0
Are Calendar Anomalies Still Alive in Major Asian Stock Markets?
Evidence on Day-of-the-Week Effect
WENYING ZHAO August, 2012
Master Thesis MSc. BA-Finance Faculty of Economics and Business
Rijksuniversiteit Groningen
Student name: Wenying Zhao, S2010941 Email Address: w.zhao@student.rug.nl Supervisor: Viola Angelini
Second Supervisor:Lammertjan Dam
1
Abstract
This paper investigates the evidence on the presence of the day-of-the-week effect on nine Asian stock market returns and volatility (conditional variance) during the period from 2002 to 2011. The data used are from Mainland China, Hong Kong China, India,
Indonesia, Japan, Malaysia, Philippines, South Korea and Thailand. The empirical study is conducted in turn by using the GARCH model and T-GARCH model. Results obtained indicate the existence of the day of the week effect on both the stock returns and volatility.
However, it is worth mentioning that the seasonality in equity returns is weak in most cases and obviously disappears in the case of India.
Key Words: Day-of-the-Week Effect, Return, Volatility, GARCH, T-GARCH JEL Classification: G15, C32
2
I. Introduction
The introduction of calendar anomalies has been documented in a considerable number of financial studies, whose investigations have covered the fields of equity, foreign exchange and the treasure bill markets. At a theoretical level, anomalies can be defined as a seasonal return behavior, suggesting that asset returns depict an anomalous but seasonal pattern during a specific period, for example every week or month. In other words, anomalies indicate market inefficiency. Fama (1970) conducts a review study on efficient market models, suggesting that if the stock market is efficient, the day-to-day price changes or returns in common stock are not interdependent. Therefore, if calendar anomalies exist in a specific equity market, relative characters in this market will definitely be not consistent with the efficient market hypothesis. Calendar anomalies, on the other hand, also indicate inadequacies in the underlying asset pricing model, which is documented by a couple of scholars [Fama and French (1992) and Avramov (2004)]. In general, these kinds of anomalies include day-of-the-week effect, weekend effect, Holiday effect, turn-of-the-year effect, January effect and the turn of the month effect. Besides, the day of the week effect, weekend effect and January effect are more popular and have been extensively studied in financial markets and especially for the stock market.
It is worth noting that almost all the kinds of calendar anomalies have been documented and analyzed in relative academic literature. However, after the results get published, anomalies often seem to disappear, reverse or be weakened. Schwert (2002) provides evidence in his studies that the weekend effect seems to have weakened or disappeared after these effects are published by relevant papers. In the meantime, practitioners start to implement investment strategies implied by some of these published papers in order to make some profits. Therefore, this raises the question of whether profit opportunities only existed in history but traders may be far away from making any arbitrage strategies, or the anomalies are simply statistic phenomena that are attractive to academic scholars and practitioners.
3
In this paper I study whether calendar anomalies are still present in equity markets after the large number of empirical studies that have been conducted on the international basis.
As shown in the relative literature, there are extensive studies of calendar anomalies in Western countries and most of their findings prove the existence of seasonality in these equity markets for a long period and with specific seasonal patterns across them [for example, Gibbons and Hess (1981), Keim and Stambaugh (1984) and Tsangarakis (2007)].
As for the other geographical areas, especially for the Asian area, fewer researches can be found compared with those in Western regions [Choudhry (2000) and Brooks and Persand (2001)]. Moreover, among their results, there is either no apparent seasonality or with weak and contradictory patterns. Therefore, the main purpose of this paper is to detect whether calendar anomalies are still present or not in some of the leading Asian markets in the recent decade. In addition, this thesis contributes to literature by further investigating whether these effects have become the general phenomenon in asset markets during recent years or their existence is still weakening. Furthermore, I only focus on the existence of one of the specific seasonality, namely the day-of-the-week effect, referring to stock returns and volatility, because anomalous changes on the daily basis are more attractive to individual investors who usually try to find some patterns on the changes of stock returns, thereby easily gaining profits by following them.
The study period I choose in this paper is a ten-year period from January 4th, 2002 to December 30th, 2011. Equity price indices on the daily basis are required. The actual Asian countries and corresponding equity indices chosen in my paper are: China, Shanghai A share and Hang Seng index; Malaysia, FTSE Bursa Malaysia KLCI; South Korea, Korea stock exchange composite; Philippines, Philippines stock exchange index (PSEi); Thailand, Bangkok SET index; Japan, Nikkei 225; India, S&P CNX 500; and Indonesia, IDX composite. All the time series data are obtained from Datastream.
The remainder of this paper is structured as follows. In the next section, a comprehensive literature review regarding the day of the week effect on both equity returns and volatility for the global markets is given. Section three introduces and justifies the methodology
4
used in this study. Section four briefly describes the data regarding the source and statistic results as well. Section five provides empirical results and analysis of the examination of calendar anomalies in the case of eight Asian countries. And possible explanations are also illustrated and discussed in section four taking the obtained results in my paper into consideration. The last section provides concluding comments.
II. Literature review
A. Theoretical background
The presence of the day of the week effect in stock markets has been widely documented in the finance literature. Taking the Efficient Market Hypothesis into account, more doubts on market efficiency have risen in stock markets where anomalous patterns have been proved. In other words, anomalies indicate market inefficiency that prices of stock markets do not follow a random walk and can be predicted by historical information.
Taking the day-of-the-week effect on equity returns into consideration, Cross (1973) proposes the possibility of dependence in successive daily price changes. He demonstrates that the distribution of price changes on Fridays and Mondays is not identical, in which case stock prices have risen on Fridays more often than on any other trading days, and has risen least often on Mondays. A similar theory is also proposed by French (1980), suggesting the calendar anomalies on daily returns of the Standard and Poor’s composite portfolio. To be specific, its average equity returns on Mondays are significantly negative while the average returns for the other four working days are positive. In other words, his theory is not consistent with the calendar time hypothesis or the trading time hypothesis where the average Monday returns should be two times higher than the expected returns for the remaining trading days or identical with the others.
The day-of-the-week patterns do not only exist in stock returns, as other studies also demonstrate the time series behavior of stock price changes in terms of volatility.
According to Fama (1965), the volatility of stock price change exhibits a long-tailed
5
distribution. Similarly, Mandelbrot (1963) explains the anomalies of price changes in his study, indicating that the movement of price changes during a specific period seems to be smoother than expected. In detail, for either the positive or the negative sign, large changes tend to be followed by large changes and small changes tend to be followed by small changes. Moreover, in the research of Connolly (1989), which conducts an analysis of the robustness of the day of week effect and weekend effects, it is evident that stock returns have time-varying volatility.
B. Empirical studies
Empirical studies of day-of-the-week effect on returns
Empirical studies on seasonality in the US equity market have found large amount of evidence. Gibbons and Hess (1981) examine the day of the week effect on returns by choosing S&P 500, Dow Jones 30 and treasury bills in the United States. They find strong and persistent negative average returns on Mondays for stocks and below-average returns for bills on Mondays as well. Besides, after including market-adjusted returns, stock returnsstill display day of the week effects even if the sign on Mondays is no more negative. Keim and Stambaugh (1984) undertake a further investigation of weekend effect in stock returns. Firstly, they extend the research period to 55 years, which is from year 1928 to year 1982. Then they include exchange-traded stocks of firms with all sizes and over-the-counter stocks that are actively traded apart from the S&P composite index. In all cases, negative Monday returns are found in their studies which are at least as strong as those reported in previous literature. Besides, the weekend effect is also present in their test, suggesting that Friday’s returns are significantly higher if Friday is the last trading day of the week. Furthermore, Lakonishok and Smidt (1988) introduce a longer period of 90 years to investigate the seasonal pattern in the rates of return on the Dow Jones Industrial Average index. They find that DJIA returns are persistently anomalous for the 90-year period, during which negative Monday returns have a remarkable tendency to persist as well as higher returns on the last trading days of the week.
6
The studies of calendar anomalies are not limited to the US equity market. Jaffe and Westerfield (1985) investigate the seasonality of daily stock returns for four other foreign countries, which are United Kingdom, Japan, Canada and Austria. In their studies, the high and positive Friday or Saturday effect is present for each country that is consistent with most previous research on the U.S. equity market. However, the lowest average returns in the case of Japan and Austria occur on Tuesdays. In addition, Athanassakos and Robinson (1994) examine the day-of-the-week calendar anomalous patterns in the Toronto Stock Exchange and conclude that significant and negative Monday stock returns and insignificant positive Tuesday returns are observed. As for the average returns on Fridays in Canada, they are higher than the average return on the other trading days of the week.
The European area also demonstrates a large amount of evidence of the existence of day-of-the-week effect on daily rates of return. Solnik and Bousquet (1990) present evidence of seasonality on the daily CAC (Cotation Assistée en Continu) index from January 1978 to December 1987 of the Paris Bourse exchange. Even though the average stock return on Fridays is higher than the remaining working days, negative and significant returns persistently occur on Tuesdays, a result which is contrary to previous studies for the U.S. but consistent with that by Jaffe and Westerfield (1985). Similar findings are observed from Barone (1990) in the Italian stock market by examining the MIB (Milano Italia Borsa) index series listed in the Milan Stock Exchange during the period January 1975 to August 1989. Although the mean for the whole period and for the three sub-periods are both significantly negative on Mondays and Tuesdays, the absolute values on Tuesdays are considerably higher than those on Mondays, which indicates the existence of Tuesday effect in Italy. On the contrary, Tsangarakis(2007) concentrates on the same research on ASE (Athens Stock Exchange) in Greece, where the time series data of general composite index of the ASE from 1981 to 2002 is introduced. Both for the whole period and for the second sub-period from 1988 to 2002, highest significant average returns occur on the last trading days on the week. However, the first sub-period does not display the same results on Fridays but has the lowest average returns on
7
Wednesdays. In other words, the day-of-the-week effect disappears between year 1981 and 1987 in Greek stock markets. Chang, Pinegar and Ravichandran (1993) conduct studies on the same subject by examining the robustness of the effect on daily returns in 23 international equity markets. Firstly, Monday effect can be significantly found in half of the cases. However, after the test on robustness, the day of the week effect is not significant in the case of Belgium, Denmark, Germany and the United States. Finally, they test the persistence of the seasonality. According to their results, the effects are statistically significant in not more than two weeks out of the month.
It is obvious that the day of the week effect has been widely studied in developed financial markets. Therefore, similar analyses in emerging markets may confirm or reject the proposition that calendar anomalies are not limited to Western countries but represent a worldwide phenomenon. There are a few studies that have analyzed emerging markets, especially for the Asian area. Loughani and Chappell (2001) evaluate the seasonal pattern in the emerging Kuwait market by employing a nonlinear GARCH (1, 1) model. Their results confirm the existence of a day-of-the-week effect in the Karachi Stock Exchange index since returns on the five trading days follow different processes. Alagidede (2008) investigates the day of the week anomalies in the largest African markets and it is worth noting that the data set involved has not been previously used. According to his results, there is no evidence of day of the week effect in the stock markets of Egypt, Morocco and Tunisia. But in the case of Zimbabwe, higher Friday returns can be detected. In addition, he also finds that the anomalies do not disappear even after accounting for market risk.
Choudhry (2000) conducts an empirical research in seven emerging Asian stock markets, which are India, Indonesia, Malaysia, Philippines, South Korea, Taiwan and Thailand.
Daily equity returns during January 1990 to June 1995 are used in this paper. According to the findings, significant weekday effects are present but they differ across these Asian markets where negative Monday effect can be observed in the markets of Indonesia, Malaysia and Thailand whereas positive Friday effect can be found in the cases of India, Malaysia, Philippines and Thailand. For the index from South Korea and Taiwan, only a negative Tuesday effect is present. Similar studies can be found in Brooks and Persand
8
(2001) as well that examine the evidence of a day-of-the-week effect in five Southern Asian stock markets for the similar research period from December 1989 to January 1996.
Contrary to Choudhry (2000), there is no evidence of the existence of any calendar anomalies in South Korean and Philippines stock markets.
Empirical studies of day-of-the-week effect on volatility
According to Kiymaz and Berument (2003), the day of the week effect is detected in major developed stock markets including Canada, Germany, Japan, the United Kingdom and the United States, and the anomalies in volatility seems to be differing across them.
Specifically, the highest volatility occurs on Mondays in the cases of Germany and Japan but on Fridays for the Canadian and American stock markets. As for the lowest volatility, it is present on Tuesdays in all the indices except one from Canada.
Balaban et al. (2001) predict the time variation of conditional variance on daily stock index returns from sixteen Western countries, Japan and Hong Kong. As shown in their paper, the nature of the seasonality in their conditional volatility of returns differs remarkably across countries and across days, as only eight out of nineteen countries exhibit significant seasonality in volatility. Ho and Cheung (1994) examine the existence of anomalous pattern in volatility in the Asian area covering the time between January 1975 and December 1989. Among the eight Asian stock markets, highest volatility can be perceived on Mondays in all cases except Korea while lowest volatility on the last trading days of the week only arise in Malaysia, Singapore and Thailand. However, the findings of highest variance of stock returns on Mondays and lowest variance on Fridays can be discovered in almost all the international stock markets chosen by Agrawal and Tandon (1998). Choudhry (2000) also investigates the day of the week effect on the conditional variance (or volatility) in seven emerging Asian stock indices by using the GARCH model.
As indicated, significant Monday effect on volatility is identified in all the markets except India, while significant negative effect on Fridays is only found in the Malaysian equity market.
9
C. Explanations for the day-of-the-week effect
The day of the week effect is still not completely explained. Even though there is still no explanation to fully satisfy the calendar anomalies in stock returns and volatility, possible explanations will be shown below which have been examined in the literature and seem to be more satisfactory.
For the explanations of calendar anomalies on returns, Damodaran (1989) suggests a theory of systematic information releases in his paper. It indicates that firms tend to delay releasing bad news till weekend and even after the close of the last trading day of the week. Thus, Friday announcements on bad news will directly lead to a negative influence on the next trading day which is Monday in most cases. Lakonishok and Levi (1982) offer a partial explanation on the higher return effect across the week. This is transaction payment procedure or settlement procedure which is about the delay between trading and settlement in stocks and in clearing checks. Take a three-day settlement period for example; stocks selling on working days give the seller three calendar days after the specific trading day to get the money. If the trading for selling stocks occurs on Wednesday, sellers will receive the payment on the following Monday, not on Saturday.
Then the two-day delay will lead the seller to get a loss from the interest of the income.
Therefore, stock purchase on Wednesday will experience higher price to compensate for two other days interest loss for sellers. Rogalski (1984) suggests that if the performance of the last trading day of the week is not ideal, the stock returns on the upcoming Monday will depict a lower result, which might be even negative. Another reason for calendar anomalies is the individual investors’ behavior suggested by Lakonishok and Maberly (1990). In their findings, evidence of increased individual trading activities can be found on Mondays. In addition, the jumped trading activity is higher for selling transactions than for purchases, which may partially explain the lower returns on Mondays.
When it comes to seasonal volatility, Foster and Viswanathan (1990) offer the explanation of liquidity and information. This assumes that informed traders own more advantages on Mondays because they receive information not only on weekdays but also on weekend.
10
Thereafter, since more public information release along with trading days of the week, variance decreases with the trading days and reach the lowest on Fridays. Then informed traders lose the advantage of using private information received on Saturdays and Sundays.
III. Methodology
In order to examine the day of the week effect on stock markets returns and conditional variance or volatility from eight major Asian countries, I first apply the GARCH model to the analysis. The GARCH model was independently developed by Bollerslev (1987) and Taylor (1986). It specially suggests that the conditional variance of the residuals can be both dependent upon previous own lags and the lags of squared errors. First, the model for the yields produced by each country is going to be estimated as follows:
= 𝛼1D1t +𝛼2D2t + 𝛼3D3t + 𝛼4D4t +𝛼5D5t+ (1) ~ N（0，𝜎 2）
where is the ith country’s stock return on day t. In other words, is the change in the daily stock price index for each country, measured by logarithmic change in the value of index compared to the previous day. Therefore, the continuously compounded daily index returns equation is the following:
= ln (v /v −1) (2)
where v and v −1 respectively represent the last value of country i stock index on day t and day t-1.
Furthermore, in equation (1), D1t, D2t, D3t, D4t and D5t are dummy variables for Monday, Tuesday, Wednesday, Thursday and Friday respectively. For example, if day t is Monday, D1t is equal to one, and otherwise it is zero. Similarly, D2t is equal to one or otherwise zero if day t is a Tuesday and so forth. The coefficients of 𝛼1 to 𝛼5 represent the daily
11
average stock returns for Monday through Friday of country i. Because of that the corresponding stock return on a specific day is significantly different from zero does not mean there is a seasonality on that day, it is necessary to specify a means test. This test concentrates on capturing the equality of average stock returns across the days of week. In other words, if the coefficients describe statistically similar average returns across the week, then the null hypothesis is accepted. Therefore, the rejection of the null hypothesis would indicate the day of the week effect is indeed present. The null hypothesis is that all the estimated average returns across the week are identical. In other words, Ho:
𝛼1 = 𝛼2 = 𝛼3 = 𝛼4 = 𝛼5.
The in equation (1) denotes random error term for day t of country i, which will cause misleading inference because of the potential autocorrelation problem of the residuals.
This means that if the errors are not correlated with one another, stock price changes might follow a random walk and calendar anomalies are indeed absent. Both Kiymaz and Berument (2003) and Apolinario et al. (2006) introduced a set of lags of return variables into the regression model, in order to address the autocorrelation problem. In detail, it is a one-week delay of the stock returns(∑ 5
4 1 − . Then the regression is the
following:
= 𝛼1D1t +𝛼2D2t + 𝛼3D3t + 𝛼4D4t +𝛼5D5t +∑ 5
4 1 − + (3)
~ N（0，𝜎 2）
If the coefficient of lagged return is significantly different from zero, it indicates residuals obtained from the regression can be auto correlated. Another problem of the error term is that the volatility of the error may not be constant over time. By introducing the GARCH model, the variance of errors can be allowed to be time dependent to capture time variation of the volatility of stock returns. Thus, error term of country i now have a mean value of zero and a time varying variance of 𝜎 2. In other words, the error term is distributed as (0，𝜎 2 .
12
In general, a GARCH (1, 1) model will be sufficient to capture the volatility clustering in the data, and rarely is any higher model estimated in the academic finance literature.
Under this condition, the conditional variance term or the volatility of the stock return for the ith country can be explained by one lag of the squared error term from the previous period and the one lagged value of previous variance, if both the coefficients of λ1i and γi
in equation (4) below are positive and significantly different zero.
𝜎 2=𝜆0 + 𝜆1 −12 + γi 𝜎 −12 (4)
Besides, the day of the week effect is also incorporated in the conditional variance equation by following Kiymaz and Berument (2003). But for the variance equation, I chose to omit one of the dummy variables and to retain the intercept. Thus, the omitted dummy variable becomes the reference category against which all the others are compared:
𝜎 2=𝜆0 +𝜆2D2t + 𝜆3D3t + 𝜆4D4t +𝜆5D5t+𝜆1 −12 + γi 𝜎 −12 (5)
The estimate of the intercept in equation (5) will be 𝜆0 on Monday, 𝜆0+𝜆2 on Tuesday and so forth. In other words, the coefficient 𝜆2 can be explained as the difference in average return between Monday and Tuesday. 𝜆3…𝜆5 will also be interpreted in the same way which is the average different between Monday and Wednesday, Thursday or Friday separately. If I reject the null hypothesis that average variation of the volatilities on stock returns across the week are same, the day-of-the-week effect would also exist in the conditional variance.
However, it is worth noting that using GARCH model has a restriction that it enforces a symmetric response of volatility to negative and positive shocks. In the conditional variance equation, the lagged error term is squared and the sign is therefore lost. But in reality, the impacts in the volatility in positive and negative yields may have different
13
effects. In particular, it has been argued that the volatility rise more from a negative shock to financial time series than a positive shock of the same magnitude. According to this, a TGARCH model is employed to further investigate whether such asymmetric behavior exists among the sample data of these eight Asian countries, which is known as leverage effect:
𝜎 2= 0 + 2D2t + 3D3t + 4D4t + 5D5t+ 1 −12 + μ −12 *dit-1+δi 𝜎 −12 (6)
The TGARCH (1, 1) model is a simple extension of GARCH (1, 1) with an additional term −12 *dit-1 added to equation (6) to capture the possible asymmetries in each country.
As shown in this conditional variance equation above, dt-1 is equal to one if it-1 <0, otherwise dit-1 is equal to zero. In the case of leverage effect, the parameter μ should be significantly positive.
IV. Data and descriptive statistics
In this section, I firstly describe the data collection required for this paper. Thereafter I discuss the summary statistics of the required data series from all eight Asian countries.
Finally I discuss the relative statistics for the time series data based on day of the week for each country.
A. Sample description and data collection
Firstly, as mentioned in the methodology, for the sake of applying the continuously compounded daily index returns to the regression analysis, the daily equity price indices from January 4th, 2002 to December 30th, 2011 are obtained in this paper. The main reason of not choosing the total index return indices directly but the price indices is that not all the total return indices are available for the eight stock markets. Then the set of daily returns are simply calculated by the first difference of the log of stock price indices.
Besides, I need to mention that all the returns are not adjusted by the dividends, since some renowned empirical researches for seasonality employed non-dividend adjusted
14
returns. For example, according to Lakonishok and Smidt (1989), dividend returns did not change any of the conclusions regarding the month-of-year effect. Moreover, for both of the day-of-the-week and turn-of-month effect, they also concluded that dividend returns were too small to explain the seasonality. Lastly, I need to remark that all the data were obtained from Datastream. Table1 below shows the actual stock indices used from these eight country equity markets in my paper.
Table1. Description of Equity Indices
Country Index Country Index
China(mainland) Shanghai stock exchange A share Thailand Bangkok SET index
China Hong Kong Hang Seng index Japan Nikkei 225
Malaysia FTSE Bursa Malaysia KLCI India S&P CNX 500 South Korea Korea stock exchange composite Indonesia IDX composite Philippines Philippines stock exchange index ( PSEi)
It is worth noting that two equity indices for China have been included which are Shanghai A share for the mainland China and the Hang Seng index for Hong Kong. The Hang Seng index is a free float-adjusted market capitalization-weighted equity index. It is priced in Hong Kong dollars and represents about 95 percentage of the total market capitalization of the stocks in Hong Kong. Unlike the Hong Kong Stock Exchange, Shanghai Stock Exchange which is the world 5th largest stock market by market capitalization at US$2.3 trillion as of December 2011 still not entirely open to foreign investors. It is mainly because of the tight controls of capital account from the Chinese mainland authorities. Therefore, I chose the A shares that are priced in the local Renmibi Yuan currency in order to capture the calendar anomalies in the domestic equity market especially for the mainland China. For the remaining data, it consists of the daily price indices of FTSE Bursa Malaysia KLCI (Malaysia), Korea stock exchange composite (South Korea), PSEi (Philippines), Bangkok SET (Thailand), Nikkei 225 (Japan), S&P CNX 500 (India) and IDX-composite (Indonesia).
B. Basic statistics for the return series from the eight countries
15
Table2. Summary Statistics of Stock Returns
As known, apart from the weekends, each country has their own national holidays and during those dates stock prices remain the same and show a zero return consequently. For the sake of avoiding the unnecessary error from this point, I excluded all the national holidays for eight Asian countries separately. Then the total number observations of yield during the period from January 4th, 2002 to December 30th, 2011 differ across countries.
Returns China(mainland)
Hong
Kong India Indonesia Japan Malaysia Philippines
South
Korea Thailand
Mean 0.0001 0.0002 0.0006 0.0009 -0.0001 0.0003 0.0005 0.0004 0.0005
Median 0.0007 0.0006 0.0018 0.0017 0.0004 0.0006 0.0005 0.0013 0.0008
Maximum 0.0903 0.1341 0.1503 0.0762 0.1323 0.0426 0.0937 0.1128 0.1058
Minimum -0.0926 -0.1358 -0.1288 -0.1095 -0.1211 -0.0998 -0.1309 -0.1117 -0.1606 Std. Dev. 0.0173 0.0163 0.0162 0.0153 0.0159 0.0082 0.0136 0.0160 0.0145 Skewness -0.1659 0.0596 -0.4816 -0.7416 -0.4732 -0.9235 -0.5453 -0.4563 -0.8273 Kurtosis 6.4200 11.7334 11.4058 9.4802 10.6250 14.3622 10.1047 7.4626 14.2478 Normality 1184.09*** 7816.22*** 7385.14*** 4463.43*** 6016.77*** 13516.24*** 5272.03*** 2137.03*** 13081.18***
Observations 2407 2459 2476 2424 2446 2448 2449 2472 2429
Notes: ***, **,* imply significant level at 1%, 5% and 10% respectively.
Normality in table is specifically checked by means of Jarque-Bera test.
16
According to the table2 of basic summary statistics, I can see that the results of mean, median, minimum and maximum are not very high. Especially, all the mean returns are very small. Similar results can also be found in Brooks and Persand (2001) and Choudhry (2000) separately, which both conduct the research of seasonality in Asian area. For equity returns, all the Asian countries except Japan experience positive mean returns for the sample period in my paper. Indonesia shows the highest average return of 0.09%, which is followed by India, Philippines and Thailand with 0.06%, 0.05% and 0.05%
separately. The lowest daily return is observed in Thailand (-16.06%), while the highest daily return is for the Indian market (15.03%). Coincidentally, both the second highest and lowest returns take place in Hong Kong stock market. As for the market risk, measured by the standard deviation, it is higher in China mainland than other countries, even if its average equity return is lower than other index except for the Japanese. Similar situation occurs in China Hong Kong, where its volatility of equity returns is second highest but with a relatively lower mean value. However, the stock returns in Malaysian market illustrate the lowest risk.
When it comes to the test of normality, it is evident that all indices are negatively skewed excluding Hang Seng index in Hong Kong. Since all kurtosis values are significantly larger than 3, these indices are all leptokurtic with a characteristic of higher peak and fatter tail. Consequently, I can conclude that all the indices are not normally distributed, which is proved by the Jarque-Bera test as well. The significant Jarque-Bera result indicates that the error term for all the indices are not in line with a normal distribution.
C. Summary statistics based on day of the week
In this section, I concentrate on the statistical description of the average value and volatility of all continuously compounding index returns on a day-of-week basis. I exclude all other statistic terms like minimum/maximum value or kurtosis, because I mainly do the research on calendar anomalies for each working day of week especially for equity returns and the volatilities.
17
Table3. Mean and Standard DeviationRefer to the Equity Returns across the Week from January 4th, 2002 to December 30th, 2011
Monday Tuesday Wednesday Thursday Friday
Returns Mean S.D. Mean S.D. Mean S.D. Mean S.D. Mean S.D.
China(mainland) 0.0014 0.0208 -0.0008 0.0156 0.0014 0.0172 -0.0012 0.0169 -0.0001 0.0153 Hong Kong 0.0007 0.0189 -0.0006 0.0161 0.0002 0.0157 0.0002 0.0158 0.0004 0.0147 India 0.0007 0.0194 0.0001 0.0148 0.0011 0.0149 0.0001 0.0146 0.0012 0.0168 Indonesia -0.0011 0.0181 0.0008 0.0141 0.0021 0.0156 0.0008 0.0148 0.0022 0.0135 Japan -0.0001 0.0163 -0.0008 0.0166 0.0001 0.0148 0.0008 0.0162 -0.0005 0.0157 Malaysia -0.0004 0.0100 0.0001 0.0074 0.0005 0.0081 0.0005 0.0079 0.0008 0.0077 Philippines -0.0005 0.0148 -0.0005 0.0140 0.0009 0.0128 0.0018 0.0131 0.0008 0.0130 South Korea -0.0001 0.0170 0.0003 0.0142 0.0011 0.0151 0.0002 0.0175 0.0004 0.0161 Thailand -0.0013 0.0167 0.0001 0.0149 0.0011 0.0144 0.00002 0.0132 0.0024 0.0127
18
According to the statistic results of mean returns and volatilities shown in table 3 for each index, I can conclude that all the average returns are negative on Mondays and positive on the remaining working days of week in the case of Indonesia, Malaysia, South Korea and Thailand. Moreover, the highest average returns are observed on Fridays for Indonesia, Malaysia and Thailand, with the value of 0.22%, 0.08% and 0.24% respectively. But in the case of South Korea, the highest mean returns occur on Wednesdays. For the country of Japan, the highest returns are shown on Thursdays, whereas the lowest returns are observed on Tuesdays. Similar negative average returns occur on both Mondays and Tuesdays for Philippines which value is around -0.05%. And the value for Philippines on Thursdays (0.18%) is higher than other working days and even one time more than that both on Wednesdays and Fridays.
Moreover, it is worth remarking that none of the negative mean returns are found on working days across the week for India. The statistic highest returns for India are found on Fridays (0.12%), which is 11 times more than the average return on the second working days of week. Oppositely, even if high and positive average returns are also observed on Mondays in the case of mainland China and Hong Kong (China), low and negative mean returns are found on Thursdays in Shanghai A share and on Tuesdays in Hang Seng index separately. This finding of lowest return for mainland China and Hong Kong are both contrary to the most studies of day of the week effect literature.
Furthermore, the volatility of the returns in term of standard deviation across the week is the highest at the first trading days of the week in all cases except Japan and the lowest at the last trading day of the week on Fridays only for China (mainland), Hong Kong, Indonesia and Thailand. However, only the volatility of returns for Hong Kong (China) and Thailand continuously decrease with the working days of week. Similarly, the volatility in the case of India decreases from 0.0194 on Mondays to the lowest of 0.0146 on Thursdays, but turns to a higher value of 0.0168 on Fridays. For the remaining equity indices, Japan and Philippines have the lowest risk or volatility on Wednesdays while
19
Malaysia and South Korea experience the same on Tuesdays.
V. Empirical results
The estimated results of the day-of-the-week effect in returns and volatility in Asian countries are illustrated in this section. First I conducted an analysis by using the general GARCH (1, 1) referring to return equation (1) and conditional variance equation (4), and thus there are only five dummy variables in the return equation (1). According to the results shown in TableA.1 in appendix, it is obvious all the variables in the variance equation (4) are significant in all the equity markets, meaning that any changes of the price will highly persistently influence the conditional variance. As for the estimated equity returns illustrated in the upper part in the Table A.1, both the lowest and highest returns seems to be differing among countries. Only Indonesia, Malaysia and Thailand have significantly higher returns on Fridays, while Japan, Philippines and South Korea have significantly higher returns on Thursdays. When it comes to Hong Kong, only higher Monday returns can be found. However, significant negative returns can only be captured in one case, which is mainland China. Since the results from the general GARCH model are not ideal, I will introduce one-week lagged returns to the original return equation (1) in order to address the potential autocorrelation problem of the residuals.
As can be seen according to the TableA.2 in appendix where return equation (3) and variance equation (4) are included, similar estimation of variables can be observed in variance equation (4), while the results on returns depict obvious improving. As mentioned already, according to the original general GARCH model, only mainland China shows significant lower returns. After including a set of delayed returns, India, Indonesia, Malaysia, Philippines, South Korea and Thailand come to display significant lower return effect as well. The lower return occurs on Thursdays in the markets of India, Indonesia and on Fridays in South Korea whereas the same condition occurs on Wednesdays in the other three. Most importantly, I also find that the coefficients of one day lagged return are considerably significant in most cases except mainland China, Hong
20
Kong, Japan and South Korea. This indicates that the autocorrelation problem really exists in most Asian countries.
Then I move to include dummy variables into the conditional variance equation (4) as well, for the sake of simultaneously investigating the day-of-the-week effect on equity returns and volatility. Table4 in next page presents the findings for the extended GARCH (1, 1) model with equation (3) and (5) to further investigates the seasonality in my sample period.
21
Table4. Day-of-the-week Effect on Equity Returns and Volatility- extended GARCH model
Coefficient
China(mainl
and) Hong Kong India Indonesia Japan Malaysia Philippines
South
Korea Thailand Return equation
Monday 0.0008 0.0015*** 0.0015*** -0.0004 0.0008 -0.0001 -0.0003 0.0007 -0.0005 (1.2867) (3.0789) (2.6900) (-0.6882) (1.4354) (-0.2606) (-0.6587) (1.2272) (-0.7509) Tuesday 0.0001 -0.0004 3.57E-05 0.0014** -0.0003 0.0003 -0.0001 0.0001 0.0006
(0.0789) (-0.7881) (0.0757) (2.4893) (-0.6374) (1.3344) (-0.2410) (0.1509) (0.7435) Wednesday 0.0014** 0.0003 0.0013** 0.0027*** 0.0003 0.0006** 0.0012** 0.0016*** 0.0016***
(2.3617) (0.6553) (2.5004) (4.9345) (0.5071) (2.0268) (2.2676) (2.9323) (3.0275) Thursday -0.0016*** 0.0008 0.0008 0.0011** 0.0012** 0.0003 0.0018*** 0.0019*** 0.0003
(-2.6758) (1.5448) (1.6278) (2.0137) (2.2585) (0.9688) (3.8517) (3.2972) (0.6510) Friday 0.0002 0.0006 0.0015*** 0.0024*** 0.0003 0.0009*** 0.0006 0.0010 0.0026***
(0.2824) (1.1333) (2.6199) (4.2168) (0.4287) (3.2272) (1.1748) (1.6446) (5.1487) Returnt-1 0.0069 0.0246 0.1165*** 0.1236*** -0.0160 0.1589*** 0.1456*** 0.0240 0.0884***
(0.3218) (1.1263) (5.1442) (5.3861) (-0.6741) (6.8125) (6.2898) (1.0548) (3.7143) Returnt-2 -0.0169 0.0095 -0.0278 -0.0181 -0.0012 0.0097 0.0253 -0.0199 0.0353
(-0.8098) (0.4489) (-1.2659) (-0.8257) (-0.0571) (0.4714) (1.2039) (-0.9522) (1.6198) Returnt-3 0.0359* 0.0057 0.0217 -0.0131 0.0071 0.0415* -0.0488** -0.0030 -0.0273
(1.7249) (0.2952) (1.1624) (-0.6147) (0.3391) (1.9479) (-2.3278) (-0.1425) (-1.2224) Returnt-4 0.0107 -0.0381* 0.0260 -0.0072 -0.0168 -0.0174 -0.0052 -0.0324 -0.0081 (0.5087) (-1.8402) (1.2300) (-0.3312) (-0.8055) (-0.8107) (-0.2464) (-1.6045) (-0.3746)
22 Variance equation
Constant 3.12E-05*** 1.42E-05** 2.10E-05*** 3.79E-05*** 2.21E-06 1.57E-06 7.65E-06 2.70E-06 7.20E-05***
(2.8450) (2.5303) (2.6527) (4.5194) (0.2539) (0.7926) (1.1616) (0.3543) (6.8256) Tuesday -6.95E-05*** -1.44E-05 -5.13E-05*** -4.08E-05*** -2.30E-05 -6.02E-06* 1.07E-05 -2.56E-05* -1.05E-05
(-3.7367) (-1.4958) (-4.3183) (-2.8746) (-1.6104) (-1.7102) (0.8518) (-1.8198) (-0.6258) Wednesday -1.72E-05 -8.67E-06 -7.12E-06 -2.59E-05** -3.36E-07 6.82E-06** -1.34E-06 9.72E-06 -9.06E-05***
(-1.1709) (-1.0679) (-0.6212) (-2.1267) (-0.0294) (2.3486) (-0.1443) (0.9331) (-8.3175) Thursday -2.60E-05 -1.70E-05* -1.22E-05 -2.36E-05* 7.88E-06 -2.41E-06 -1.09E-05 1.82E-05 -5.54E-05***
(-1.6062) (-1.8359) (-1.1574) (-1.9072) (0.6119) (-0.8013) (-1.0374) (1.5396) (-3.9645) Friday -2.48E-05 -2.29E-05** -6.69E-06 -4.09E-05*** 2.57E-05* 5.56E-07 7.27E-06 -1.13E-06 -7.81E-05***
(-1.2593) (-2.3347) (-0.5344) (-3.1276) (1.6615) (0.2096) (0.6496) (-0.0829) (-6.0653) RESID(-1)^2 0.0693*** 0.0708*** 0.1376*** 0.1403*** 0.1095*** 0.1284*** 0.1345*** 0.0836*** 0.1506***
(9.6636) (9.5737) (12.6603) (11.8992) (11.6943) (12.0865) (9.9170) (9.6784) (7.9975) GARCH(-1) 0.9191*** 0.9229*** 0.8455*** 0.8097*** 0.8743*** 0.8574*** 0.8182*** 0.9059*** 0.7287***
(122.6696) (114.9233) (79.5642) (59.2966) (77.1027) (70.2299) (47.2845) (97.1481) (28.3446)
Notes: ***, **, * imply significance at 1%, 5% and 10% level respectively, z-statistics in parentheses.
The whole period used to conduct this analysis is from January 4th, 2002 to December 30th, 2011.
The extended GARCH model is as follows:
𝑡𝑖 = 𝛼1𝑖D1t +𝛼2𝑖D2t + 𝛼3𝑖D3t + 𝛼4𝑖D4t +𝛼5𝑖D5t +∑4𝑗 1α𝑗 5𝑖 𝑟𝑡− + 𝑡𝑖 (3)
𝑡𝑖 ~ N（0，𝜎𝑖𝑡2）
23
The day of the week effect results, with respect to returns, are shown in the upper part of Table4, which indicates the seasonality differs throughout countries. Although the negative Monday returns can be found in the case of Indonesia, Malaysia, Philippines and Thailand, all the coefficients are not significantly different than zero. However, apart from Monday effect, there is obvious seasonality for the remaining trading days for these four Asian countries. In detail, the highest returns on Wednesday (0.27%) can be found in the market of Indonesia, which result is positive and significantly higher than that on Tuesdays and Thursdays with the value of 0.14% and 0.11% separately. Positive Friday effect can be found in both the market of Malaysia and Thailand, which results are statistical and significantly different from zero. For the Philippines equity market, the Thursday effect is obvious and thus the estimated return on Tuesdays is 0.18%. It is worth mentioning that, only in the market of Hong Kong and India are the Monday mean returns found to be significant and even at the level of 1%, but the coefficient are both positive.
However, I still cannot conclude that the seasonality of returns exists in India. The significant returns in India on Mondays (0.15%), Wednesdays (0.13%) and Fridays (0.15%) are similar even if not identical. According to the hypothesis of day-of-the-week effect, if the seasonality exists in the Indian market, the estimated returns on Mondays, Wednesdays and Fridays should be significantly different with one another. Therefore, I can accept the null hypothesis that the seasonality in returns is not present in the Indian equity market. For the remaining indices, significant positive Wednesday effect occurs in mainland China while Japan and South Korea experience the same on Thursdays. In additional, only the parameters on the one day lagged return shows considerably significantly positive persistence for India, Indonesia, Malaysia, Philippines and Thailand, but not for the remaining. This positive sign indicates that a good day is followed by a good day as well and vice versa.
Obviously, there are no significantly negative returns occurring on Mondays in all the equity markets. This finding contradicts with most of empirical results for the western economies, for example United States [Gibbons and Hess (1981)] or Canada
