from Table 5, the three coefficients ω (constant), ARCH term ( α ) and GARCH term ( β ) for GARCH (1,1) are statistically significant and with expected sign, also, the sum of the two estimated ARCH and GARCH coefficients α + β (persistence coefficients) in the GARCH (1,1) is larger than one, suggesting that the conditional variance process is explosive. Using the Wald test, the null hypothesis that the day of the week dummy variables are jointly equal to zero is accepted as appear in Panel B of Table 5, confirming the absence of the day of the week effect for Khartoum stock exchange during the study period. In Panel C of Table 5, ARCH-LM test does not indicate the presence of a significant ARCH effect in the residual series which means that the conditional variance equitation is well specified.

Estimation Results of the GARCH-M(1,1) Model In this paper GARCH-M(1,1) model is applied to test whether the day of the week effect is influenced by the stock market risk, the results of estimation are presented in Table 6. Table 6:

Variable SUN MON TUS WED THU rt −1

λ SUN MON TUS WED THU

ω α β

Statistics F-Statistic Chi-Square

The Day of the Week Effect in Return Equation

Coefficient -0.000111 -0.000456 0.000647 0.000435 -1.81E-07 -0.100887 5.192247

Panel A: Coefficient Estimates Mean Equation Std. Error 0.989180 199.1669 1.423118 197.8735 0.076008 0.050641

Z-Statistic -0.000113 -2.29E-06 0.000454 2.20E-06 -2.38E-06 -1.992205

1.877326 -2.765768 Variance Equation -1.50E-06 0.000783 -0.001920 -1.64E-06 0.259416 -6.32E-06 -1.69E-06 0.081362 -2.07E-05 -1.59E-06 0.178061 -8.95E-06 -9.47E-08 1.33E-07 -0.714445 8.95E-05 1.08E-05 8.329700 0.150000 0.025536 5.873994 0.599998 0.045412 13.21228 Panel B: Diagnostic Checking: Wald Test Value Probability 1.530036 0.177311 7.650179 0.176598

Probability 0.9999 1.0000 0.9996 1.0000 1.0000 0.0463 0.0057 0.9985 1.0000 1.0000 1.0000 0.4750 0.0000 0.0000 0.0000

177


Table 6:

The Day of the Week Effect in Return Equation - continued

Lags 5 10 15

Panel C: Diagnostic Tests ARCH-LM test statistic 1.9453 1.0987 1.0569

Prob. Chi-square 0.1012 0.0834 0.0598

The GARCH-M (1,1) model is estimated by allowing the mean equation of the returns series to depend on a function of the conditional variance. From estimation results in Table 6, the estimated coefficient (risk premium) of σ 2 in the mean equation ( λ ) is positive, which indicates that the mean of the return sequence depends on past innovations and the past conditional variance. In other words, conditional variance used as a proxy for risk of returns is positively related to the level of returns. This result is consistent with the theory of a positive risk premium on stock indices which states that higher returns are expected for asset with higher level of risk. By using the Wald test, the null hypothesis that there is no gay of the week effect in the conditional variance equation is accepted. The AECH-LM test statistic rejects the null hypothesis of no ARCH effect left.

6. Conclusions The presence of calendar anomalies particularly the day of the week effect in financial markets has been investigated extensively across different regions and countries for the last few decades. Most of these investigations provide evidence that there are differences in distribution of stock returns for each day of the week and come to the conclusion that Mondays’ average returns are negative and Fridays’ are positive, which means the stock exchange market starts downwards and ends upwards. However, empirical research on the topic of these calendar anomalies is fragmented as there is no work in the Sudanese stock market, so the current study attempts to fill this gap. This paper attempted to empirically investigate the presence of the day of the week effect on both stock market returns and the volatility for the Sudanese stock market by using daily observations of the general price index series from Khartoum Stock Exchmange (KSE), the main stock market in Sudan for the period 2nd January 2006 to 30th October 2011. Three different models have been used; the Ordinary Lease Squares (OLS) and two different Generalized Autoregressive Conditional Heteroscedastic (GARCH) model. The paper applied the GARCH–M (1,1) model to test whether the day of the week effect is influenced by the market risk. Empirical results of the different models find negative and statistically insignificant mean returns for all days of the week which indicates the absence of the day of the week effect in both return and volatility equations for the Khartoum stock exchange. The paper concludes that the return for the KSE index is independent of the day of the week which contradicts the empirical finance literature of the day of the week effect during the period of the study.

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