Calendar anomalies in African stock markets

Abstract In this paper, we investigate the day of the week and the month of the year effects in African stock markets, both in the Gregorian and the Hijri calendars. Specifically, we investigate Monday effect, Friday effect, January effect and Ramadan effect, from January 2009 to December 2019, using OLS regression with robust standard errors. January is the first month of the Gregorian calendar, while Ramadan is the 9th and the most sacred month of the lunar calendar, used in Muslim countries. The results obtained show the existence of Monday effect in BRVM and Namibia, Friday effect in Kenya and Namibia, January effect in Botswana and Zambia, December effect in Botswana, BRVM and Egypt and Ramadan effect in Tunisia.


PUBLIC INTEREST STATEMENT
Stock markets may be characterized by the existence of abnormal variations in some days of the week, some weeks or some months. Abnormal variations mean that they are excessively higher or lower on some days (e.g., day of the week effect, week-end effect, holiday effect), weeks (e.g., Turn of the Year effect, Week of the Year effect) or months (January effect, December effect). These abnormal variations related to time are called calendar anomalies. In this paper, we analyze the existence of calendar anomalies related to the Gregorian calendar and those related to the Hijri calendar (the Islamic calendar) in the African stock markets. The existence of these calendar anomalies in a stock market are very important and crucial as it influences portfolios strategies of the investors. Our study shows strong evidence of the existence of calendar anomalies (Day of the Week effect, Month of the year effect and Ramadan effect) in African stock indices.

Introduction
While efficient market hypothesis EMH indicates that stock markets are efficient, stock prices follow a random walk and are thus unpredictable (Fama, 1965(Fama, , 1970(Fama, , 1995, several authors found that stock markets are characterized by calendar anomalies. These anomalies are time related (Floros & Salvador, 2014) and may depend on days, weeks or months. Indeed, calendar anomalies imply that stock returns are different (higher or lower) on some days (day of the week effect, week-end effect and holiday effect), weeks (Turn of the Year effect, Week of the Year effect), months (January effect, Ramadan effect, Halloween effect) than other days, weeks and months of the year. In this paper, we investigate the Day of the Week (Monday and Friday), January and Ramadan effects in African stock markets. The January and Ramadan effects are related to months and are detected in two different calendars: the Gregorian calendar and the Hijri calendar.
The majority of countries adopt the Gregorian calendar as official calendar. The Gregorian calendar is a solar calendar composed from 12 months. Precedent research works show that some months (generally January or April) may be characterized by abnormal returns. This effect is called the January effect and implies that stock returns in January are higher than the others months of the year (Moller & Zilca, 2008;Shen et al., 2020). Wachtel (1942) is the first to find evidence of seasonal movements during December and January in the DJIA between 1927 and 1942. Several authors find evidence of January effect in the US (Haug & Hirschey, 2006;Poterba & Weisbenner, 2001;Reinganum, 1983;Rendon & Ziemba, 2007;Rozeff & Kinney, 1976), in the UK (Reinganum & Shapiro, 1987), in Canada (Berges et al., 1984) and in Irland (Lucey & Whelan, 2004)). In Asia, different authors found evidence of January effect in Japan (Kato and Schallheim (1985), in China (Zhang & Li, 2006) and in Taiwan (Chien & Chen, 2008;Shen et al., 2020). In Africa, Brishan (2012) find evidence of January effect in nine industrial sector (oil and gas, basic materials, industrials, consumer goods, health care, consumer services, telecommunications, financials and technology) indices in South Africa, between 1995 and 2012. Bundoo (2011) find evidence of January effect in Mauritius stock exchanges. Other papers investigate January effect at international level. Thus, Gultekin and Gultekin (1983) find evidence of January effect in major industrialized countries (Australia, Austria, Belgium, Canada, Denmark, France, Germany, Italy, Japan, Netherlands, Norway, Singapore, Spain, Switzerland, the UK and the US). Chui and Wei (1998) find evidence of January in Hong Kong (large firms) and in South Korea (small firms). Choudhry (2001) find evidence of January effect in the UK and the US and no evidence in Germany. However, Raj and Thurston (1994) find evidence of April effect in New Zealand. This effect is explained by the « tax loss selling » hypothesis (Reinganum, 1983). According to this hypothesis, investors sell, before the end of the year, stocks that prices have declined during the year to reduce their taxes, which impacted negatively their prices. In January, stocks sale decreases and prices increases. Thus, Paul and Theodore (2006) find evidence of Month of the year effect (April) in Ghana as the end of the year and the date of the submission of company reports is March, which confirms the tax-loss hypothesis. In the UK, Arsad and Andrew Coutts (1997) find evidence of January and April effects. Recent papers also documented calendar anomalies in cryptocurrencies (Kinateder and Papavassiliou (2019) find reverse January and March effects; Kaiser (2019) find reverse January effect; and Baur et al. (2019) find no evidence of January effect. and find that volatility declines during the month of Ramadan while there was no evidence of stock returns changes during and after Ramadan. Al-Hajieh et al. (2011) investigate Ramadan effect in Middle Eastern countries (namely Bahrain, Egypt, Jordan, Kuwait Qatar, Saudi Arabia, Turkey and UAE) between 1992 and 2007 and find evidence of Ramadan effects in the majority of stock markets (except Bahrain and Saudi Arabia). Ramadan effect in these markets is attributed, according to the authors, to the positive mood of investors during Ramadan. Ariss et al. (2011) find evidence of Ramadan and December effects on GCC (Gulf Cooperation Council) stock markets. Białkowski et al. (2012) investigate Ramadan effect in 15 markets (Bahrain, Egypt, Indonesia, Jordan, Kuwait, Malaysia, Morocco, Oman, Pakistan, Qatar, Saudi Arabia, Tunisia, Turkey and UAE). Results obtained show that stock returns during Ramadan were higher and less volatile and the authors conclude to the existence of Ramadan effect. Al-Khazali (2014) investigates Ramadan effects in the same sample as Al-Hajieh et al. (2011), over the period 1989-2012 and five sub-periods. Results confirm results of Białkowski et al. (2012) and show evidence of Ramadan effects. Khan et al. (2017) investigate Ramadan effect on the Karachi Stock Exchange (Pakistan) using GARCH and OLS models. While results obtained using GARCH model show a minor positive impact of Ramadan on the stock market, results obtained using OLS model show that stock market variations during this month are less volatile. Gavriilidis et al. (2016) find evidence of herding behavior in seven stock markets (Bangladesh, Egypt, Indonesia, Malaysia, Morocco, Pakistan and Turkey). Sonjaya and Wahyudi (2016) find evidence of Ramadan effect in 10 countries (8 Asian countries namely Bahrain, Indonesia, Jordan, Malaysia, Kuwait, Oman, Qatar and Saudi Arabia; and 2 African countries namely Morocco and Tunisia). Lai and Windawati (2017) find evidence of Ramadan effect in the Indonesian and Malaysian stock markets. Wasiuzzaman and Al-Musehel (2018) investigate Ramadan effect in Saudi and Iranian stock markets and find evidence of Ramadan effect on Saudi Arabia market while they find no evidence of Ramadan effect in the Iranian stock market. Yousaf et al. (2018) find no evidence of herding behavior during Ramadan in the Pakistani stock exchange. Also, Hassan and Kayser (2019) investigate the effect of Ramadan on Dhaka stock exchange (Bangladesh) and find no evidence of Ramadan effect on market volatility.
The day of the week has also been well documented. Thus, Dubois and Louvet (1996) find evidence of day of the week effect in nine countries (Australia, Canada, France, Germany, Hong Kong, Japan, Switzerland, the UK and the US). Results show low return in the first days of the week but not necessary on Monday. Also, Chiah and Zhong (2019) find evidence of Monday effect (positive returns) and Friday effect (negative returns) in 24 developed countries. Zhang et al. (2017) find evidence of Monday effect (on Argentina, China, Italy, Poland, Singapore, the US «Dow Jones Industrial index»), Tuesday effect (on Canada and the US «S&P 500», Wednesday effect (on Australia, Germany, Indonesia, Japan, Mexico, New Zealand, Switzerland), Thursday effect (on Czech Republic, the Philippines) and Friday effect (on Brazil, Chile, Hong Kong, India, Malaysia, Russia, Spain, Turkey). In Asia, Wong et al. (1992) find evidence of Monday and Tuesday effect (negative returns) and Friday effect (positive returns) in Hong-Kong, Malaysia, Singapore and Thailand stock markets. Basher and Sadorsky (2006) find evidence of day of the week effect on Pakistan, Taiwan and the Philippines. Ke et al. (2007) find evidence of day of the week effect on the three first days of the week on Taiwan. Ariss et al. (2011) investigate day of the week effect on Gulf Cooperation Council (GCC) stock markets, and as the weekend on these countries is on Friday and Tuesday, the authors find evidence of Wednesday effect (Wednesday in GCC is last day of the week before the weekend). H. Berument and Kiymaz (2001) find evidence of Wednesday and Monday effect (low returns) and Friday and Wednesday effect (low returns) on the S&P 500 index. Keef and Roush (2005) find evidence of weekend effect in preholiday returns on the S&P 500 index. Caporale and Zakirova (2017) find evidence of Monday and Friday effects in the Russian stock market. Evidence of calendar anomalies was also detected in the Thai stock market (Wuthisatian, 2021). Ma and Tanizaki (2019)  Previous studies that investigate aspects of the behavioral finance in African stock exchanges concerned specific stock markets-e.g., the Ghana Stock Exchange (Paul & Theodore, 2006), the Mauritius Stock Exchange (Agathee, 2012), the Casablanca Stock Exchange , the South African stock exchange (Bhana, 1985;Brishan, 2012;Du Toit et al., 2018), the Tunisian Stock exchange (Derbali & Hallara, 2016)-or a panel of stock markets (Chukwuogor, 2008;Guney et al., 2017;Kalidas et al., 2013).
African stock markets are members of the African Stock Exchanges Association (ASEA). According to Table 1, the oldest African stock market is the Egyptian Exchange, created in 1883, then the South African stock market "Johannesburg Stock Exchanges, four years later; in 1887. The Namibian stock market has also more than one hundred years (created in 1904). The youngest African stock markets are Lusaka stock exchange (1994), Dar Es Salam Stock Exchange (1996), Uganda Securities Exchange (1997) and Rwanda Stock Exchange (2005). The big five African stock markets (using market capitalization) are the Johannesburg Stock Exchange (867,2 billion $), the Namibian stock Exchange (130,3 billion $) and the Moroccan stock market "Casablanca Stock Exchange" (56 billion $). Three stock markets have more than one hundred listed companies: Johannesburg Stock Exchange (352), Egyptian Exchange (245) and Nigerian Stock Exchange (159). This paper is a replication the study of Obalade and Muzindutsi (2019), in which the authors investigate calendar anomalies in African stock markets. However, while the authors use Markov switching models, we apply in the present paper the usual approach that permit the detection of calendar anomalies in financial markets (Gibbons & Hess, 1981;Peterson, 1990;Solnik & Bousquet, 1990;Raj & Thurston, 1994;Keef & Roush, 2005;Ariss et al., 2011;M. H. Berument & Dogan, 2012;Caporale & Zakirova, 2017;Aharon & Qadan, 2019). We extend the sample to 16 African stock indices. 1 Also, while Obalade and Muzindutsi (2019) study two calendar anomalies (the month of the year and the intra-months effects) in the Gregorian calendar, we extend the calendar anomalies studied and investigate the Day of the week effect (Monday effect and Friday effect) and the Month of the year effect (January effect and Ramadan effect) both in the Gregorian and the Hijri calendars.
In this paper, we investigate the existence of calendar anomalies in African stock markets (Botswana, Cote d'Ivoire, Egypt, Kenya, Mauritius, Morocco, Namibia, Nigeria, Rwanda, South Africa, Tanzania, Tunisia, Uganda and Zambia) for the period post-subprime crisis and pre-Covid-19 crisis (for the period 2009-2019). We focus on three main anomalies, namely the Day of the Week effect (DOW) and the Month of the Year effect MOY (in both the Gregorian and Hijri calendars). The originality of the present paper lies to the inexistence, to the best of our knowledge, of a paper that examines calendar anomalies in a panel of 14 African countries, for the period post-subprime crisis and pre-Covid-19 crisis. This study presents two main contributions. First, as our literature review shows that there is a lack of studies on calendar anomalies in African markets, this paper contributes to extending the existing literature and its contribution cannot be underestimated. Second, results of this study have practical implications both for researchers, investors and authorities since the existence of calendar anomalies in African stock markets influences optimal portfolios strategies. One of the specificities of African markets is that they are relatively recent. In fact, 50% of the markets studied are less than 50 years old. The rest of this paper is organized as follows: section 2 presents the methodology adopted and data used, section 3 discusses obtained results and section 4 presents our conclusions.

Methodology and data
In this paper, we investigate the day of the week and the month of the year effects, using OLS regression with Huber-White robust standard errors. Thus, following the papers of Gibbons and Hess (1981), Peterson (1990), Solnik and Bousquet (1990), Raj and Thurston (1994), Keef and Roush (2005)

For january effect
where R it is the daily return of index i, M ti are dummy variables for months. M 1i is equal to 1 when day t is in January and 0 otherwise. M 2i is equal to 1 when day t is in February and 0 otherwise, and so on. The parameters β are estimated using OLS regression with Huber-White robust standard errors. The January effect is detected if the coefficient β 1i is significantly positive or higher than other coefficient β estimated. ε ti is the error term.

For ramadan effect
To detect the existence of Ramadan effect, we first convert our Gregorian calendar data to a lunar calendar data. 2 Then, we generate new dummy variables for Hijri months and estimate the following equation: where R it is the daily return of index i, M ti are dummy variables for months. M 1i is equal to 1 when day t is in Muharram and 0 otherwise. M 2i is equal to 1 when day t is in Safar and 0 otherwise, and so on. The parameters β are estimated using OLS regression with Huber-White robust standard errors. The Ramadan effect is detected if the coefficient β 1i is significantly different than other coefficient β estimated. ε ti is the error term.

For day of the week effect
We also investigate the existence of day of the week effect. Thus, we estimate the following equation: where R it is the daily return of index i, D 1i are dummy variables for days. D 1i is equal to 1 when day t is in Monday and 0 otherwise. D 2i is equal to 1 when day t is in Tuesday and 0 otherwise, and so on. The parameters β are estimated using OLS regression with Huber-White robust standard errors. The existence of Monday effect is detected if the parameter β 1i is significantly different than other and a coefficient β 5i significantly different than the other parameters indicates the existence of Friday effect.
The aim of this paper is to investigate day of week and month of the year effects, using both the Gregorian and the Hijri calendars, in African stock market. Thus, we selected 14 main African stock markets. Our sample is defined according to the availability of data (Table 2). Data are drawn from Investing.com database. We do not consider 2008 and 2020 to isolate bias from the 2007-2008 financial crisis and Covid-19 pandemic crisis. Initially, we investigate the existence of calendar anomalies in African stock markets for the period 2009 to 2019, but for some stock markets (Cote d'Ivoire, Egypt, Namibia, Nigeria, Rwanda, Tanzania, Uganda and Zambia), data are available for shorter periods.
To investigate Ramadan effect, we choose four countries (Egypt, Morocco, Nigeria and Tunisia), which are Muslim majority countries, as they are more exposed to Hijri calendar anomalies. Daily stock return is calculate as follows: where P t is closing price of day t. The conduction of Augmented Dickey-Fuller unit root test show that African indices time series are stationary. Figure 1 gives an overview of the evolution of African stock indices during the period of the study. We remark that indices of Egypt, Kenya, Mauritius, Namibia, South Africa, Tunisia and Uganda have experienced a growing trend during the last decade, while stock indices of Botswana, Morocco and Nigeria exhibit an up-down cycle. Table 3 presents descriptive statistics of daily African indices returns. We remark that, during the period of the study, Rwanda All Share exhibit the highest mean return and standard deviation while "La Bourse Régionale des Valeurs Mobilières Composite" and BSE Domestic Company exhibit, respectively, the lowest mean return and standard deviation. As presented above, we estimate equations 1, 2 and 3 using OLS regression with Huber-White robust standard errors, to detect the month of the year (Gregorian and Hijri months) and day of the week effects.

Results
Results of the estimation of equation 1 are presented in Table 4  Results of the month of the year effect, using the Gregorian calendar, are presented in Table 5. We remark that January returns are positive for indices of Botswana and Mauritius and negative in BVRMCI Regarding the Month of the Year in the Hijri calendar, and as the exposed stock markets are Muslim majority countries, we select four stock exchanges: Egypt, Morocco, Nigeria and Tunisia. Precedent studies show that, generally, stock exchanges in majority Muslim majority countries are more exposed to Ramadan effect. According to Table 6, our results show that the Egyptian index is characterized by a significant and positive returns on Safar, Jumada al-Thani and Shuwwal (the month after Ramadan). Our results show also significant and negative returns in Morocco in Jumada al-Thani and Rajab. The Tunisian index Tunindex is also characterized by positive returns in Rabi' al-Thani, Jumada al-Awwal, Shaaban, Ramadan and Shuwwal, which confirms precedent results (Białkowski et al., 2012;Sonjaya & Wahyudi, 2016). However, the Nigerian index does not

Conclusion
Calendar anomalies are time related and depend on days, weeks or months. The existence of these anomalies suggest that abnormal returns are predictable for some days, weeks and months, contrary to the EMH hypothesis which suppose that stock prices follow a random walk and stock returns are thus unpredictable. Calendar anomalies in stock markets are well documented. In this paper, we investigate the day of the week and the month of the year effects in African stock markets. Specifically, we investigate January effect and Ramadan effect. January is the first year of the Gregorian calendar while Ramadan is the 9th and the most sacred month of Muslims calendar.
In this replication study, we confirm precedent results of Obalade and Muzindutsi (2019) regarding the Mauritian Index. Indeed, we detect the presence of January, September and December effects. However, we also detect the existence of February and March effects. This paper confirms precedent results regarding the existence of May and December effects in Nigeria. Also, both studies find no evidence of January effect. However, contrary to the precedent study, we find evidence of October and November effects. Also, unlike the precedent study, we find evidence of July effect in South Africa. Concerning Morocco, our study confirms precedent results as we find evidence of March effect. However, we find also evidence of February, March, and October effect (precedent paper find evidence of January, June, August and November effects). Results regarding Tunisia confirm the existence of April, June, July and August effects. We also find new evidences of May and September effects, while the precedent study find evidence of January effect). Our results confirm those of Bundoo (2011) regarding the Wednesday effect. Also, unlike precedent studies that found evidence of Ramadan effect in Egypt and Morocco (Al-Hajieh et al., 2011;Białkowski et al., 2012;Sonjaya & Wahyudi, 2016), we find no evidence of Ramadan effect in these stock markets. However, we find evidence of Ramadan effect in Tunisia, which confirms results obtained by Białkowski et al. (2012) and Sonjaya and Wahyudi (2016). We believe that these discrepancies in the results are due to the differences of the studied periods. Thus, while we investigate calendar anomalies during the period post-subprime crisis and pre-Covid-19 crisis, other studies used different periods (Al-Hajieh et al., 2011;Białkowski et al., 2012;Bundoo, 2011;Sonjaya & Wahyudi, 2016).