Stock return seasonality in emerging markets:
The January effect
Aylin Alpteki
6076114
July 2014
Master Thesis
Supervised by dr. P.J.P.M. Versijp
MSc Business Economics, Finance track
Abstract
This study employs parametric and non-parametric methods to test for seasonality in the monthly stock market returns of the countries that make up the MSCI Emerging Markets Index over the period 1983-2013. Evidence is provided that monthly seasonal effects are present in the stock returns of all countries. However, very little proof is found for the existence of the January effect. According to the results of the parametric tests, evidence in favor of the anomaly is available for Malaysia, Brazil and Turkey. On the other hand, the non-parametric test results only provide evidence for the existence of the anomaly in the Philippines. Further, it is found that tax-loss-selling and seasonal patterns in the risk-return relationship do not explain the January effect in these countries.
Table of contents
1. Introduction ... 4
2. Random walk theory and the efficient market hypothesis ... 6
2.1 Random walk theory ... 6
2.2 Versions of the efficient market hypothesis ... 6
2.3 Deviations from the efficient market hypothesis ... 7
3. Literature review ... 8
3.1 Evidence from the United States ... 8
3.2 International evidence ... 9 3.3 Possible explanations ... 10 3.4 Recent developments ... 12 4. Empirical research ... 14 4.1 Data ... 14 4.2 Methodology ... 15 5. Empirical results ... 17 5.1 Seasonality ... 17
5.2 The January effect and tax-loss-selling ... 18
5.3 Risk ... 22
5.4 Monthly return differences ... 22
6. Robustness ... 25
6.1 Kruskal-Wallis test ... 25
6.2 Post-hoc analysis ... 26
6.3 Results ... 27
7. Conclusions and discussion ... 28
References ... 33
1. Introduction
Since its introduction into the literature by Eugene Fama in 1965, the efficient market hypothesis has been a favorite subject of empirical research. In a nutshell, the hypothesis posits that stock prices immediately react to information and, because of that, represent fair market values. It is closely related to the idea that stock prices follow a random walk, as suggested by Malkiel (1973). If both the efficient market hypothesis and the random walk theory hold true, prices are fair and changes in prices are unpredictable, making it impossible for individual and institutional investors to outperform the market.
While most of the early studies on the efficient market hypothesis (e.g., Fama and Blume, 1966; Jensen, 1969; Fama, Fisher, Jensen and Roll, 1969) supported the theory, several inconsistencies, referred to as stock market anomalies, were uncovered in more recent years. Prominent examples of anomalies include the January effect (e.g., Rozeff and Kinney, 1976; Keim, 1983), the size effect (e.g., Banz, 1981; Reinganum, 1981), post-earnings-announcement price drift (e.g, Ball and Brown, 1968, Watts, 1978) and the Halloween indicator (e.g., Bouman and Jacobsen, 2002; Jacobsen and Visaltanachoti, 2009). Some of these anomalies, such as the January effect and the Halloween indicator, are based on the calendar. The presence of these so-called calendar effects enables investors to predict and exploit seasonal patterns in stock returns.
This study investigates the existence of the January effect. The January effect, also known as the turn-of-the-year effect, refers to the phenomenon that January stock returns tend to exceed the returns of the remaining months of the year. The existence of this pattern has puzzled academics in finance and economics for decades. In theory, the January effect should disappear in anticipation of the larger returns in January as investors try to take advantage of this phenomenon in advance. In reality, however, the seasonal pattern in January is observed in all kinds of asset markets.
A number of explanations have been put forward to account for the existence of the January anomaly. Examples include tax-motivated transactions (e.g., Branch, 1977; Dyl, 1977), seasonal patterns in the risk-return tradeoff (e.g., Rogalski and Tinic, 1986; Keim and Stambaugh, 1986), window dressing actions by institutional managers (e.g., Lakonishok, Schleifer, Thaler and Vishny, 1991), new information releases (e.g., Merton, 1987; Chen and Singal, 2004), insider trading activity (e.g., Glosten and Milgrom, 1985; Seyhun, 1988) and cash-flow effects (e.g., Ogden, 1990). Regardless of the extensive research, however, there is no consensus view on the cause of the anomaly.
A large body of research has examined the existence of the January effect in the United States and other industrialized countries. Less research has been done on the presence of the anomaly in emerging markets however. As emerging markets have higher average returns and volatility than developed markets, it might be profitable yet risky to invest in them. The existence of a predictable pattern in emerging market stock returns may therefore be of interest to investors. This study thoroughly analyzes the January effect in the 21 countries that comprise the MSCI Emerging Markets Index. The main research question is: Does the January effect exist in emerging markets between January 1983 and December 2013? Other questions ask whether tax-motivated transactions and seasonal patterns in the risk-return tradeoff explain the existence of the January effect in these markets and whether seasonal effects other than the January effect are present in their stock returns.
To empirically test the existence of seasonality and the potential causes of such patterns, this research study examines the monthly stock market returns of the countries that make up the MSCI Emerging Markets Index over the period 1983-2013. In addition, it explores the volatility or standard deviation of these returns. Most of the analysis consists of ordinary least squares (OLS) regressions of returns and volatility on dummy variables that indicate the months of the year. To evaluate the robustness of the estimates of this parametric method, the study also uses non-parametric tests developed by Kruskal and Wallis (1952) and Siegel and Castellan (1988).
This study adds to the existing literature on the January effect in at least three ways. First, it covers a large number of emerging markets. Previous research on seasonality in emerging markets has mainly focused on a handful of countries. Second, it contains a long time series of data, including the last decade. The development of the January effect in more recent years is one of the important debates in the literature. The analysis of this time period contributes to this discussion. Third, it employs different empirical methodologies to test for the January effect. Prior studies have either used parametric or non-parametric methods. A combination of the two is, however, more powerful than any single method (Wu and Zhang, 2006).
The remainder of the paper is organized as follows. The next section explains the random walk theory and the efficient market hypothesis. Section 3 reviews the existing literature on the January effect. Section 4 describes the data and presents the research methodology. The main results are discussed in section 5. The results of additional robustness checks are presented in section 6. Section 7 summarizes the findings, limitations and implications of the study and provides directions for future research.
2. Random walk theory and the efficient market hypothesis
This section provides the background that supports this investigation. First, the random walk theory of stock prices will be explained. Then, the different versions of the efficient market hypothesis and their implications will be discussed. Finally, deviations from the efficient market hypothesis will be described.
2.1 Random walk theory
The random walk theory is a financial concept that can be traced back to the nineteenth century, but was popularized by Malkiel (1973) in his best-selling book “A Random Walk Down Wall Street”. The theory asserts that changes in stock prices are unpredictable. The idea behind this theory is that prices reflect all available information (Bodie, Kane and Marcus, 2011, p.372). Hence, there is no information left that investors can use to predict the direction in which prices will move.
This is because if there would be information available that suggests that a certain stock is undervalued, all investors would want to purchase that stock, which would cause its price to rise instantly. Similarly, the availability of information that suggests that a stock is overvalued would induce all investors to sell that stock, which would cause its price to fall instantly. In short, stock prices immediately react to information and, because of that, represent fair market values.
When prices are fair, it is impossible for investors to outperform the market. The only way to achieve higher returns is by increasing risk. However, if it were possible to predict changes in stock prices because not all information is reflected in them, investors would be able to exploit profit opportunities and the market would not be called efficient. Therefore, the theory that prices reflect all available information is known as the efficient market hypothesis (Bodie et al., 2011).
2.2 Versions of the efficient market hypothesis
Eugene Fama introduced the concept of efficient markets into the literature in 1965. Today, it is considered to be one of the pillars of modern finance (Caldentey and Vernengo, 2010). There are three different versions of the efficient market hypothesis: the weak, semi-strong and strong form. These three forms determine the level of market efficiency and differ in the way ‘all available information’ is defined (Bodie et al., 2011).
If all the public information that is currently available in the market, including past price series and trading volume data, is reflected in prices, the market is called weak-form efficient. This kind of information can be obtained easily and cheaply. If the weak form of the efficient market hypothesis holds, technical analysis is useless because technicians use past prices to predict future stock price movements.
If prices adjust quickly to newly available public information, such earnings forecasts, stock split announcements and interest rate expectations, the market is called semi-strong-form efficient. This type of insemi-strong-formation is not too costly to gather. If the semi-strong semi-strong-form of the efficient market hypothesis holds, fundamental analysis is of no value, because fundamental analysts use all public information to identify undervalued stocks.
If both public and private information is reflected in prices, the market is called strong-form efficient. Private information refers to information that is only available to the insiders of a company. Therefore, this version of the efficient market hypothesis is acknowledged to be rather extreme. Based on the three definitions of market efficiency, it can be said that the easier or cheaper it is to obtain information, the more likely it is that this information is already reflected in prices.
2.3 Deviations from the efficient market hypothesis
As explained in section 2.1, the main argument of the efficient market hypothesis is that prices represent fair market values because all available information is incorporated in them. The efficiency of markets assures that changes in prices are random and unpredictable (Bodie et al., 2011). Therefore, it should be impossible to find patterns in stock returns and outperform the market using investment strategies that exploit predictability.
Nevertheless, different kinds of patterns have been uncovered in security returns. Such patterns are inconsistent with the efficient market hypothesis and are therefore referred to as efficient market anomalies (Bodie et al., 2011). Some of these anomalies, such as the January effect, are based on the calendar. These so-called calendar effects allow investors to predict seasonal patterns in stock returns and make highly profitable trades.
The existence of anomalies may thus be evidence of inefficient markets, but there are also other, more simple interpretations. Lo and MacKinlay (1990), for instance, argue that over-exploring datasets, known as data snooping, will eventually lead to the discovery of patterns that may not even be real. Fama and French (1993) claim that market anomalies simply represent risk premiums. All of these interpretations are still subject to discussion.
3. Literature review
This section provides an overview of previous research on the January effect. First, evidence from the United States will be discussed. Then, international evidence from other industrialized countries will be reviewed. Thereafter, possible causes of the January effect in stock returns will be explained. Finally, recent developments in the literature on the January effect will be described.
3.1 Evidence from the United States
Early studies on the existence of the January effect focused primarily on American equity markets. Rozeff and Kinney (1976) were the first to present evidence on the existence of seasonality in monthly stock returns on the New York Stock Exchange from 1904 through 1974. They calculated stock return distributions by month and found that the mean of the January return distribution was higher than the means of the return distributions of the remaining eleven months of the year. Specifically, the mean January return over the entire time period was 3.48 percent, while the means of the other months ranged from –0.52 percent in September to 1.9 percent in July.
Keim (1983) examined the relationship between the abnormal returns and size of NYSE and AMEX firms over the period 1963 through 1979. He also found that the means of the January abnormal return distributions were high compared with the other months of the year and that abnormal returns were negatively related to firm size, especially in January. Moreover, he found that half of the January premium was caused by large abnormal returns during the first five trading days of the month. Based on this evidence, he concluded that the January effect did exist and was more pronounced for small firms.
Subsequent research by Reinganum (1983) and Jones, Lee and Apenbrink (1991) provided more evidence in favor of the idea that the January effect is a small firm anomaly. On the other hand, Bhardwaj and Brooks (1992) argued that “the January anomaly is a low share price phenomenon, rather than a small firm effect” (p.573). They studied NYSE and AMEX stocks over the period 1967–1986 and found that low price stocks earned abnormal returns in January before transaction costs. After consideration of transaction costs, however, abnormal January returns were no longer positive in the ten-year period from 1977 to 1986. Because transaction costs are larger for small, low price firms, the authors concluded that for typical investors exploitation of the anomaly appeared to be limited.
In contrast, Haugen and Jorion (1996) argued that individual investors could share transaction costs by investing through mutual funds and in this way be able to inexpensively exploit the January effect. To test the persistence of the anomaly, they investigated all stocks on the NYSE from 1926 through 1993. If the U.S. stock market would have been efficient, investors would have exploited the anomaly and its existence would have disappeared over time. However, even seventeen years after its discovery, they found no evidence that the January effect had vanished from the New York Stock Exchange.
3.2 International evidence
After several studies on the January effect proved the anomaly to be existent in the United States, academics took their research to other developed markets. Gultekin and Gultekin (1983) were the first to provide international evidence for the January effect. Using the same methodology as Rozeff and Kinney (1976), they examined seasonal effects in the stock markets of 17 industrialized countries over the period 1959 through 1979. Consistent with earlier research on American equity markets, they found the January effect to be present in most of the sampled international capital markets. However, as opposed to Keim (1983), Reinganum (1983) and Jones, Lee and Apenbrink (1991), Gultekin and Gultekin did not relate the anomaly to firm size.
Berges, McConnell and Schlarbaum (1984) investigated 391 companies listed on the Toronto Stock Exchange or the Montreal Stock Exchange from 1950 to 1980 and found that January stock returns in Canada also exceed the returns of the remaining months of the year. Moreover, they documented that this January effect was more pronounced for small firms and it was not caused by tax-loss-selling, which is one of the most cited reasons for the existence of the anomaly and will be explained in detail in section 3.3.
Likewise, Kato and Schallheim (1985) documented the presence of January and size effects in the Japanese stock market over the period 1964–1981. Besides, their results did not support the tax-loss-selling hypothesis either. Furthermore, Mills and Coutts (1995) provided evidence for the existence of the January effect from the London Stock Exchange, as they found the anomaly to be present in the returns of the FTSE 100, FTSE Mid 250 and FTSE 350 indices during the 1986-1992 period. Additionally, because the effect was more marked in the Mid 250 index, their results also confirmed the firm-size explanation of Keim (1983).
In summary, research on the January effect in the United States and other developed capital markets has proved the anomaly to be existent in most of these major industrialized
countries. Less research has been done on the presence of the anomaly in emerging markets however. Aggarwal and Rivoli (1989) were one of the first to study patterns in the stock returns of emerging countries. They investigated the existence of the January effect and the so-called weekend effect in the stock markets of Hong Kong, Malaysia, Singapore and the Philippines from 1976 to 1988. Their results indicated the presence of the January effect in Hong Kong, Malaysia and Singapore as January returns in these countries were higher than the returns of all the other months of the year.
More extensive research on seasonality in emerging markets was conducted by Fountas and Segredakis (2002). They examined patterns in the returns of eighteen emerging equity markets from 1987 through 1995 and found significant monthly effects in all the countries included in the sample. However, the January effect was only detected in the stock markets of Chile, Greece, Korea, Taiwan and Turkey. Moreover, the authors tested for the tax-loss selling hypothesis but found hardly any evidence to support this explanation of the January effect.
3.3 Possible explanations
Throughout the years, many different theories to explain the existence of the January effect have been offered. As already mentioned in section 3.2, tax-motivated transactions are one of the most-often advanced explanations for the anomaly. Branch (1977) and Dyl (1977) were the first to find evidence to support the so-called tax-loss-selling-pressure hypothesis. This theory asserts that at the end of the tax year investors sell stocks that perform badly in order to realize capital losses. This is done to offset gains on other stocks and thereby reduces one’s tax liability. Since in most countries the tax year ends in December, tax-loss-selling causes prices to go down at the end of the year. When investors start buying stocks again in January, prices go up and the January effect arises.
More evidence for the tax-loss-selling hypothesis was provided by Reinganum (1983), Roll (1983), Givoly and Ovadia (1983) and Chen and Singal (2004). On the other hand, just like the studies by Berges et al. (1984), Kato and Schallheim (1985) and Fountas and Segredakis (2002) mentioned in section 3.2, Jones, Pearce and Wilson (1987) argued that tax-loss-selling could not explain the January effect because they found that “the January effect existed long before income taxes had an effective impact and that no significant change occurred in the effect after income taxes were imposed” (p.454).
Rogalski and Tinic (1986) proposed a risk-based explanation for the January effect. They argued that most studies on seasonality in stock returns wrongly assumed that risk stays the same throughout the year. After studying an equally weighted index of New York Stock Exchange and American Stock Exchange securities over the period 1963–1982, they showed that both the risks and returns of stocks are higher in January than in any other month. Based on this finding, they reasoned that investors require higher rates of return in January to compensate them for the increased risk in this month, which led them to conclude that the January effect is not a real anomaly, but rather a matter of risk measurement.
Just like the tax-loss-selling hypothesis, the risk-based explanation of the January effect has received much attention from researchers. Tinic and West (1984, 1986), Keim and Stambaugh (1986), Hillion and Sirri (1987) and Chang and Pinegar (1988) were among the first to further examine seasonal patterns in the risk-return tradeoff. All of them related large January returns to the increase in risk in this month and thereby provided more evidence to support the risk-based explanation. However, subsequent research did not always confirm this hypothesis. Seyhun (1993) was the first to argue that seasonal variations in risk can not cause the January effect. More recently, Sun and Tong (2010) rejected the theory that risk compensation explains the January effect as they did not find clear evidence that risk is higher in January.
Another well-known explanation of the January effect is the window dressing hypothesis developed by Lakonishok, Shleifer, Thaler and Vishny (1991). This theory states that institutional managers, who are evaluated based on their performance, sell poorly performing stocks at the end of the year to make their portfolio’s look safe and successful. Then, in January, after the year-end evaluations, they buy back the loser stocks. Because of these window dressing actions, prices go down in December, which causes December returns to be low, and up in January, which causes January returns to be high.
Chen and Singal (2004) examined the window dressing hypothesis, but did not find much support for this theory. They argued that if window dressing causes the January effect, it should also cause a seasonal pattern in the stock returns of July, because institutions are evaluated on a semiannual basis. However, they found that the size of abnormal returns in July was not economically significant for stocks traded on the New York Stock Exchange, the American Stock Exchange and Nasdaq from 1993 to 1999.
Besides the window dressing hypothesis, Chen and Singal (2004) also examined the investor recognition hypothesis of Merton (1987). According to this theory, investors tend to buy more stocks when firms release new information, because this type of information
increases their awareness. As new information is typically released at the beginning of the year, investors will be induced to place more buy orders in this period and, as a result, the returns of stocks will be significantly larger in January.
However, the results of Chen and Singal’s (2004) study were not consistent with this hypothesis either. The investor recognition hypothesis implies that stocks will be traded more frequently in January than in December because traders will postpone investments until the new year, when new information will be published by many firms. Nonetheless, Chen and Singal (2004) found that the turnover for NYSE, AMEX and Nasdaq securities during 1993-1999 was greater in December than in January and therefore dismissed the investor recognition hypothesis as the explanation of the January effect. On the other hand, a study by Barry and Brown (1984) did provide evidence in favor of this hypothesis.
Yet another explanation for the January effect is the insider trading hypothesis of Glosten and Milgrom (1985). According to this theory, average uninformed investors are more likely to trade against informed corporate insiders in January and will therefore require higher rates of return in this month to compensate them for the increased possibility of incurring losses. To test this hypothesis, Seyhun (1988) analyzed a sample of insider transactions in 769 firms listed on the New York Stock Exchange and the American Stock Exchange between 1975 and 1981. As he did not find any evidence of increased insider trading activity in January, he reasoned that the risk of trading against informed insiders in January is not higher than the same risk in any other month and therefore concluded that the insider trading hypothesis is not a valid explanation of the January effect.
The liquidity hypothesis of Ogden (1990) offers one final explanation for the January effect. This hypothesis states that a surge in stock returns occurs at the turn of the year because individual investors realize extra cash receipts, such as holiday payments and yearly salary bonuses, in this period and reinvest these funds in the stock market. To test this hypothesis, Ogden (1990) used the Center for Research in Security Prices value-weighted and equally weighted daily stock index returns for the period 1969-1986 and confirmed that the January effect is due, at least partially, to the increase in cash-flows at the turn of the year.
3.4 Recent developments
As described in the previous subsections, in the eighties and nineties, much evidence for the existence of the January effect was found across the world. In more recent years however, mixed results have been reported. While some studies documented the persistence of the
anomaly, others found that the effect had declined, moved to other months of the year or even disappeared. Mehdian and Perry (2002), Chen and Singal (2003), Haug and Hirshey (2006) and Moosa (2007) are among the scholars who have documented these developments.
Mehdian and Perry (2002) examined the Dow Jones Composite, the NYSE Composite and the S&P 500 over the period 1964-1998 and found that after the 1987 stock market crash January mean returns were no longer significantly positive. Similarly, Gu (2003) investigated major U.S. indices from 1929 to 2000 and claimed that the Dow Jones 30 Industrial Average and the S&P 500 have experienced a decline in the January effect since 1988.
Chen and Singal (2003) provided evidence for the shift in the January effect. They studied NYSE, AMEX and Nasdaq stocks over the period 1963 through 2001 and found a significant December effect. In their study of futures markets, Rendon and Ziemba (2007) also found that the January effect had moved to December. Likewise, in his “Stock Trader’s Almanac”, Hirsch (2011) claimed that the January effect now starts in December.
Conversely, Haug and Hirschey (2006), who studied CRSP equal weighted portfolio returns from 1927 to 2004, found that the January effect was consistent over time and remained alive more than thirty years after its discovery. Similarly, Easterday, Sen and Stephan (2009) documented the persistence of the January effect in NYSE, AMEX and Nasdaq firms over the period of time between 1946 and 2007.
On the contrary, other authors found proof for the disappearance of the January effect. Moosa (2007) examined Dow Jones Industrial Average returns from 1970 to 2005 and found that the anomaly vanished in the 1990-2005 period and instead a negative July effect surfaced. Three years earlier, Szakmary and Kiefer (2004) had already documented the disappearance of the January effect in cash and futures post-1993.
In the next section, a new study on the January effect will be described. This study examines the presence of the anomaly in emerging markets in the 1983-2013 period. Even though tests for the January effect have provided varying results in the past couple of years, it is assumed that stock markets have become more efficient and the January effect no longer exists. Thus, this study tests the hypothesis that returns are equal for each month of the year against the alternative that January returns are higher than the returns of the other months. Moreover, a general test for seasonality and tests for the two most researched explanations of the January effect, the tax-loss-selling hypothesis and the risk-based explanation, will be discussed.
4. Empirical research
This section describes the data and presents the research methodology of this study. First, the data sources and descriptive statistics will be provided. Then, the econometric models used to test for seasonality, the January effect, the tax-loss-selling hypothesis and the risk-based explanation of the anomaly will be described.
4.1 Data
Monthly closing values (in U.S. dollars) of the stock indices of Brazil, Chile, Colombia, Mexico, Peru, the Czech Republic, Egypt, Greece, Hungary, Poland, Russia, South- Africa, Turkey, China, India, Indonesia, Korea, Malaysia, the Philippines, Taiwan and Thailand are used in this analysis. These twenty-one countries make up the MSCI Emerging Markets Index as of today. The data are drawn from the DataStream database and cover the thirty-year period from 1983 to 2013. For indices found later than January 1983, the initiation date is used as the starting point for collecting data. Table 1 provides an overview of the country indices used for this study and the time period for which data was available.
Table 1. Countries and indices
Country Index Period
Brazil BOVESPA January 1983 – December 2013
Chile IPSA February 1990 – December 2013
Colombia IGBC August 2001 – December 2013
Mexico IPC February 1988 – December 2013
Peru IGBL February 1991 – December 2013
Czech Republic PX May 1994 – December 2013
Egypt HERMES February 1995 – December 2013
Greece ATHEX October 1988 – December 2013
Hungary BUX February 1991 – December 2013
Poland WIG20 May 1994 – December 2013
Russia RTSI October 1995 – December 2013
South-Africa JSE July 1995 – December 2013
Turkey BIST100 February 1988 – December 2013
China SSE February 1991 – December 2013
India SENSEX January 1983 – December 2013
Indonesia IDX May 1983 – December 2013
Korea KOSPI January 1983 – December 2013
Malaysia KLCI January 1983 – December 2013
Philippines PSE February 1986 – December 2013
Taiwan TAIEX January 1985 – December 2013
Table 2 presents average returns and standard deviations for each of the twenty-one emerging markets. A visual inspection of this table reveals that the average return in January is higher than the average return in the remaining months of the year in Chile, Colombia, Egypt, Greece, Hungary, Poland, Russia, Turkey, Korea, Malaysia, the Philippines, Taiwan and Thailand. This seems to indicate the existence of the January effect in the stock returns of these countries.
Table 2. Average January returns versus average returns for other months of the year Average Average February - January December Return SD Return SD Brazil -0.0780 0.3211 0.0026 0.2223 Chile 0.0273 0.0812 0.0126 0.0713 Colombia 0.0420 0.0984 0.0208 0.0863 Mexico 0.0024 0.1083 0.0186 0.0918 Peru 0.0196 0.1085 0.0242 0.1119 Czech Republic -0.0015 0.0839 0.0065 0.0837 Egypt 0.0602 0.1593 0.0053 0.0782 Greece 0.0297 0.1049 0.0066 0.1070 Hungary 0.0450 0.1781 0.0086 0.0918 Poland 0.0117 0.1274 0.0077 0.1075 Russia 0.0258 0.1509 0.0232 0.1418 South-Africa -0.0018 0.0793 0.0093 0.0766 Turkey 0.0704 0.1941 0.0128 0.1617 China 0.0126 0.1574 0.0209 0.1750 India 0.0055 0.0948 0.0115 0.0894 Indonesia -0.0007 0.1011 0.0106 0.1190 Korea 0.0339 0.1493 0.0094 0.0947 Malaysia 0.0118 0.0685 0.0071 0.0842 Philippines 0.0314 0.0933 0.0121 0.1022 Taiwan 0.0395 0.1163 0.0111 0.1100 Thailand 0.0277 0.0887 0.0083 0.0956 4.2 Methodology
To find out whether seasonality exists and what may potentially cause such patterns, four different statistical tests are performed. Three of them use monthly stock returns, which are calculated for each country as the value of the index at the end of month t divided by the value of the index at the end of month t-1 minus one. The fourth one uses volatility, which is measured as the standard deviation of monthly returns.
To test for seasonal patterns in monthly stock returns, the approach by Fountas and Segredakis (2002) is used. It involves estimating the following regression:
Rt = α1D1t+ α2D2t + α3D3t + α4D4t + … + α12D12t + et (1)
In the regression, Rt is the monthly stock return, et is the stochastic error term and the dummy
variables indicate the months of the year (i.e. D1t = 1 if the return is observed in January and
D1t = 0 otherwise). The dummy coefficients represent the average returns for January through
December. If the coefficients on some dummy variables are statistically significant while others are not, seasonal effects are present in the stock returns of the months that do have significant coefficients.
To test specifically for the January effect, the approach by Keim (1983) is used. It involves estimating the following regression:
Rt = α1+ α2D2t + α3D3t + α4D4t + … + α12D12t + et (2)
In this regression, the constant term represents the return for January. The dummy variables once again indicate the months of the year and their coefficients stand for the differences between the return for January and the returns for the other eleven months. The null hypothesis is that the coefficients on the dummy variables are equal to zero. The alternative hypothesis is that the coefficients on the dummy variables are less than zero. If the F-statistic measuring the joint significance of the dummy variables is statistically insignificant, returns are the same for each month of the year and the null hypothesis can not be rejected.
To test for the January effect and the tax-loss-selling hypothesis at the same time, the approach by Fountas and Segredakis (2002) is used. It involves estimating the following regression:
Rt = α0 + α1D1t + et (3)
In this regression, the constant term represents the return for the first month of the tax year. In most countries, the first month of the tax year is January. In that case, the dummy variable takes the value of zero during the month of January and one otherwise. If the coefficient on the dummy variable is significantly less than zero, this means that January returns are higher than the returns of the other months and tax-loss-selling appears to explain this effect. The same logic applies to countries in which the tax year does not correspond to the calendar year.
However, it should be cautiously noted that factors that are not captured in regression model (3) might also cause a similar pattern in stock returns.
To test the risk-based explanation of the January effect, the model in equation (2) is applied to the volatility of stock returns. Hence, the following regression is performed:
Volt = α1+ α2D2t + α3D3t + α4D4t + … + α12D12t + et (4)
In this regression, the constant term represents the volatility in January. As before, the dummy variables indicate the months of the year and their coefficients stand for the differences between the volatility in January and the volatility in the other eleven months. If the F-statistic measuring the joint significance of the dummy variables is F-statistically insignificant, volatility stays the same throughout the year and higher returns in January can not be attributed to higher risk in the same month.
5. Empirical results
This section presents the results of the tests described in the previous section. The main findings will be analyzed and related to the literature discussed in section 3. Finally, information on the relative size of monthly stock returns will be provided and it will be explained how investors can benefit from monthly return differences.
5.1 Seasonality
Table 3 shows the results of the test for seasonal effects in monthly stock returns. This test is based on the regression in equation (1). From the table it can be seen that statistically significant returns are present in all of the twenty-one emerging markets, but the strength of the evidence varies by country. In Brazil, South-Africa, China and Thailand, significant returns are only found at the 10 percent level. In Mexico, Egypt and Indonesia, the evidence is much stronger as significant returns are even found at the 1 percent level.
A further inspection of the table shows that seasonal effects occur more frequently in some months than others. Not a single country exhibits statistically significant returns in June. January returns are statistically significant in eight countries and April returns are statistically significant in seven countries. December returns are most prone to seasonality as statistical significance applies for no less than sixteen countries during this month.
It is noteworthy that seasonal effects occur more frequently in December than in January. On top of that, December returns are positive in each country, whereas January returns are negative in some. These findings might indicate that the January effect has moved up a month and is now already detectable in December, which would be consistent with the results of Chen and Singal (2003), Rendon and Ziemba (2007) and Hirsch (2011).
5.2 The January effect and tax-loss-selling
Table 4 reports the results of the test for the existence of the January effect. This test is based on the regression in equation (2). The results show that the F-statistic is insignificant in all but one country. In Malaysia, the null hypothesis of equal returns for each month of the year is rejected at the ten percent level based on an F-statistic of 1.63. Here, the negative difference between the return for January and the return for August is statistically significant at the ten percent level, which indicates the presence of the January effect in the KLCI return series.
Table 5 shows the results of another test for the January effect. This test is based on the regression in equation (3) and simultaneously tests for the tax-loss-selling hypothesis. The results show that evidence for the January effect is found at the ten percent level in Brazil and Turkey. However, in Brazil, a reverse effect is observed, as January returns are lower than the returns of the other months of the year. Moreover, as January is the first month of the tax year in both of these countries, tax-los-selling seems to be related to the existence of the anomaly.
In other countries, the tax year does not correspond to the calendar year (Central Intelligence Agency, 2014). In Egypt, the first month of the tax year is July. In South-Africa and India, the tax year starts in April and in Thailand it starts in October. In these countries, no significant results were found. The returns of the month in which the tax year starts, are not higher than the returns of the other months of the year. Therefore, these results are inconsistent with the tax-loss-selling hypothesis.
In summary, the tests for the January effect provide very little evidence for the existence of the anomaly. The absence of the January effect in the majority of the countries in the sample is in line with the results of Mehdian and Perry (2002), Gu (2003) and Moosa (2007), whom all found that the anomaly had diminished or even disappeared over time. Furthermore, this finding is consistent with the random walk theory and the efficient market hypothesis discussed in section 2. However, it contradicts the results of Haug and Hirschey (2006) and Easterday et al. (2009), who found that the presence of the January effect was consistent over time.
Table 3. Test for seasonality in monthly stock returns Rt = α1D1t + α2D2t + α3D3t + α4D4t + α5D5t + α6D6t + α7D7t + α8D8t + α9D9t +α10D10t + α11D11t + α12D12t + et α1 α2 α3 α4 α5 α6 α7 α8 α9 α10 α11 α12 R2 Observations Brazil -0.078 0.011 0.018 0.037 -0.045 -0.005 0.022 -0.069 0.038 -0.041 0.011 0.051 0.033 372 (-1.87*) (0.26) (0.42) (0.90) (-1.08) (-0.13) (0.54) (-1.65*) (0.92) (-0.99) (0.26) (1.23) Chile 0.027 0.034 0.008 0.025 0.008 0.007 0.012 -0.008 0.005 0.019 0.004 0.025 0.061 287 (1.81*) (2.32**) (0.53) (1.68*) (0.53) (0.48) (0.80) (-0.53) (0.32) (1.27) (0.29) (1.70*) Colombia 0.042 0.022 0.000 0.050 -0.009 -0.005 0.054 0.004 0.009 0.010 0.036 0.056 0.127 149 (1.66*) (0.87) (0.01) (1.98**) (-0.35) -(0.20) (2.14**) (0.18) (0.37) (0.43) (1.47) (2.30**) Mexico 0.002 0.015 0.047 0.025 0.024 0.006 0.028 -0.017 0.000 0.015 0.037 0.024 0.065 311 (0.13) (0.84) (2.59***) (1.39) (1.30) (0.34) (1.54) (-0.94) (0.01) (0.82) (2.03**) (1.30) Peru 0.020 0.054 0.042 0.024 0.017 0.002 0.016 0.003 0.046 0.005 0.011 0.046 0.068 275 (0.82) (2.29**) (1.82*) (1.03) (0.72) (0.07) (0.70) (0.12) (1.96*) (0.21) (0.48) (1.95*) Czech Republic -0.002 0.012 0.018 0.022 -0.019 -0.011 0.041 0.001 -0.006 -0.004 -0.024 0.041 0.066 236 (-0.08) (0.64) (0.96) (1.14) (-1.02) (-0.58) (2.24**) (0.06) (-0.31) (-0.21) (-1.30) (2.22**) Egypt 0.060 -0.004 -0.007 0.021 -0.012 -0.031 0.015 0.013 0.033 -0.001 -0.006 0.038 0.085 227 (2.94***) (-0.18 (-0.34) (1.03) (-0.62) (-1.57) (0.76) (0.63) (1.63) (-0.05) (-0.28) (1.89*) Greece 0.030 0.013 -0.010 0.047 -0.012 -0.005 0.041 -0.014 0.011 -0.010 -0.018 0.029 0.050 303 (1.39) (0.61) (-0.45) (2.21**) (-0.58) (-0.25) (1.94*) (-0.65) (0.54) (-0.48) (-0.85) (1.40) Hungary 0.045 -0.004 0.007 0.038 -0.009 0.006 0.033 -0.003 -0.004 -0.002 -0.017 0.049 0.059 275 (2.09**) (-0.21) (0.35) (1.80*) (-0.44) (0.30) (1.57) (-0.13 (-0.21) (-0.07) (-0.79) (2.13**) Poland 0.012 0.011 0.009 0.052 -0.021 -0.016 0.040 -0.015 -0.020 0.005 0.001 0.041 0.054 236 (0.47) (0.46) (0.36) (2.07**) (-0.88) (-0.68) (1.66*) (-0.61) (-0.82) (0.21) (0.05) (1.70*) Russia 0.026 0.054 0.062 0.058 0.001 0.032 -0.004 -0.008 -0.034 0.018 0.004 0.070 0.074 219 (0.77) (1.62) (1.85*) (1.72*) (0.04) (0.94) (-0.12) (-0.24) (-1.00) (0.56) (0.12) (2.15**) South-Africa -0.002 0.016 0.009 0.033 -0.015 -0.006 0.006 -0.011 0.004 0.016 0.015 0.035 0.050 222 (-0.1) (0.86) (0.51) (1.80*) (-0.83) (-0.31) (0.37) (-0.63) (0.22) (0.90) (0.85) (1.96*) Turkey 0.070 -0.011 -0.022 0.046 -0.037 0.029 0.031 -0.035 0.043 0.008 0.018 0.070 0.058 311 (2.15**) (-0.35) (-0.67) (1.43) (-1.14) (0.9) (0.97 (-1.08) (1.35) (0.26) (0.56) (2.17**) China 0.013 0.035 0.005 0.049 0.072 0.007 -0.011 0.049 -0.004 -0.013 0.037 0.003 0.036 275 (0.34) (0.96) (0.14) (1.34) (1.96*) (0.20) (-0.31) (1.35) (-0.10) (-0.35) (1.01) (0.09) India 0.006 0.028 0.002 0.018 -0.003 0.018 0.020 0.007 0.021 -0.015 -0.004 0.035 0.039 372 (0.34) (1.73*) (0.15) (1.10) (-0.20) (1.13) (1.22) (0.42) (1.30) (-0.94) (-0.23) (2.17**) Indonesia -0.001 0.016 0.022 0.027 0.010 0.007 0.016 -0.020 -0.028 0.013 -0.002 0.057 0.036 368 (-0.03) (0.75) (1.04) (1.28) (0.45) (0.31) (0.75) (-0.96) (-1.34) (0.62) (-0.09) (2.72***) Korea 0.034 -0.010 0.034 0.020 -0.002 -0.003 0.036 -0.025 -0.003 0.011 0.028 0.017 0.049 372 (1.89*) (-0.57) (1.88*) (1.13) (-0.13) (-0.18) (2.03**) (-1.38) (-0.19) (0.62) (1.56) (0.95) Malaysia 0.012 0.036 0.001 0.026 0.014 -0.003 0.010 -0.024 -0.006 -0.001 -0.012 0.038 0.055 372 (0.80) (2.41**) (0.07) (1.77*) (0.94) (-0.19) (0.66) (-1.63) (-0.38) (-0.09) (-0.83) (2.56**) Philippines 0.031 0.011 0.014 0.017 0.017 0.018 0.023 -0.045 -0.007 0.034 0.007 0.045 0.064 335 (1.62) (0.58) (0.71) (0.91) (0.89) (0.94) (1.19) (-2.38**) (-0.39) (1.81*) (0.37) (2.35**) Taiwan 0.039 0.045 0.021 0.029 -0.007 -0.016 0.007 0.000 0.003 -0.018 0.022 0.035 0.049 348 (1.92*) (2.20**) (1.04) (1.43) (-0.32) (-0.78) (0.36) (0.01) (0.13) (-0.87) (1.07) (1.68*) Thailand 0.028 0.018 0.002 0.026 -0.001 0.010 0.006 -0.008 0.004 0.007 -0.005 0.034 0.029 372 (1.61) (1.03) (0.11) (1.53) (-0.08) (0.58) (0.35) (-0.49) (0.23) (0.39) (-0.30) (1.96*)
Note:The dummy variables indicate in which month of the year the return is observed (D1t = January,D2t = February, etc.), and the estimated t-statistics are in parentheses.
Table 4. Test for the January effect in stock returns Rt = α1 + α2D2t + α3D3t + α4D4t + α5D5t + α6D6t + α7D7t + α8D8t + α9D9t +α10D10t + α11D11t + α12D12t + et Degrees of α1 α2 α3 α4 α5 α6 α7 α8 α9 α10 α11 α12 R2 F-statistic freedom Brazil -0.078 0.089 0.096 0.115 0.033 0.073 0.100 0.009 0.116 0.037 0.089 0.129 0.032 1.09 11;360 (-1.87*) (1.51) (1.62) (1.96*) (0.56) (1.23) (1.70*) (0.15) (1.97**) (0.63) (1.51) (2.19**) Chile -0.027 0.007 -0.019 -0.002 -0.020 -0.020 -0.015 -0.040 -0.023 -0.009 -0.023 -0.002 0.026 0.68 11;275 (1.81*) (0.33) (-0.92) (-0.12) (-0.92) (-0.95) (-0.73) (1.66*) (-1.07) (-0.40) (-1.08) (-0.10) Colombia 0.042 -0.020 -0.042 0.008 -0.051 -0.047 0.012 -0.038 -0.033 -0.032 -0.006 0.014 0.068 0.92 11;137 (1.66*) (-0.56) (-1.17) (0.22) (-1.42) (-1.31) (0.34) (-1.07) (-0.94) (-0.9) (-0.18) (0.4) Mexico 0.002 0.013 0.045 0.023 0.021 0.004 0.026 -0.020 -0.003 0.013 0.035 0.021 0.033 0.92 11;299 (0.13) (0.49) (1.72*) (0.88) (0.82) (0.15) (0.99) (-0.75) (-0.1) (0.48) (1.33) (0.82) Peru 0.020 0.034 0.023 0.005 -0.003 -0.018 -0.003 -0.017 0.026 -0.015 -0.008 0.026 0.025 0.62 11;263 (0.82) (1.02) (0.68) (0.14) (-0.08) (-0.54) (-0.09) (-0.5) (0.78) (-0.44) (-0.25) (0.78) Czech Republic -0.002 0.014 0.020 0.023 -0.017 -0.009 0.043 0.003 -0.004 -0.002 -0.022 0.043 0.061 1.33 11;224 (-0.08) (0.51) (0.74) (0.86) (-0.66) (-0.35) (1.62) (0.10) (-0.16) (-0.09) (-0.85) (1.61) Egypt 0.060 -0.064 -0.067 -0.040 -0.073 -0.092 -0.045 -0.048 -0.028 -0.061 -0.066 -0.023 0.074 1.57 11;215 (2.94***) (-2.23**) (-2.34**) (-1.39) (-2.54**) (-3.20***) (-1.57) (-1.67*) (-0.97) (-2.14**) (-2.30**) (-0.79) Greece 0.030 -0.017 -0.039 0.017 -0.042 -0.035 0.012 -0.043 -0.018 -0.040 -0.047 -0.0004 0.044 1.21 11;291 (1.39) (-0.55) (-1.3) (0.58) (-1.39) (-1.16) (0.39) (-1.44) (-0.6) (-1.33) (-1.59) (-0.02) Hungary 0.045 -0.049 -0.038 -0.007 -0.054 -0.039 -0.012 -0.048 -0.049 -0.047 -0.062 0.004 0.047 1.18 11;263 (2.09**) (-1.64*) (-1.25) (-0.23) (-1.80*) (-1.28) (-0.4) (-1.58) (-1.64*) (-1.54) (-2.04**) (0.12) Poland 0.012 -0.0003 -0.003 0.040 -0.033 -0.028 0.029 -0.027 -0.032 -0.007 -0.011 0.030 0.405 1.05 11;224 (0.47) (-0.01) (-0.08) (1.13) (-0.95) (-0.81) (0.82) (-0.76) (-0.91) (-0.19) (-0.3) (0.85) Russia 0.026 0.029 0.036 0.032 -0.024 0.006 -0.030 -0.034 -0.059 -0.007 -0.022 0.044 0.049 0.97 11;207 (0.77) (0.6) (0.76) (0.68) (-0.52) (0.12) (-0.63) (-0.72) (-1.25) (-0.16) (-0.47) (0.95) South-Africa -0.002 0.017 0.011 0.035 -0.013 -0.004 0.008 -0.009 0.006 0.018 0.017 0.036 0.038 0.76 11;210 (-0.10) (0.67) (0.43) (1.34) (-0.52) (-0.15) (0.33) (-0.37) (0.22) (0.70) (0.66) (1.43) Turkey 0.070 -0.082 -0.092 -0.025 -0.107 -0.042 -0.039 -0.105 -0.027 -0.062 -0.053 -0.0008 0.047 1.35 11;299 (2.15**) (-1.78*) (-2.00**) (-0.53) (-2.33**) (-0.90) (-0.85) (-2.29**) (-0.59) (-1.35) (-1.14) (-0.02) China 0.013 0.022 -0.008 0.036 0.059 -0.005 -0.024 0.037 -0.016 -0.025 0.024 -0.009 0.023 0.56 11;263 (0.34) (0.43) (-0.14) (0.69) (1.13) (-0.11) (-0.46) (0.70) (-0.31) (-0.48) (0.47) (-0.18) India 0.006 0.022 -0.003 0.012 -0.009 0.013 0.014 0.001 0.016 -0.021 -0.009 0.030 0.024 0.83 11;360 (0.34) (0.98) (-0.13) (0.54) (-0.38) (0.56) (0.62) (0.05) (0.68) (-0.91) (-0.4) (1.29) Indonesia -0.0007 0.017 0.023 0.028 0.010 0.007 0.016 -0.020 -0.027 0.014 -0.001 0.058 0.033 1.10 11;356 (-0.03) (0.55) (0.76) (0.93) (0.34) (0.24) (0.55) (-0.65) (-0.91) (0.46) (-0.04) (1.93*) Korea 0.034 -0.044 -0.0001 -0.014 -0.036 -0.037 0.003 -0.059 -0.037 -0.023 -0.006 -0.017 0.037 1.25 11;360 (1.89*) (-1.74*) (-0.00) (-0.54) (-1.43) (-1.46) (0.10) (-2.31**) (-1.47) (-0.90) (-0.23) (-0.66) Malaysia 0.012 0.024 -0.011 0.014 0.002 -0.015 -0.002 -0.036 -0.018 -0.013 -0.024 0.026 0.047 1.63 11;360 (0.80) (1.14) (-0.52) (0.68) (0.09) (-0.70) (-0.10) (-1.72*) (-0.84) (-0.63) (-1.16) (1.25) Philippines 0.031 -0.020 -0.018 -0.014 -0.014 -0.013 -0.009 -0.077 -0.039 0.003 -0.024 0.013 0.047 1.45 11;323 (1.62) (-0.75) (-0.65) (-0.52) (-0.53) (-0.49) (-0.32) (-2.82***) (-1.43) (0.11) (-0.90) (0.49) Taiwan 0.039 0.006 -0.018 -0.010 -0.046 -0.056 -0.032 -0.039 -0.037 -0.057 -0.018 -0.005 0.035 1.10 11;336 (1.92*) (0.20) (-0.62) (-0.35) (-1.58) (-1.91*) (-1.11) (-1.35) (-1.27) (-1.97**) (-0.61) (-0.17) Thailand 0.028 -0.010 -0.026 -0.001 -0.029 -0.018 -0.022 -0.036 -0.024 -0.021 -0.033 0.006 0.019 0.62 11;360 (1.61) (-0.41) (-1.06) (-0.06) (-1.19) (-0.73) (-0.89) (-1.48) (-0.97) (-0.86) (-1.35) (0.25)
Note: The dummy variables indicate in which month of the year the return is observed (D
2t = February,D3t = March, etc.), and the estimated t-statistics are in parentheses. The F-statistic tests the hypothesis
Table 5. Test for the January effect and the tax-loss-selling hypothesis
Rt = α0 + α1D1t + et Czech
Brazil Chile Colombia Mexico Peru Republic Egypt Greece Hungary Poland Russia α0 -0.078 0.027 0.042 0.002 0.020 -0.002 0.015 0.030 0.045 0.012 0.026
(-1.87*) (1.81*) (1.66*) (0.13) (0.82) (-0.08) (0.76) (1.39) (2.09**) (0.47) (0.77) α1 0.081 -0.015 -0.021 0.016 0.005 0.008 -0.006 -0.023 -0.036 -0.004 -0.003
(1.85*) (-0.94) (-0.81) (0.83) (0.18) (0.40) (-0.29) (-1.03) (-1.62) (-0.15) (-0.07) South-Africa Turkey China India Indonesia Korea Malaysia Philippines Taiwan Thailand
α0 0.033 0.070 0.013 0.018 -0.001 0.034 0.012 0.031 0.039 0.007
(1.80*) (2.15**) (0.34) (1.10) (-0.03) (1.89*) (0.80) (1.62) (1.92*) (0.39) α1 -0.026 -0.058 0.008 -0.007 0.011 -0.025 -0.005 -0.019 -0.028 0.003
(-1.41) (-1.68*) (0.21) (-0.44) (0.50) (-1.31) (-0.31) (-0.95) (-1.32) (0.19)
Note:The dummy variable takes the value of zero for the month in which the tax year starts, which is July in Egypt, April in South-Africa and India, October in Thailand and January in the rest of the countries. The estimated t-statistics are in parentheses. * and ** indicate statistical significance at the 10 and 5 percent levels respectively.
5.3 Risk
Table 6 contains the results of the test for the risk-based explanation of the January effect. This test is based on the regression in equation (4). The results show that the F-statistic is insignificant for all countries except Egypt and Hungary. The F-statistic of 4.26 for Egypt is significant at any level and the F-statistic of 1.70 for Hungary is significant at the ten percent level. This implies that in these countries stock return volatility does not remain constant over the calendar months. In fact, in both Egypt and Hungary, January volatility is higher than the volatility in ten other months.
In the rest of the countries, volatility stays the same throughout the year. In section 5.2, evidence for the existence of the January effect in Malaysia, Brazil and Turkey was provided. Volatility is thus invariant over time in the countries where January returns are higher than the returns of the other months of the year, while it is significantly higher in January in the countries where the anomaly was not found. Therefore, these results do not support the risk-based explanation of the January effect.
This finding contradicts the proposition by Tinic and West (1984, 1986), Keim and Stambaugh (1986) and Rogalski and Tinic (1986) that the January effect is due to risk premiums that are required by investors to compensate them for the higher risk that they bear in this month. On the other hand, it is consistent with the results of Seyhun (1993) and Sun and Tong (2010), who do not relate January returns to seasonal patterns in the risk-return relationship.
5.4 Monthly return differences
Even though very little evidence is found for the existence of the January effect, the presence of other monthly seasonal effects can still be advantageous to investors. Table 7 contains monthly return differences for all countries in the sample. Based on the results shown in table 3, the months in which returns are statistically significant are listed in panel A. The months in which returns are significantly lower than those reported in panel A, are listed in panel B and the months in which returns are significantly higher than those reported in panel A, are listed in panel C. Following Fountas and Segredakis (2002), a dummy variable model in which the dummies represent the months of the year and the constant term indicates the return observed in the respective month of panel A is estimated multiple times to determine these months.
Table 6. Test for the January effect in stock return volatility Volt = α1 + α2D2t + α3D3t + α4D4t + α5D5t + α6D6t + α7D7t + α8D8t + α9D9t +α10D10t + α11D11t + α12D12t + et Degrees of α1 α2 α3 α4 α5 α6 α7 α8 α9 α10 α11 α12 R2 F-statistic freedom Brazil 0.226 -0.027 -0.053 -0.031 -0.072 -0.110 -0.136 -0.091 -0.066 -0.065 -0.084 -0.086 0.035 1.18 11;359 (6.48***) (-0.55) (-1.08) (-0.64) (-1.48) (-2.26**) (-2.77***) (-1.86*) (-1.34) (-1.32) (-1.72*) (-1.75*) Chile 0.048 0.007 -0.004 0.003 -0.010 -0.001 -0.010 -0.003 0.004 0.016 0.009 -0.009 0.032 0.82 11;274 (5.40***) (0.53) (-0.34) (0.20) (-0.77) (-0.04) (-0.80) (-0.26) (0.30) (1.28) (0.70) (-0.70) Colombia 0.062 -0.006 -0.006 -0.014 -0.006 -0.001 0.013 -0.008 -0.017 -0.001 0.033 -0.013 0.068 0.90 11;136 (4.18***) (-0.29) (-0.29) (-0.66) (-0.29) (-0.04) (0.62) (-0.40) (-0.84) (-0.06) (1.61) (-0.63) Mexico 0.060 0.002 0.020 -0.004 0.007 0.020 -0.004 0.003 0.012 0.015 0.010 -0.010 0.026 0.72 11;298 (5.06***) (0.10) (1.21) (-0.25) (0.45) (1.23) (-0.25) (0.20) (0.71) (0.93) (0.60) (-0.62) Peru 0.079 -0.005 -0.002 0.000 0.011 -0.013 -0.033 -0.029 0.004 -0.009 -0.006 -0.001 0.026 0.63 11;262 (4.73***) (-0.22) (-0.10) (0.02) (0.49) (-0.55) (-1.43) (-1.24) (0.18) (-0.38) (-0.26) (-0.06) Czech Republic 0.057 -0.001 0.016 -0.029 -0.004 0.008 -0.005 0.005 -0.003 -0.004 0.010 0.009 0.046 0.98 11;223 (4.92***) (-0.07) (0.99) (-1.76*) (-0.25) (0.47) (-0.30) (0.31) (-0.20) (-0.27) (0.59) (0.58) Egypt 0.093 0.023 -0.029 -0.053 -0.045 -0.036 -0.035 -0.036 -0.043 -0.042 -0.045 -0.040 0.180 4.26*** 11;214 (8.79***) (1.53) (-1.98**) (-3.61***) (-3.07***) (-2.47**) (-2.36**) (-2.46**) (-2.93***) (-2.84***) (-3.03***) (-2.72***) Greece 0.055 0.015 0.014 0.024 0.031 0.035 0.011 0.029 0.025 0.004 -0.001 0.055 0.029 0.78 11;290 (4.00***) (0.76) (0.70) (0.69) (1.23) (1.62) (1.80**) (0.59) (1.48) (1.29) (0.23) (-0.04) Hungary 0.109 -0.005 -0.053 -0.044 -0.041 -0.043 -0.052 -0.038 -0.046 -0.034 -0.060 -0.042 0.067 1.70* 11;262 (7.85***) (-0.25) (-2.72***) (-2.23**) (-2.10**) (-2.18**) (-2.65***) (-1.93**) (-2.39**) (-1.75*) (-3.07***) (-2.17**) Poland 0.089 -0.003 -0.006 -0.019 0.001 -0.003 0.008 0.005 -0.008 0.012 -0.005 0.031 0.024 0.51 11;223 (5.35***) (-0.14) (-0.24) (-0.82) (0.03) (-0.12) (0.32) (0.20) (-0.33) (0.52) (-0.20) (-1.33) Russia 0.113 -0.021 -0.015 -0.027 -0.038 -0.022 -0.017 -0.011 -0.027 0.007 -0.048 -0.025 0.028 0.53 11;206 (5.44***) (-0.70) (-0.52) (-0.90) (-1.30) (-0.76) (-0.59) (-0.37) (-0.92) (0.25) (-1.65*) (-0.85) South-Africa 0.070 -0.014 -0.007 -0.021 -0.008 -0.007 0.021 -0.020 -0.001 -0.016 -0.016 -0.030 0.029 0.57 11;209 (5.80***) (-0.84) (-0.41) (-1.21) (-0.48) (-0.40) (-1.23) (-1.22) (-0.06) (-0.97) (-0.93) (-1.77*) Turkey 0.126 0.022 0.001 -0.007 0.008 -0.040 -0.015 -0.012 -0.024 -0.012 0.003 0.026 0.031 0.86 11;298 (6.23***) (0.77) (0.02) (-0.26) (0.30) (-1.40) (-0.52) (-0.43) (-0.85) (-0.44) (0.11) (0.91) China 0.081 -0.014 -0.012 0.008 0.054 0.067 0.007 0.028 0.015 -0.025 0.012 -0.006 0.031 0.76 11;262 (2.52***) (-0.31) (-0.26) (0.18) (1.20) (1.50) (0.16) (0.63) (0.33) (-0.56) (0.26) (-0.13) India 0.063 -0.004 0.025 0.013 0.007 0.016 0.001 -0.005 0.002 0.001 0.005 0.001 0.026 0.87 11;359 (6.57***) (-0.29) (1.86*) (0.97) (0.49) (1.17) (0.05) (-0.39) (0.18) (0.05) (0.38) (0.04) Indonesia 0.082 -0.020 -0.040 -0.029 -0.008 -0.023 -0.025 0.002 -0.002 -0.006 -0.012 -0.003 0.025 0.82 11;355 (5.53***) (-0.96) (-1.92*) (-1.38) (-0.39) (-1.09) (-1.22) (0.10) (-0.10) (-0.28) (-0.60) (-0.15) Korea 0.090 -0.008 -0.023 -0.018 -0.017 -0.032 -0.031 -0.012 -0.023 -0.012 -0.026 -0.036 0.022 0.73 11;359 (7.07***) (-0.47) (-1.29) (-1.01) (-0.95) (-1.80*) (-1.75*) (-0.70) (-1.29) (-0.66) (-1.47) (-2.04***) Malaysia 0.043 0.011 0.015 0.004 0.012 -0.002 -0.001 0.012 0.023 0.031 0.026 0.008 0.031 1.05 11;359 (4.01***) (0.76) (0.98) (0.30) (0.80) (-0.11) (-0.08) (0.80) (1.57) (2.05***) (1.76*) (0.53) Philippines 0.070 -0.002 -0.017 -0.014 -0.013 0.010 0.006 0.003 0.007 0.014 0.017 -0.005 0.032 0.97 11;322 (6.22***) (-0.13) (-1.06) (-0.88) (-0.80) (0.61) (0.35) (0.21) (0.43) (0.87) (1.05) (-0.32) Taiwan 0.101 -0.007 -0.036 -0.049 -0.038 -0.050 -0.029 -0.033 -0.035 -0.005 -0.024 -0.025 0.046 1.48 11;335 (7.46***) (-0.38) (-1.91*) (-2.57***) (-1.98**) (-2.63***) (-1.53) (-1.73*) (-1.82*) (-0.26) (-1.25) (-1.32) Thailand 0.067 0.017 -0.007 -0.004 -0.016 -0.015 -0.019 -0.015 0.001 0.002 0.018 0.012 0.040 1.37 11;359 (6.13***) (1.07) (-0.46) (-0.27) (-1.01) (-0.96) (-1.21) (-0.94) (0.08) (0.13) (1.20) (0.76)
Table 7. Relative size of monthly stock returns
Panel A: Panel B: Panel C:
Month in which returns Months in which returns are Months in which returns are are statistically significantly lower than the return significantly higher than the return Country significant of the month in panel A of the month in panel A
Brazil January - Apr, July, Sept, Dec
August - Apr, Sept, Dec
Chile January Aug -
February Aug - April - - December - - Colombia January - - April - - July May -
December May, June -
Mexico March Jan, Aug, Sept -
November Aug -
Peru February - -
March - -
September - -
December - -
Czech Republic July May, June, Sept, Oct, Nov - December May, June, Sept, Oct, Nov - Egypt January Feb, March, May, June, Aug, Oct, Nov -
December May, June -
Greece April March, May, June, Aug, Oct, Nov - July March, May, Aug, Oct, Nov -
Hungary January Feb, May, Sept, Nov -
April November -
December Feb, May, Aug, Sept, Oct, Nov -
Poland April May, June, Sept -
July May, Sept -
December May, June, Sept -
Russia March Sept -
April Sept -
December Aug, Sept -
South-Africa April May, Aug -
December May, Aug -
Turkey January Feb, March, May, Aug -
December Feb, March, May, Aug -
China May - -
India February Oct -
December May, Oct, Nov -
Indonesia December Jan, June, Aug, Sept, Nov -
Korea January Feb, Aug -
March Feb, Aug -
July Feb, Aug -
Malaysia February March, June, Aug, Sept, Oct, Nov -
April Aug, Nov -
December March, June, Aug, Sept, Oct, Nov -
Philippines August - Jan, Feb, March, April, May, June, July,
a a a Oct, Nov, Dec
October Aug -
December Aug, Sept -
Taiwan January June, Oct -
February May, June, Oct -
December June, Oct -
Based on the information provided in table 7, different countries in the sample can be grouped together. In some countries, the return of a particular month is significantly higher than the returns of many other months. For instance, January returns are higher than the returns of seven other months in Egypt and April returns are higher than the returns of six other months in Greece. The opposite is true for the Philippines, where August returns are lower than the returns of no less than ten other months. Investors can take the month of the year into account when investing in countries like these and benefit from monthly return differences.
In other countries, this type of information may be of less importance to investors. In some of these countries, there is not much difference in the returns of the months of the year. In Russia, South-Africa and Thailand for instance, the return of any particular month only differs from one or two other months. In others, like Peru and China, there is no difference at all. In countries like these, investors can not use the month of the year to their advantage as there is no clear seasonal effect to exploit.
6. Robustness
This section describes the non-parametric tests that are used to cross-check the results of the parametric test for the January effect presented in section 5.2. First, the procedure will be explained. Thereafter, the results of both methods will be compared and the consistency of the outcomes will be evaluated.
6.1 Kruskal-Wallis test
Following Gultekin and Gultekin (1983), the Kruskal-Wallis test is used for the purpose of non-parametric analysis. This test is designed to assess whether multiple samples derive from the same distribution. In this application, the returns of each month of the year represent a sample and testing whether these twelve samples originate from the same distribution comes down to testing the equality of means of monthly returns.
The following model is used to describe returns:
Rtm = μ + λm + etm, t = 1,2,…,nm, m = 1,2,…,12 (5)
In this model, Rtm is the rate of return in month m of year t, μ is the mean rate of return, λm is
distributed error term. The null hypothesis is that all λ’s are equal. The alternative hypothesis is that at least two λ’s are not equal. When the null hypothesis is true, there are no seasonal effects in stock returns, i.e. returns are the same for each month of the year.
The Kruskal-Wallis test assigns ranks to all N observations. These ranks are indicated by rtm. The test statistic is given by
(6)
where nm denotes the number of observations for month m and is the average rank of the
mth month’s observations such that . Under the null hypothesis, the test statistic is approximately distributed as chi-square with m-1 degrees of freedom. The null hypothesis should be rejected when KW ≥ χ2
(11, α). The critical values at the 10, 5 and 1 percent levels are 17.28, 19.68 and 24.72 respectively.
The main advantage that non-parametric methods, such as the Kruskal-Wallis test, have over parametric methods is that they require few assumptions about the distribution of the data. Moreover, these types of tests are less sensitive to outlying observations because they are based on ranks. These properties increase the flexibility, robustness and applicability of non-parametric techniques (Hollander, Wolfe, Chicken, 2013).
6.2 Post-hoc analysis
When the Kruskal-Wallis test statistic is significant, it indicates that there are differences between the mean returns of the months of the year. However, it does not identify the months that are responsible for seasonal effects in stock returns. To determine where the differences come from, a non-parametric test procedure developed by Siegel and Castellan (1988) is used. In this test a comparison is made between a control month and eleven treatment months.
Returns are described as in equation 5 and the null hypothesis once again states that all λ’s are equal. The alternative hypothesis, however, is not the same and states that the effect of control month c is greater than the effect of treatment month u (λc > λu). The test procedure at
the α level of significance is decide that λc > λu if
where is the average rank of the control month’s observations, is the average rank of treatment month u’s observations, z is the critical value from the standard normal curve, k is the total number of months, N is the total number of observations, nc is the number of
observations in the control month and nu is the number of observations in treatment month u.
In order to test the hypothesis that mean returns are significantly larger in January, January is used as the control month. However, because January returns might not be the (only) source of seasonality, the remaining months are used as controls as well and comparisons are made between all possible pairs of means.
6.3 Results
Table 8 provides a summary of the non-parametric test results. Panel A shows that the Kruskal-Wallis test statistic is insignificant in all countries, except Malaysia and the Philippines. The K-W test statistic of 20.266 for Malaysia is significant at the five percent level and the K-W test statistic of 18.211 for the Philippines is significant at the ten percent level. In these countries, the null hypothesis that returns are the same for each month of the year is rejected.
Panel B shows that the month of January is not responsible for seasonality in the stock market of Malaysia. January returns are no different than the returns of the other months of the year. However, as can be seen from panel C, December returns are significantly larger than November returns. Thus, the non-parametric tests identify December as the month that causes seasonal effects in Malaysian stock returns.
Panel B also shows that the January effect is present in the stock market of the Philippines as January returns are significantly larger than August returns. Besides, panel C shows that December returns are significantly larger than August returns as well. Therefore, differences between the mean returns of the months of the year in the Philippines are caused by the significantly larger means of January and December returns.
These findings are partly consistent with the results of the F-test shown in table 4. As discussed in section 5.2, this parametric test for the January effect only rejected the hypothesis that returns are the same for each month of the year for Malaysia and provided evidence for the presence of the January effect in the Malaysian stock market as January returns were found to be significantly larger than August returns.
Since the Kruskal-Wallis test also detected seasonality in the stock returns of Malaysia, this finding seems robust. In the case of Malaysia, the only inconsistency lies in the fact that the non-parametric tests did not find proof for the January effect. When it comes to the Philippines, however, the results of the parametric and non-parametric tests contradict each other, as the Kruskal-Wallis test did detect seasonality in Philippine stock returns while the F-test did not.
Overall, there are no material differences between the parametric and non-parametric test results. Regardless of the methodology used, in the majority of the countries no differences were found between the mean returns of the months of the year. The disagreement over Malaysian test results merely concerns the month that causes stock return seasonality. The biggest discrepancy lies in the contradictory results for the Philippines.
Table 8. Non-parametric test results
Panel A Panel B Panel C
Kruskal-Wallis For which month u is equation 7 satisfied For which month u is equation 7 satisfied Country test statistic when January is the control month? when January is not the control month?
Brazil 14.816 - - Chile 5.817 - - Colombia 11.710 - - Mexico 10.902 - - Peru 5.264 - - Czech Republic 14.998 - - Egypt 15.023 - - Greece 14.007 - - Hungary 13.376 - - Poland 8.028 - - Russia 7.865 - - South-Africa 9.166 - - Turkey 11.814 - - China 7.852 - - India 12.961 - - Indonesia 13.379 - - Korea 14.746 - -
Malaysia 20.266** None November* (control is December) Philippines 18.211* August* August* (control is December)
Taiwan 11.628 - -
Thailand 5.082 - -
Note: * and ** indicate statistical significance at the 10 and 5 percent levels respectively.
7. Conclusions and discussion
This study has tested for stock return seasonality in the twenty-one emerging markets that make up the MSCI Emerging Markets Index. Although the analysis has mainly focused on the presence of the January effect, potential causes of the anomaly as well as other seasonal effects have also been examined. More specifically, this paper addressed the following
