Day of the Week Effect onNigerian Stock Market Returns and Volatility
Amadi, AU1.Aleke SF2 and Duruzor IG3
Department of Banking and Finance, College of Management Sciences, Michael Okpara University of Agriculture Umudike, Umuahia, Abia State.
3 Department of Accountancy/ Business Administration/Banking and Finance, Alex EkwuemeFederal University Ndufu Alike Ikwo, Ebonyi State Nigeria
Corresponding email: [email protected]
This study examined the day of the week effect on Nigerian stock market returns and volatility from 2008 to 2016. Secondary data extracted from various issues of Nigerian stock Exchange Factbook were used. Analysis of data was done with the help of E-Views Statistical Package using time series data.The autoregressive conditional heteroscedsticity (ARCH) model was used to find out if there is ARCH effect which is a justification for the application of thegeneralized autoregressive conditional heteroscedsticity(GARCH) model. GARCH model was then used to find out how persistent the volatility shock in the day to day activities of the stock market. The study revealed the presence of high persistent volatility shock in the daily activities of the Nigerian stock market.The study recommended that information dissemination in the Nigerian stock exchange should be widened to reduce the presenceof speculators in the market. Further research may be needed to look at the effect specific day of the week in particular has on the returns of the Nigerian Stock Market. Besides, the weekly returns and yearly returns are all worth looking into.
Keywords: Autoregressive,Hetroscedasticity, Returns, Nigeria, Stock market
Over the past decades, the study of stock market anomalies has gradually become one of the most interesting areas of financial market research. Anomalies are empirical results that seem to deviate from maintained theories of asset-pricing behaviour. They reflect either market inefficiency (profit opportunities) or inadequacies in the underlying asset-pricing model (Schwert, 2003). However, majority of these studies have focused on US and European markets and a few number of the studies on the Asian stock exchanges. Unfortunately, research on emerging African markets is practical scanty. Recent empirical evidence shows that market anomalies such as the small-firm effect, turn-of- the-year effect, momentum effect, weekend effect and holiday effect still appear to exist(Gultekin and Gultekin,1983).
The efficient market hypothesis (EMH) asserts that stock prices fully reflect all the information in an efficient market. It emphasizes on indifferent-returns of stocks regardless of start and end of the week or any other specific day. According to(Fama, 1965) an efficient market is one where returns cannot be exploited by trading in a specificpattern. However, in some financial markets, a number of habitual effects may create higher orlower stock returns depending on certain day, month and time periods. This particular phenomenon is beingobserved in many developed as well as emerging stock markets for over two decades. They are called seasonal orcalendar anomalies, and traditional asset pricing model is unable to fully explain this phenomenon. Among suchpatterns the most recurrent are the week-of-the-month effect,month-of-the-year effect (Rozeff and Kinney, 1976), and day-of-the-week (DOW) effect (Cross, 1973; French, 1980).
The existence of such anomalies in the stock market explains the break away from and deviation from the efficientmarket hypothesis, as the case may be mostly in weak-form market efficiency, because asset prices cease to be random rather becomepredictable with any seasonal and calendar variation. However this makes investors to build up trading strategies tomake abnormal profits in the markets. Take for instance, investors may willingly buystocks on a particular day and sell on another depending on certain trends in the market on these specific days inorder to take advantage ofthese effects. This variation in returns may be far above normal or below normal. This situation can affect investors in decision making with regards to their investment strategy, portfolio selection and portfolio management (AnwarandMulyadi, 2012). Ordinarilyinvestors do not feel safe or encouraged to invest in the stock market in thepresence of such phenomena. Therefore, it is pertinent to say that unveiling these volatility patterns in returns might benefit riskmanagement and portfolio optimization of valued investors in the market.
The objective of this study is to examine, the effect of the day of the week on the returns and volatility ofNigerian stock market. We used daily returns of the Nigerian stock exchange index (ASI) for the period of study: from 31 December 2008 to 31 December 2016. For the econometricmodel, the study employedautoregressive conditional heteroscedasticity (ARCH) and generalized autoregressive conditional heteroscedasticity (GARCH).The remainder of this paper is organized as follows; Section 2 presents a review of literature on related studies. Section 3 deals with the methodology. Section 4 deals with data analysis, discusses the application of data to the various models as well as the empirical results. Section 5 draws conclusion as well as appropriate recommendation.
2.0Review of Related Literature
2.1 Theoretical Framework
This study is anchored on asset pricing theory, owing to the fact that this study x-rayed day of the week effect on Nigerian stock market returns and volatility; it is not out of place to lay emphasis on asset pricing. Based on that, we reviewed the Capital Asset Pricing Model (CAPM).
2.1.1Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) proponents opined that expected return on an asset asthe sum of the return on the risk-free asset plus an expected premium for risk,where the risk premium is a function of the asset covariance with the marketreturn (beta).
E(Ri) = Rf+ßiE (Rm,t) – Rf (1)
The risk of a stock can be divided into two components. The first component is thesystematic risk (beta), which has to do with the overall market, and the second componentis non-systematic risk, which is peculiar to the individual stock. The fundamentalassumption of the CAPM is that the market will reward only the holding of systematicrisk as the unsystematic risk can be minimized by holding a diversified portfolio of assets.Unfortunately, financial managers cannot directly observe beta but must estimate it. Toestimate the beta of a firm, a time-series regression is used and the financialmanager is required to select both a return interval and an estimation period.
2.2 Empirical Review
There are few literatures on the day-of-the-week effect on Nigeria stock market return and volatility. Some include;Osazevbaru andOboreh (2014) who examined stock market anomalies in Nigeria using the OLS methods and the GARCH model under the normal error distribution assumption with data spanning from January 1995 to December 2009. They found out that there is Monday effect anomaly in the Nigerian stock market.
Osarumwense(2015)also assessed the influence of error distributional assumption on appearance or disappearance of day-of-the-week effects in returns and volatility using the Nigerian stock exchange (NSE-30). The Gaussian, Student-t, and the Generalized error distribution were incorporated in the GARCH (2,1) and EGARCH (2,1) models. Result reveals that day-of-the-week effects are sensitive to error distribution. The study also revealed that evidence of good or bad news in volatility does not only depend on the asymmetric model but also the choice of the error distribution.
Ajobola and Nwakanma (2014), studied market anomalies using 140 listed companies in the Nigeria equity market. They employed both the parametric and non-parametric methodology. Using the normal error distribution assumption with GARCH and TGARCH model, they concluded that there is a significant market anomaly in the Nigeria stock exchange. Other non-parametric methods used are the Lilliefors, Crammer-Von-mises, and the Anderson-Darling tests.
However, other studies that examined other stock markets around the world includes:Liu and Li (2010) Studied day-of-the-week effects in the top 50 Australian companies across different industry sectors. Unlike other Australian studies, they studied weekday seasonality using stock return data of individual companies. Utilizing the daily data for the period of January 2001 through June 2010, they found out that weekday anomalies are mixed across companies and industries. The study also revealed that the largest mean weekday returns occurs on Monday for 15 companies, most of which are the materials and energy companies. Further tests indicate that returns on Monday are significant larger than the other four days for six companies.
Berument and Kiymaz (2001) in their study test the presence of the day of the week effect on stock market volatility by using the S&P 500 market index during the period of January 1973 and October 1997. Their findings show that the day of the week effect is present in both volatility and return equations. While the highest and lowest returns are observed on Wednesday and Monday, the highest and the lowest volatility are observed on Friday and Wednesday, respectively. Further investigation of sub-periods reinforces their findings that the volatility pattern across the days of the week is statistically different.
3.1 Design of the Study
The design for this study is ex-post facto. This is because it relies on secondary data collected. It aims at determining and measuring the relationship between one variable and another or the effect of one variable on another in such a way that the variables involved will be manipulated by the research
3.2Natureand Sources of Data
Generally secondary data were used in this study. The data are time series data that reflects the dailyseries of All Share Index (ALSI), from 2008 to 2016.
These secondary data were sourced and extracted from existing documents and material. Data was collected from various issues of the Nigerian stock exchange fact book.
To investigateday of the week effect on Nigerian stock market returns and volatility, we employ the following model:Broadly, the GARCH model is specified as:
Yt = ? +?Yt-1 + €t …………….. (1)
Yt = dependent variable in time t
Yt -1 = lag value of the dependent variable in time t-1
€t = error term in time t
In line with the above specified broad model, the GARCH model for the study is specified as:
ALSIt = ? + ?ALSIt-1 + €t ………….. (2)
ALSIt = All share index in time t
ALSIt-1 = Lagged All share index in time t-1
t = Day of the week time series (from 2008 – 2016)
4.0 Empirical Results and Discussions
Auxiliary OLS Result
Dependent Variable: E2 Method: Least Squares Date: 01/20/17 Time: 08:10 Sample (adjusted): 1/04/2008 1/04/2016
Included observations: 1967 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 95608.46 9414.694 10.15524 0.0000
E2(-1) 0.317501 0.021386 14.84652 0.0000
R-squared 0.100859 Mean dependent var 140203.6
Adjusted R-squared 0.100401 S.D. dependent var 417227.0
S.E. of regression 395728.1 Akaike info criterion 28.61586
Sum squared resid 3.08E+14 Schwarz criterion 28.62154
Log likelihood -28141.70 Hannan-Quinn criter. 28.61794
F-statistic 220.4191 Durbin-Watson stat 2.110000
Prob(F-statistic) 0.000000 Source: Author’s computation using E-views 8.0 software
First, we try to establish whether there exists an ARCH (volatility) effect or not. The Autoregressive Conditional Heteroscedasticity (ARCH) test is made to find if there is ARCH effect and this is the justification for us to run the GARCH models. If the R-squared of the auxiliary regression result multiplied by the number of observations is greater than the critical value of 3.48, we reject the null hypothesis of no ARCH effect. From the result, the R-squared of the auxiliary regression (0.100859) multiplied by 1970 (number of observations) gave a value: 198.69223 which is greater than the critical value 3.48. Hence, we conclude that there is an ARCH (volatility) effect on the day-of-the week activities of the Nigerian Stock Exchange. Having fulfilled this condition, the estimation of the GARCH model is justified.
Dependent Variable: ALSI Method: ML – ARCH (Marquardt) – Normal distribution
Date: 01/20/17 Time: 08:14 Sample (adjusted): 1/03/2008 1/04/2016 Included observations: 1968 after adjustments Convergence achieved after 35 iterations Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 10.25201 17.33860 0.591283 0.5543
ALSI(-1) 0.999418 0.000546 1832.024 0.0000
Variance Equation C 4354.594 461.9454 9.426641 0.0000
RESID(-1)^2 0.250793 0.015754 15.91884 0.0000
GARCH(-1) 0.745599 0.013240 56.31515 0.0000
R-squared 0.998744 Mean dependent var 31612.48
Adjusted R-squared 0.998743 S.D. dependent var 10588.81
S.E. of regression 375.4018 Akaike info criterion 14.23542
Sum squared resid 2.77E+08 Schwarz criterion 14.24961
Log likelihood -14002.65 Hannan-Quinn criter. 14.24063
Durbin-Watson stat 1.142785 Source: Author’s computation using E-views 8.0 software
Secondly, the GARCH result shows that both ? and ? are significant as reflects their probability values which are less than 0.05 (i.e. P < 0.05) and this complies with the a priori expectation on non-negativity. The sum of both terms (0.996392) shows there is high persistence of volatility in the day of the week returns of the Nigerian Stock Exchange. The closer the sum to 1, the higher the persistence of volatility shock and this implies that the day to day activities in the Nigerian Stock Exchange conditional variance will experience slow reversion to its long run average whenever it experiences volatility shocks.
5.0Conclusion and Recommendation
This study examined the day of the week effect on theNigerian stock market returns and volatility for the period of 2008 to 2016 using the All share index (ALSI) market proxy for market returns. The autoregressive conditional hetroscedsticity(ARCH) model was used to find out if there is ARCH effect which is a justification for the application of GARCH model. The study found out that there is ARCH effect on the daily activities of the Nigerian Stock Market.
Furthermore empirical evidence reveals that the GARCH result complied with the apriori expectation of non negativity. The study found out that there is high persistent volatility shock in the daily activities of the Nigerian stock market. The study concluded that Nigerian stock market conditional variance will take a long time to be corrected whenever it experiences volatility shock.
Information dissemination in the Nigerian stock exchange should be widened to curb the activities of speculators in the market.Further research may be needed to look at the effect each day of the week in particular has on the returns of the Nigerian Stock Market. Besides, the weekly returns and yearly returns are all worth looking into.
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