Discussion Papers In Economics
And Business
A Study on the Level of Market Efficiency inFive Markets
Guoxi Duan
Hisashi Tanizaki

Discussion Paper 21-24-Rev.

December 2021

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Study on the Level of Market Efficiency in Five Markets

Guoxi Duan†
Hisashi Tanizaki†

Abstract
This paper examines the weak form market efficiency in five stock markets, China (CSI 300 index), Hong
Kong (HSI), Japan (Nikkei 225), the US (NASDAQCOM) and Germany (DAX) from the perspective ofrandom walk hypothesis. The methods for testing random walk are autocorrelation, runs test, strategy. This
paper also examine three calendar effects in all stock markets: January effect, the-turn-of-the-month effect(the TOM effect), the day-of-the-week-effect (the DOW effect). The results are: (1)From the viewpoint of
autocorrelation, the most efficient market among five stock markets is the market in Hong Kong while strong
evidence of autocorrelation is found in China, CSI 300 and The US, NASDAQCOM. (2) The results of runs
tests do not found evidence against randomness in daily returns for CSI 300, HSI from 2006 to 2020 but finda little evidence for Nikkei 225, NASDAQCOM, DAX. The higher level of efficient markets among fivestock markets are the markets in China and Hong Kong. (3) The strategy analyzed in this paper does not findevidence indicating inefficient market for five indexes. (4) January effect did not exist in five indexes. (5) All
five indexes are characterized with a TOM effect in different level and therefore the hypothesis of an
efficient market is rejected for five markets. (6) All five indexed are found the-day-of-week effect which also
indicates inefficient stock markets. we conclude that all five market are not efficient from 2006 to 2020. (7)After the consideration of time-varying volatility, we found January effect in Nikkei 225 in returns. Except
Nikkei 225 all the other indexes are verified with the turn-of-the-month-effect and only CSI 300 are verified
with the day-of-the-week-effect in returns.

Keywords: market efficiency hypothesis, random walk, January effect, the-turn-of-the-month effect, theday-of-the-week-effectJEL Classification: G10, G14, C22——————————————————————†Graduate School of Economics, Osaka University, Osaka 560-0043, Japane-mail: u729096j@ecs.osaka-u.ac.jp†Graduate School of Economics, Osaka University, Osaka 560-0043, Japane-mail: tanizaki@econ.osaka-u.ac.jp

1.Introduction
We talked about the market efficiency using data of CSI 300 and its 300 constituent stocks with sevenmarket efficiency measures and the systematic market efficiency among the market in China. From thischapter, we also talk about the market efficiency but in different markets and with different data. We try toanswer other questions on the study of market efficiency.
The capital market hypothesis has always been the context in which serious discussion of the regulation offinancial markets takes place. In order to utilize some theoretical models in economics to analyze problems,many studies consider the financial market in the real world as an efficient market in which there is no costto get information and the market always quickly and accurately reacts to new information. However, thehypothesis of market efficiency is not a well-defined and empirically refutable hypothesis (Sewell (2012)).
On one hand, Gilson and Kraakman (1984) holds the view that market efficiency is easily explained under
perfect market assumptions, information is immediately and costlessly available to all participants, but thiskind of view is almost ‘absolutely accurate and totally useless’. On the other hand, Malkiel (2003) thinks thatmarkets can be efficient even if many market participants are quite irrational and can be efficient even if
stock prices exhibit great volatility than can apparently be explained by fundamentals.
From many previous studies, an efficient market is summarized as such a market during which prices at any
time fully reflect all available information and therefore available information does not enough for any
profitable trading strategies or arbitrage opportunities (Fama (1970), Gilson and Kraakman (1984), Malkiel(2003), Ozdemir (2008), Nisar and Hanif (2012)).
Fama (1970) is one of the famous paper in studying market efficiency, during which lots of studies before
1970 were reviewed and the results were consistent with an efficient market. Around 1990, despite someanomalies, many studies considered that the capital market responded efficiently to information. However,Malkiel (2003) said that after 1990 there were many papers that found evidence against efficient market. Theview on the level of market efficiency is gradually changing. According to Fama (1970), there are three typesof market efficiency: the weak form, the semi-strong form and the strong form. The weak form market
considers that historical return can not predict future return. Th semi-strong form market considers that not
only historical information but also public information can not be used to make higher profit than market
portfolios. The strong form market considers that all information released is contained in the price series andreturn series also include private information held by individual investors.
Among many methods for testing the level of market efficiency, the random walk hypothesis is the most
examined hypothesis in previous studies. The efficient market hypothesis considers that security prices
follow a random walk and it should be impossible to predict future returns based on publicly available
information (Thaler (1987)). Liu and He (1991) considered two important features in a random walk process:unit root and uncorrelated increments. If stock price follows random walk process, any shock to stock priceis permanent with no tendency in price to return to a trend path over time and this property implies that
future returns are unpredictable based on previous observations (Ozdemir (2008)). Some studies also believethat although stock prices or returns do not follow random walk the markets can be efficient.
The studies on stock market are of many types. French and Roll (1986) found evidence that supported theimportance of private information in producing a higher volatility in trading-hours compared with nontrading hours. French and Roll (1986) said that if daily returns were independent, the variance for a longholding period would equal the cumulated daily variances within the period while if daily returns aretemporarily affected by trading noise, the long period variance will be smaller than the cumulated daily
variances. French and Roll (1986) also proposed a viewpoint that if pricing errors were corrected within
three weeks and bid/ask errors were corrected overnight, most of the three-month return reflected a rational
assessment of the information arriving during the three-month period. Fama and French (1988) said that aslowly mean-reverting component of stock prices tended to induce negative autocorrelation in returns. Jones,
Kaul and Lipson (1994) found that public information was the major source of short-term return volatility.
Solnik, Boucrelle and Fur (1996) said that international correlation increased in periods of high market
volatility and this was bad news for investors because if the domestic market was quite unstable it was thetime when international risk diversification was needed. Mubarik and Javid (2009) said that the trading
volume could serve as a proxy measure fr unobservable amount of information that flowed into the market
and found that there was significant interaction between trading volume and return volatility. More
importantly, previous day’s returns and volume has explanatory power in explaining the current market
returns. All above studies tried to figure out the anomalies in a stock market.
Anyway, the main methods for testing random walk hypothesis are unit root test, autocorrelation of returns,
runs test and variance-ratio test. The reason why unit root test can be used to test the market efficiency is thatmarket efficiency demands randomness (non stationary) in security prices and unit root test examines
whether time series is non stationary or not (Nisar and Hanif (2012)). If the time series is stationary and thenull hypothesis of randomness is rejected. The other tests are normally used and will be reviewed in the nextpart.
After 1990, the evidence against random walk hypothesis is much. Many paper examined the
autocorrelation in daily, weekly and monthly return series. Reliable evidence of nonzero autocorrelation but
close to 0 is common. Therefore, they considered that the predictability of returns was not significant and thestock market under study was efficient. Pan, Chan and Fok (1997) found little evidence against the random
walks null hypothesis for four current futures and non-randomness was found in Japanese yen. Afego (2012)
studied the Nigerian stock market with runs tests and found that Nigerian Stock Exchange displayed apredictable component. Nisar and Hanif (2012) focused on four stock exchange of South Asia and the results
suggested that none of the four stock markets followed random walk. Zarei and Jadari (2020) also foundevidence against random walk and against the market efficiency hypothesis in the Tehran stock exchange.
Although there are many papers has examined the level of market efficiency using different stock returns
from different stock markets, there is no consensus among researchers and economists on the conclusion
whether the market is efficient or not (Sewell (2012)). Some found evidence indicating a weak form efficient
market like Fama (1970), Ozdemir (2008) and Sewell (2012). Sewell (2012) did an analysis of daily, weekly,monthly and annual Dow Jones Industrial Average log returns and found that the test results were almost theleast consistent with an efficient market. However, as Malkiel (2003) said, more researchers are becoming tobelieve that the stock returns are at least partially predictable, which indicates an inefficient market. Nisar
and FCMA (2012) tested the weak form efficient market hypothesis for four stock exchanges of South Asiaand found that none of the markets followed random walk and therefore were not weak form efficient
market. Rosch, Subrahmanyam and Van Dijk (2017) suggest that there may be a significant systematiccomponent to the time-varying behavior of market efficiency measures and there may be a systematic market
efficiency component across stocks. Their results are: (1) The different efficiency measures tend to provide asimilar indication of the relative degrees of price efficiency of individual stocks. (2) There exists a systematic
market efficiency component.
Calendar anomalies are another evidence for inefficient markets because the existence of consistent patterns
in returns is a signal of arbitrage opportunities. They have puzzle financial economists for over sixty years.
Thaler (1987) said that abnormal price returns occurred around the turn of the year, the turn of the month, theturn of the week, the turn of the day and before holidays.
The January effect is known to be the most important calendar anomaly: “as goes January, so goes the year”
is a popular rule in the stock market (Rossi (2015)). Jones, Lee and Apenbrink (1991) said that the January
effect was evidence of return seasonality rather than a misspecification of the Capital Asset Pricing Model.
Moller and Zilca (2008) found evidence that the first part of the January had abnormal returns and the second

part of January had lower abnormal returns in 1995-2004 period but the overall magnitude of the January
effect appeared similar to its magnitude in the previous 1965-1994 period.
The day-of-the-week-effect is another interesting stock market anomaly which attracts researchers. Thiskind of effect could help investors to make higher profit through buying stocks on days with abnormally
Lowe returns and selling stocks on days with abnormally high returns (Basher and Sadorsky (2006)). The
day-of-the-week effect refers to the existence of a patten on the part of stock returns. The results fromprevious papers are: mainly in the USA, the last trading days of the week (Friday) are characterized withpositive returns and the first trading days of the week (Monday) are characterized with negative returns(Poshakwale (1996)). Poshakwale (1996) found clear evidence that the average returns were different oneach day of the week in Bombay Stock Exchange over a period of 1987-1994. Kenourgios, Samitas andPapathanasiou (2006) investigated the-day-of-the-week effect in the Athens Stock Exchange General Indexand found that this effect was present. However, Basher and Sadorsky (2006) examined the day-of-the-weekeffect in 21 emerging stock markets from 1992 to 2003 and found that the effect was present for Philippines,
Pakistan and Taiwan. Therefore they concluded that the day-of-the-week-effect was not present in the
majority of emerging stock markets and some emerging markets exhibited strong day-of-the-week-effect.
Apolinario, Satana, Sales and Caro (2006) said that most European markets did not reflect the-day-of-theweek-effect.
Many papers found evidences of the turn-of-the-month-effect for various financial markets. If a stock
market shows the turn-of-the-month-effect, it records higher returns during a short time period around theend of the old months and the beginning of the new month, than during the remainder of the month (Arendas
and Kotlebova (2019)). Studies find that the turn-of-the-month-effect seems to be persistent across different
markets. Martikainen, Perttunen and Puttonen (1995) found significant turn-of-the-month-effect in the
Finnish stock index futures, options and cash markets. Kunkel, Compton and Beyer (2003) investigatednineteen country stock market indexes from 1988 to 2000 and found that the four-day turn-of-the-montheffect period accounted for 87% of the monthly return on average. They showed that the turn-of-the-montheffect persisted throughout the 1990s at least in sixteen of nineteen countries. McConnell and Xu (2006)
found that the turn-of-the-month-effect persisted over the interval of 1987-2005 using CRSP daily returns
and this effect was not confined to small or low-priced stocks, to the December-January turn-of-the-month orto the U.S. Stefanescu and Dumitriu (2011) explored the turn-of-the-month-effect on Bucharest Stock
Exchange with two indexes: BET-C and RAQ-C. They found evidence of this effect only for BET-C. Liu(2013) examine the US equity market from 2001 to 2011 and found that the turn-of-the-month-effect still
existed but its occurrence had moved to earlier dates. Arendas and Kotlebova (2019) investigated thepresence of this kind of effect in the stock markets of eleven Central and Eastern European countries andfound that during a twenty-year period, 1999-2018, there was significant turn-of-the-month-effect in returns
in seven stock markets.
In this paper, we try to examined the level of market efficiency for five markets with six method using daily
and monthly returns. The rest of the paper is organized as follows. Part two states methodology used in thispaper to test the level of market efficiency: autocorrelation, runs test, strategy, January effect, day-of-theweek-effect and turn-of-the-month-effect. Part three summarizes statistics of daily and monthly returns forfive indexes. Part four shows the empirical results and Part five concludes all the paper.
2.Methodology
In order to test the randomness in return series, three methods are used in this paper: autocorrelation, runs
test and a specific trading strategy. We also examine three calendar anomalies: January effect, day-of-theweek-effect and turn-of-the-month-effect.
2.1 Autocorrelation

The autocorrelation in stock returns is one of the most important anomalies in financial market worldwide(Blandon (2007)). A common but important test of the random walk hypothesis for an individual time series
is to check the serial correlation of return series. If the returns exhibit a random walk, they should be
uncorrelated at all leads and lags (Borges (2010)).
Because the autocorrelation among return series is the most common method for testing the random walkhypothesis, we use the autocorrelation of daily returns at lag1 as the first method for market efficiency level(Mubarik and Javid (2009), Sewell (2012)). When no significant correlations are found, we can judge thatthe market under consideration is consistent with an efficient market.
The autocorrelation function at lag k denoted by ρk is defined as (k = 1, 2, ……, 15 in this paper):Ri: the return on ith day
Ri-k: the return on (i-k)th day
2.2 Runs test
Runs tests is always used to check the randomness in a two-valued series. The advantage of runs test is thatit dose not require the distribution of return series to be normal distribution and therefore is commonly andwidely used as a way to examine the random walk hypothesis. A run of a sequence is a maximal segment of
sequence consisting of adjacent equal elements. The number of runs in a sequence, which has n1 positive
values and n2 negative values, is a random variable whose conditional distribution is approximately normal
with:Mean : (2*n1*n2)/(n1+n2) + 1
Variance : (Mean-1)*(mean-2)/(n1+n2-1).
If the number of runs is significantly higher or lower than mean value, the hypothesis of independence ofreturns is rejected. Here, we use runs test as a second way to examine the market efficiency level (Karemera,
Ojah and Cole (1999), Borges (2009)).
2.3 Strategy
Strategies have been a hot topic for investors because they are always seeking for higher profits with own
asset portfolios but not market portfolio. Chang, Mcleavey and Rhee (1995) said that contrarian strategies
recommended buying past losers and selling past winners to earn significant abnormal returns. Because wetry to examine the level of market efficiency of different stock markets, the strategy we consider here is theone based on the change of returns.
The strategy constructed in this paper will make higher profit when the stock return series is positively
correlated. The specific process is: (1)in a calendar year, form the start date of the year, try to find the firstday of the strategy by finding the date on which the return in the day is higher (lower) than a (b). Buy (sell)
one share in the following day to start the strategy (action 1). (2) Then find the next day on which the second
action will be down by finding the day on which the return in the day is lower (higher) than b (a). Sell (buy)one share to cover the trading and sell (buy) one more share to start a new trading (action2). (3) Repeat (2)until the end of the calendar year. (4) In the last day, only buy or sell on share to end the strategy (action n).
The strategy stated above is noted as S(a,b) in the following part. a and b mean the criterion value for buying
and selling action. The total return of this strategy is calculated as the following function:
Return of one certain strategy =xi: the return of one action in a specific strategy
n: the number of actions in a specific strategy.
If the market is efficient, the return of strategies should not significantly higher than the return of holding
the same share in the same period as the strategies.

2.4 January effect
The January effect is the best-known example of anomalous behavior in security markets: at the turn of theyear, certain types of securities tend to produce abnormal returns (Jones, Lee and Apenbrink (1991), Haugen
and Jorion (1996)). The January effect states: the observations of the month of January appears to havesystematically higher returns than other months of the year. This phenomenon is primarily concentrated insmaller firms. From previous studies, two theories provide an explanation for higher return in January: taxloss selling hypothesis and the window dressing hypothesis. An anomaly would quickly disappear afterinvestors attempt to study and exploit it. However, the January effect was still going strong seventeen years
after its discovery (Haugen and Jorion (1996)). Kim (2006) said that the January seasonality was one of thestrong empirical inconsistencies with market efficiency. If the market is efficient, investors should eliminate
abnormal returns in January by readjusting their portfolios.
Although stocks with small market capitalization tend to produce greater returns than large stocks, we try tofind whether the magnitude of the effect have changed significantly in different months with stock indexes.
The specific method is the following regression (Patel(2016)):

Rt: the monthly returns of stock index
JANUARYt: a dummy variable equal to 1 for January returns and to 0 for the other month returns
a: constantb: the coefficient of January effectIf b is statistically positive, it indicates the existence of January effect.
2.5 Turn-of-the-month-effect
In order to examine the turn-of-the-month-effect in stock returns, we first calculate the mean returns of a -5
to 5 window (Martikainen, Perttunen and Puttonen (1995), Liu (2013)). 1 (2, 3, 4, 5) means the first (second,
third, fourth, fifth) trading day in the month under consideration. -1 means the last trading day in last monthand therefore -2, -3, -4, -5 means the trading day before last trading day, two trading days before last trading
day, three trading days before last trading day and four trading days before last trading day in last month.
Then we calculate the mean return of TOM (here, the -5 to 5 period) period and ROM period (the rest of themonth or the other days of the month).
we also do a OLS regression as follow (Kunkel, Compton and Beyer (2003), Razvan and Ramona (2011)):

Rt: the daily returns of stock index
a: constant indicating the mean return in ROM period
Dit: equals to 1 when the return at time t is on the ith trading days in a month and equals to 0 on other days
D-it: equals to 1 when the return at time t is on the last trading days, the day before last day, two days before
last day, three days before last day, four days before last day in one month and equals to 0 on other days
bi: the coefficient of the turn-of-the-month-effectIf any bi is significantly different from zero, there is the turn-of-the-month-effect in stock returns.
2.6 Day-of-the-week-effect
In the day-of-the-week-effect case, it considers that a negative equity return on the first trading day in aweek and an abnormal high return on the last trading day of the week, usually Friday (Poshakwale (1996),
Blandon (2007)). In the USA, low mean returns are observed on Monday and mean returns on Friday areobserved to be positive and abnormally higher than the mean returns on other days of the week (Rossi(2015)).

In order to examine the day-of-the-week-effect in stock returns, we also use ordinary least squares
regression (OLS) method (Kenourgios, Samitas and Papathanasiou (2005), Apolinario, Satana and Caro(2006), Basher and Sadorsky (2006)):

Rt: the daily returns of stock index
Mt, TUt, Wt, THt, Ft: the dummy variable which equal to 1 when the day is Monday, or Tuesday, orWednesday, or Thursday, or Friday respectively and to 0 when the day is the other days
bi: the coefficients of the-day-of-the-week effectIf more than one coefficients from bi are significant from 0, there exists the-day-of-the-week-effect inreturns.
3.DataThis paper try to analyze five stock market from China, Hong Kong, Japan, the US and Germany. The
specific index data are respectively the daily close prices of CSI 300, HSI, Nikkei 225, Nasdaq Composite
index and DAX stock index for each market. The data are in daily and monthly types from 20060101 to
20201231 collecting from NetEase Finance1 and Yahoo Finance2.
The CSI 300 is a stock index which contains 300 stocks listed in Shanghai Stock Exchange and Shenzhen
Stock Exchange and is seen as an important indicator in reflecting the market condition in China. The HSI is
one of the earliest stock market index in Hong Kong and has become the most widely quoted indicator of theperformance of the Hong Kong stock market. The Nikkei 225 consists of 225 stocks in the first section of theTokyo Stock Exchange and has been used as the indictor of the movement of Japanese stock markets. The
Nasdaq Composite index is a index of over 2500 equities listed on the Nasdaq stock exchange. The DAX is astock index that represents thirty of the largest and most liquid German companies that trade on the Frankfurt
Exchange.
Table 1, 2 summarizes descriptive statistics of daily and monthly returns in a calendar year for all indexes.

——————————NetEase Finance1: https://money.163.com
Yahoo Finance2: https://finance.yahoo.com

Table 1 Summary statistics of daily returns for five indexes
Note: This table shows the summary statistics of daily returns for five indexes including CSI 300, HSI,NIKKEI 225, NASDAQCOM and DAX. Mean is the mean value of daily returns. SD is the standard
deviation of daily returns. JB is the value of Jarque-Bera test. The time span is from 20060101 to 20201231.
CSI 300

HSI

NIKKEI 225

NASDAQCOM

DAX

Mean

0.000470.000160.000140.000460.00024SD

0.017320.01494

0.015170.013810.01398

Skewness-0.576-0.035-0.473-0.496-0.241

Kurtosis

6.867

11.77810.83312.30811.089JB

2473.237

11844.548

9512.961

13783.087

10394.722

Table 2 Summary statistics of monthly returns for five indexes
Note: This table shows the summary statistics of monthly returns for five indexes including CSI 300, HSI,NIKKEI 225, NASDAQCOM and DAX. Mean is the mean value of daily returns. SD is the standard
deviation of daily returns. JB is the value of Jarque-Bera test. The time span is from 20060101 to 20201231.
CSI 300

HSI

NIKKEI 225

NASDAQCOM

DAX

Mean

0.00940.00335

0.00279

0.00986

0.00541SD

0.093030.06036

0.05698

0.05069

0.05459

Skewness-0.479-0.661-0.888-0.653-0.782

Kurtosis

4.323

4.8

5.374

4.186

4.976

JB

19.91838.02365.55423.72148.409From Table 1 and 2, the mean value of both types of returns are all positive with highest daily return
0.00047 in CSI 300 and highest monthly return 0.00986 in NASDAQCOM. The most volatile daily return is
CSI 300 with 0.01732 and the most volatile monthly return is also CSI 300 with 0.09303. All ten stock returnseries are thinner than normal distribution because of kurtosis higher than 3. According to the Jarque-Berastatistics in Table 1 and 2, normal distribution of return series is rejected for almost all markets from 2006 to
2020. Rejection of normal distribution is the same as Mubarik and Javid (2009) and some other papers.
4.Empirical results
4.1 Autocorrelation
We first calculate the autocorrelation at lag1 to lag10 for whole period from 2006 to 2020 and then separate
the fifteen years in to three sub-periods, 2006-2010, 2011-2015, 2015-2020, and calculate once more. The
results are summarized in Table 3.
Table 3 The autocorrelations of five indexes
Note: This table shows the autocorrelations from lag1 to lag 10 for five indexes. *** means very significant
with p value lower than 0.01. ** means significant with p value higher than 0.01 but lower than 0.05. *means a little significant with p value higher than 0.05 but lower than 0.1. No * means insignificant.

(1) The autocorrelations of CSI 300
Lag

2006-2020

2006-20102011-20152016-2020

1

0.0273*0.02730.0623**-0.03802-0.027*-0.0221-0.0706***

0.036330.0314**0.0473-0.0208**0.0441

4

0.0515***0.0775**0.0674***-0.0613**50.006***-0.0012**0.0368***-0.0414**6-0.0639***-0.0541**-0.0918***-0.0511**70.0305***0.0237**0.0324***0.0266**8

0.0092***-0.022**0.1004***-0.0347**90.0117***-0.0142*0.0293***0.0474**100.0055***0.0346*-0.0558***

0.0253**(2) The autocorrelations of HSI
Lag

2006-2020

2006-20102011-20152016-2020

1-0.0203-0.0398

0.0315-0.02142

0.00790.00790.0136-0.0034

3-0.0218-0.0506-0.0346

0.0724*

4-0.0323-0.0281-0.0438-0.032*5-0.0024-0.01020.00980.0025

6-0.01440.0000-0.0004-0.0747**70.02020.01340.04800.0076**8

0.02580.0566-0.0341-0.0024*9-0.0288**-0.0646*

0.03610.0039*10-0.0482***-0.0673**-0.0265-0.0124*(3) The autocorrelations of Nikkei 225
Lag

2006-2020

2006-20102011-20152016-2020

1-0.0373**-0.0514*-0.0416-0.006620.0106*-0.0266

0.04070.0446

3-0.0234*-0.0302-0.0180-0.0204

4-0.0137*

0.0059-0.0849***

0.02625-0.0173*-0.04190.0382***-0.0387Lag

2006-2020

2006-20102011-20152016-2020

6-0.0122-0.0086-0.0084**-0.0223

70.00250.02210.0196**-0.06308-0.0003-0.0050

0.0135**-0.013490.0100-0.03100.0709***0.017110

0.02720.0627-0.0337***

0.0291(4) The autocorrelations of NASDAQCOM
Lag

2006-2020

2006-20102011-20152016-20201-0.1182***-0.0957***-0.0095-0.2241***20.0084***-0.0826***

0.01560.1337***30.0182***0.0815***-0.1013***-0.0012***4-0.0345***-0.0434***-0.0167***-0.0369***5-0.0019***-0.0081***-0.0802***

0.0552***

6-0.0410***0.0017***0.0160***-0.1395***

70.0586***0.0013***-0.0269***

0.1946***8-0.0591***

0.0061***0.0284***-0.2112***90.0507***0.0045***-0.0404***

0.1727***100.0074***0.0290***0.0694***-0.0650***(5) The autocorrelations of DAX
Lag

2006-2020

2006-20102011-20152016-2020

1

0.0020-0.0325

0.04340.00672-0.0089-0.0455-0.02900.0689**3-0.0027-0.0302-0.02480.0538**40.00330.0666**-0.0408-0.0394**5-0.0265-0.0468**-0.0476

0.0263**60.00010.0321**

0.0219-0.0699***70.0248-0.0286**

0.0454*0.0816***8-0.0370-0.0076**-0.0158-0.1025***9-0.0064-0.0472**-0.00140.0409***100.00920.0406**-0.0087-0.0140***

Mubarik and Javid (2009) reported significant autocorrelation of first order in return series. Sewell (2012)
found that first-order autocorrelation of daily, weekly, monthly and annual log returns was small but positive
for all time periods but we find more information than that. From Table 3 (1), (2), (3), (4) and (5), the resultsof autocorrelation are different among five markets. From Table 3 (1) and (4), there is strong evidence ofautocorrelation for CSI 300 and NASDAQCOM, but some evidence for DAX from Table 3 (5), a little
evidence for HSI and Nikkei 225 from Table 3 (2) and (3). Hamid, Suleman, Shah and Akash (2010) usedmonthly stock returns of fourteen countries including China, the autocorrelation of there counties were allminus at log1. In Table 3 (1), there are only two lags at which the autocorrelations are negative for CSI 300
from 2006 to 2020 while there are at least four lags at which the autocorrelations are negative for the otherindexes. From the viewpoint of autocorrelation, the most efficient market among five stock markets is themarket in Hong Kong.
4.2 Runs test
We first examine the randomness with runs test for whole period for five indexes from 2006 to 2020. Then
separate the whole period into three sub-period the same as above. The results are summarized in Table 4.
Table 4 Runs tests of five indexes
Note: This table shows the results of runs tests for five indexes. *** means very significant with p value
lower than 0.01. ** means significant with p value higher than 0.01 but lower than 0.05. * means a little
significant with p value higher than 0.05 but lower than 0.1. No * means insignificant.
(1) Runs tests of CSI 300
2006-2020

2006-20102011-20152016-2020-0.8797-0.7955-0.5965

0.1924

2006-2020

2006-20102011-20152016-2020

0.2721-0.12250.400

0.3298

2006-2020

2006-20102011-20152016-2020

2.1553**2.2819**0.91280.4732

2006-2020

2006-20102011-20152016-2020

1.3106-0.0475-0.14142.5227**

2006-2020

2006-20102011-20152016-2020

1.7947*1.1356-0.03541.9110*Z-value(2) Runs tests of HSI

Z-value(3) Runs tests of Nikkei 225

Z-value(4) Runs tests of NASDAQCOM

Z-value(5) Runs tests of DAX

Z-value

From Table 4 (1), (2), (3), (4) and (5), the results of runs tests do not found evidence against randomness indaily returns for CSI 300, HSI from 2006 to 2020 but find a little evidence for Nikkei 225, NASDAQCOM
and DAX. The randomness hypothesis is rejected for Nikkei 225 in sub-period of 2006-2010, forNASDAQCOM in sub-period 2016-2020 and for DAX in sub-period 2016-2020. Moreover, the z-values ofruns test for CSI 300 and NASDAQCOM are negative for sub-period 2006-2010 and 2011-2015 indicating
the real runs of a return series are less than the mean value of runs and therefore meaning a positive
autocorrelation in return series. This is the same as what we found in 4.1 Autocorrelation. Our findings aredifferent from Ozdemir (2008), in which the results of runs test failed to reject the randomness, is similar to
Karemera, Ojah and Cole (1999), Dorina and Simina (2007) and Borges (2009). From the viewpoint of runs
test, the higher level of market efficiency among five stock markets are the markets in China and HongKong. The markets in Japan, The US and Germany are not efficient.
4.3 Strategy
S(0.01, -0.01) are used here for all indexes and all periods, which means buying shares when yesterday’s
return is higher than 0.01 and selling shares when yesterday’s return is lower than -0.01. We calculate returnsof holding stocks in the same intervals based on the strategy S(0.01, -0.01). We also calculate the return of
every trading and use approximate normal distribution as the distribution of the mean return of S(0.01,-0.01). If the z-value is higher than 2, the S(0.01, -0.01) makes more profit than holding the stock all thetime. The results are summarized in Table 5.
Table 5 S(0.01, -0.01) for five indexes
Note: This table shows the results of strategy S(0.01, -0.01) for five indexes. S(0.01, -0.01) means the meanvalue of strategy. Buy-and-hold means the mean value of holding index in the same period with strategy. ***means very significant with p value lower than 0.01. ** means significant with p value higher than 0.01 but
lower than 0.05. * means a little significant with p value higher than 0.05 but lower than 0.1. No * means
insignificant.
(1) S(0.01, -0.01) for CSI 300
2006-2020

2006-20102011-20152016-2020

S(0.01, -0.01)

0.287250.65404-0.51503

0.03639

Buy-and-hold1.68125

1.19001

0.185510.45861(2) S(0.01, -0.01) for HSI
2006-2020

2006-20102011-20152016-2020

S(0.01, -0.01)-0.56409-0.22136-0.03966-0.25952

Buy-and-hold

0.57840.10654-0.10275

0.2862(3) S(0.01, -0.01) for Nikki 225
2006-2020

2006-20102011-20152016-2020

S(0.01, -0.01)

1.06515-0.03635

0.70223

0.29436

Buy-and-hold

0.5171-0.47480.58473

0.4387(4) S(0.01, -0.01) for NASDAQCOM
2006-2020

2006-20102011-20152016-2020

S(0.01, -0.01)

0.36576-0.22136-0.12572

0.65364

Buy-and-hold1.69730.106540.62768

0.99299

(5) S(0.01, -0.01) for DAX
2006-2020

2006-20102011-20152016-2020

S(0.01, -0.01)-1.04201-0.28766-0.56347-0.1933

Buy-and-hold

0.90138

0.234170.42840.32173

From Table 5 (1), (2), (3), (4) and (5), the results are almost the same for five indexes except Nikkei 225.
The strategy S(0.01,-0.01) failed to make higher returns than buy-and-hold strategy in any periods except
Nikkei 225. Therefore, in long period, S(0.01,-0.01) does not have any advantage. Although in period of
2006-2020, 2006-2010, 2011-2015, from Table 5 (3), S(0.01,-0.01) preformed better than buy-and-hold with
Nikkei 225, the result does not have any significance.
4.4 January effect
The results of regression of (1), testing January effect for five indexes are showed in Table 6. The monthly
return is calculated as the following function:lnPt - lnPt-1.
Pt: the close price on the first trading in this monthPt-1: the close price on the first trading day in last month
Table 6 January effect in five indexes
Note: The January effect is examined by regression:

Rt: the monthly returns of stock index
JANUARYt: a dummy variable equal to 1 for January returns and to 0 for the other month returns
a: constantb: the coefficient of January effectIf b is significantly different from zero, there is January effect in specific indexes. *** means very significant
with p value lower than 0.01. ** means significant with p value higher than 0.01 but lower than 0.05. *means a little significant with p value higher than 0.05 but lower than 0.1. No * means insignificant.
(1)The January effect in CSI 300
Regression Coeﬃcient

2006-2020a0.0071b

0.029(2) The January effect in HSI
Regression Coeﬃcient

2006-2020a0.0041b-0.0129(3) The January effect in Nikki 225

Regression Coeﬃcient

2006-2020a0.0046b-0.0236(4) The January effect in NASDAQCOM
Regression Coeﬃcient

2006-2020a0.0102**b-0.0078(5) The January effect in DAX
Regression Coeﬃcient

2006-2020a0.0062b-0.0156

From Table 6 (1), (2), (3), (4) and (5), the coefficient b in regression (1) are not significant for five indexes
indicating that the January effect did not exist from 2006 to 2020.
The volatility clustering is common in stock returns. In order to take time-varying volatility into
consideration and check if the January effect changes after considering time-varying volatility, we also
regress a EGARCH(1, 1) model. The results are showed in Table 7. The EGARCH (1, 1) model are regressedwith Stata15.1.
Table 7 The January effect in five indexes—EGARCH(1,1)
Note: This table shows the result of regression:

Rt: the monthly return of stock index
b: the January effect in conditional mean function
λ1: the January effect in conditional variance function*** means very significant with p value lower than 0.01. ** means significant with p value higher than 0.01
but lower than 0.05. * means a little significant with p value higher than 0.05 but lower than 0.1. No *means insignificant.
(1)The January effect in CSI 300
Coeﬃcient

Estimate

Standard error

Z-valueb-0.00443

0.02072-0.21

c0.00851

0.005481.55

λ10.821220.34839

2.36**

λ0-0.40159

0.16614-2.42**

α0.106810.05579

1.91*

Coeﬃcient

Estimate

Standard error

Z-valueγ0.42052

0.137423.06***

δ

0.93165

0.0330228.21***

Coeﬃcient

Estimate

Standard error

Z-valueb-0.00847

0.01433-0.59

c0.00786

0.004451.77*

λ10.481800.447521.08

λ0-1.30259

0.57345-2.27**

α-0.89522

0.06460-1.39

γ0.406120.10455

3.88***

δ

0.77803

0.09823

7.92***

Coeﬃcient

Estimate

Standard error

Z-valueb-0.02794

0.01630-1.71*

c

0.005450.004291.27

λ10.19371

0.539180.36

λ0-6.90102

1.46607-4.71***

α-0.25088

0.11719-2.14**

γ

0.28827

0.143932.00**

δ-0.18035

0.25273-0.71(2)The January effect in HSI(3)The January effect in Nikkei 225(4)The January effect in NASDAQCOM
Coeﬃcient

Estimate

Standard error

Z-valueb0.001230.010810.11

c0.00932

0.00377

2.47**

λ1

0.233210.37278

0.63

λ0-1.19896

0.46927-2.55*

α-0.21922

0.10112-2.17**

γ

0.399920.17835

2.24**

δ

0.80851

0.0751310.76***(5)The January effect in DAX

Coeﬃcient

Estimate

Standard error

Z-valueb-0.017746

0.01768-1.00

c0.006100.003911.56

λ10.72106

0.409391.76*

λ0-2.35711

0.65044-3.62***

α-0.43933

0.08620-5.10***

γ

0.077240.170170.45

δ

0.61706

0.10620

5.81***

From Table 7 (1), (2), (3), (4) and (5), after the consideration of time-varying volatility, it is interesting that
we found January effect in returns in Nikkei 225 while it did not exist from the result in Table 6 (3) because
of insignificant b. The return of Nikkei 225 in January is lower than the other month with -0.02794. The
January effect exists in variance in CSI 300 and DAX because of significant λ1. All five indexes are
examined with arch effect or garch effect. Except HSI, other four indexes have a leverage effect because ofsignificant α. Moreover, the leverage in CSI 300 is 0.10681, a positive value, which implies that positive
innovations are more destabilizing than negative innovations. The leverage in other three indexes are-0.25088, -0.21922, -0.43933, negative values, which implies that negative innovations are moredestabilizing than positive innovations. Because there exists January effect in Nikkei 225, the market in
Japan is inefficient.
4.5 Turn-of-the-month-effectWe first calculate the mean returns in -5 to 5 days. The mean returns for five markets are showed in Table 8.
Table 8 The turn-of-the-month-effect in five indexes
Note: 1, 2, 3, 4, 5 means the first, second ,third, fourth, fifth trading day’s return in a month. -1, -2, -3, -4, -5means the last day, the day before last day, tow days before last day, three days before last day, four days
before last day’s return in last month. 0 means the other days except -5 to 5 days in one month.
(1) -5 to 5 window in CSI 300
2006-2020

2006-20102011-20152016-2020

0-0.00002

0.00049-0.00048-0.00006-5-0.00110-0.00084-0.00366

0.00121-40.000200.00019-0.00028

0.00069-3-0.00115

0.00074-0.00093-0.00325-2-0.00141-0.00208-0.00205-0.00009-1

0.002170.00052

0.004150.0018510.003620.006130.00362

0.0021520.00267

0.002370.001220.0044130.00205

0.004440.001250.0004540.00100

0.001700.00219-0.00088

2006-2020

2006-20102011-20152016-2020

0.001660.00191

0.002100.00096

2006-2020

2006-20102011-20152016-2020

0-0.00028-0.00054-0.00036

0.00005-50.000100.00035-0.00018

0.00014-40.00085

0.00288

0.00029-0.00061-30.00081-0.00051

0.002800.00014-20.00159

0.00476-0.00023

0.00024-10.00101

0.002190.00165-0.00082

1

0.002770.004070.00171

0.002752-0.00022

0.00079-0.001550.000103-0.00038

0.00167-0.00138-0.0014540.00040-0.00056

0.000470.001295-0.00059-0.00270-0.00088

0.00181

2006-2020

2006-20102011-20152016-2020

00.00001-0.00109

0.000610.00050-5-0.00034-0.00007-0.00136

0.00041-40.00125

0.002930.00147-0.00064-30.00194

0.002480.00049

0.00285-20.001160.002990.00122-0.00074-1-0.00043-0.001200.00140-0.00150

1-0.00058-0.00212-0.00007

0.0006820.000360.00180-0.00126

0.00055

3-0.00052

0.00112-0.00120-0.0014840.00056-0.00131

0.002020.00098

5-0.00067-0.00324

0.000960.00026

5(2) -5 to 5 window in HSI(3) -5 to 5 window in Nikki 300(4) -5 to 5 window in NASDAQCOM

2006-2020

2006-20102011-20152016-2020

00.000370.00008

0.000520.00050-5-0.00092

0.00040-0.00141-0.00174-40.003280.004610.00095

0.00429-30.00100

0.00098

0.00298-0.00096-20.00085-0.00028

0.001160.00166-1-0.00025-0.00166-0.00019

0.0011010.001320.00146-0.00001

0.0026720.000270.001390.00081-0.0014030.00104-0.001020.00167

0.002484-0.00014-0.00258-0.00008

0.002245-0.00077-0.00132-0.001290.00030

2006-2020

2006-20102011-20152016-2020

00.00011-0.00025

0.000170.00041-50.000780.002890.00182-0.00236-40.001440.00147

0.00343-0.00057-30.001630.00188

0.002130.00089-20.000030.000120.00088-0.00091-1-0.00003

0.000520.00104-0.0016510.001190.00274-0.00054

0.001962-0.00070

0.00110-0.00316-0.00005

30.000750.00101

0.000670.00057

4-0.00145-0.00373-0.00114

0.0005350.00026-0.00121

0.000160.00182(5) -5 to 5 window in DAX

From Table 8, it is easy to find that the returns around the turn of the month, -5 to 5 window, seem higher
than the other days, showed in Table 8 row 0. From Table 8 (1), in CSI 300, the mean returns on the first day
and second day in one month are 0.00362 and 0.00267, seem higher than the mean returns of the former days
and the latter days. The other indexes show similar phenomena: in whole period, from Table 8 (2) column
2006-2020, the return on the first day in one month is 0.00277, from Table 8 (3) column 2006-2020, thereturn on two days before last day in a month is 0.00194, from Table 8 (4) column 2006-2020, the returns on
the first day and third day in a month are 0.00132 and 0.00104, from Table 8 (5) column 2006-2020, thereturn on the first day in a month is 0.00119. They all seem to be higher than the other days.

The results of regression (2) are summarized in Table 9. To save space, only significant coefficients inregression (2) are included in Table 9.
Table 9 The turn-of-the-month effect in five indexes
Note: The results in this table are the results of regression:

Rt: the daily returns of stock index
a: constant indicating the mean return in ROM period
Dit: equals to 1 when the return at time t is on the ith trading days in a month and equals to 0 on other days
D-it: equals to 1 when the return at time t is on the last trading days, the day before last day, two days before
last day, three days before last day, four days before last day in one month and equals to 0 on other days
bi: the coefficient of the turn-of-the-month-effect (i = 1, 2, 3, 4, 5, -1, -2, -3, -4, -5)*** means very significant with p value lower than 0.01. ** means significant with p value higher than 0.01
but lower than 0.05. * means a little significant with p value higher than 0.05 but lower than 0.1. No *means insignificant.
(1) The turn-of-the-month-effect in CSI 300
Significant
coeﬃcients

2006-2020

2006-20102011-2015b-3

2016-2020-0.00319*b-1

0.00463**b1

0.00364***b2

0.00269**

0.00563*0.0041*0.00447***(2) The turn-of-the-month-effect in HSI
Significant
coeﬃcients

2006-2020

2006-2010

b-3
b-2
b1

2011-20152016-2020

0.00316*0.0027*

2011-20152016-20202011-20152016-2020

0.0053**0.00305***

0.00461*(3) The turn-of-the-month-effect in Nikkei 225
Significant
coeﬃcients

2006-2020b-2

2006-2010
0.00408*(4) The turn-of-the-month-effect in NASDAQCOM
Significant
coeﬃcients

2006-2020

2006-2010b-4

0.00291***0.00453**b-3

0.00379**
0.00245*(5) The turn-of-the-month-effect in DAX
Significant
coeﬃcients

2006-2020

2006-20102011-20152016-2020

b-4
b2-0.00333*

b4-0.00348*

0.00327*

From Table 9 (1), (2), (3), (4) and (5), the turn-of-the-month-effect exists in all indexes for significant bi
although different sub-periods shows different days with positive returns around the turn of the month. First,
the TOM window for five indexes are (-3,2), (-3,1), (-2), (-4,-3) and (-4,4). The TOM effect almost exists inthe early time of the turn of the month. This result is similar to early studies. In whole period from 2006 to
2020, from Table 9 (1), the returns on the first day and second day in one month for CSI 300 are significant
higher than the other days. From Table 9 (2), the return on the first day in one month for HSI is significant
higher. From Table 9 (3), the return on the day before last day in one month for Nikkei 225 is significant
higher in the sub-period 2006-2010. From Table 9 (4), the return on three days before last day in one monthfor NASDAQCOM is significant high. From Table 9 (5), the return on fourth day in one month is significant
higher in the sub-period 2006-2010. Second, from Table 9 (1) and (2), CIS 300 and HSI, we can find that the
turn-of-the-month-effect is becoming earlier and earlier. From Table 9 (1), the results of CSI 300, in subperiod 2006-2010, the abnormal return happened on the first day in one month while in sub-period
2015-2020, the abnormal return happened on two days before last day in one month. This finding is also thesame with early papers. Third, the existence of TOM effect is evidence against efficient market. All fiveindexes examined here is characterized with a TOM effect in different level and therefore the hypothesis ofefficient market is rejected for five markets.
Similarly, we regression a EGARCH(1, 1) model in Table 10. Because the excess variables in theconditional variance function failed to be regressed, here we only choose four days (the first day and secondday, the last day and the day before last day in one month) for CSI 300, HSI, Nikkei 225 and DAX but twodays (two days before last day and three days before last day in one month) for NASDAQCOM.
Table 10 The turn-of-the-month-effect in five indexes—EGARCH(1, 1)
Note: This table shows the result of regression:

Rt: the daily return of stock index
bi: the turn-of-month-effect in conditional mean function (i = 1, 2, -1, -2)
λi: the turn-of-month-effect in conditional variance function (i = 1, 2, -1, -2)*** means very significant with p value lower than 0.01. ** means significant with p value higher than 0.01
but lower than 0.05. * means a little significant with p value higher than 0.05 but lower than 0.1. No *means insignificant.
(1)The turn-of-the-month-effect in CSI 300
Coeﬃcient

Estimate

Standard error

Z-valueb1

0.00406

0.00124

3.29***

Coeﬃcient

Estimate

Standard error

Z-valueb2

0.001850.00089

2.09*

b-1

0.001750.00083

2.12*

b-2

-0.00030

0.00106-0.29

c

0.000170.000220.78

λ10.598240.08632

6.93***

λ2-0.51335

0.07541-6.81***

λ-1-0.11591

0.09977

-1.16

λ-2

0.03430

0.082330.42

λ0-0.06190

0.01450-4.27***

α-0.00166

0.00495-0.33

γ0.15769

0.00906

17.39***

δ

0.991590.00166

596.03***(2)The turn-of-the-month-effect in HSI
Coeﬃcient

Estimate

Standard error

Z-valueb1

0.002960.000963.08***

b2

0.000170.00095

0.18

b-1-0.00045

0.00071

-0.63

b-2

0.00109

0.000851.28

c0.00040.000200.20

λ10.534450.14401

3.71***

λ2-0.14663

0.10544

-1.39

λ-1

-0.21310

0.14503

-1.47

λ-2

0.201230.108921.85*

λ0-0.17722

0.20670-8.56***

α-0.06482

0.00675-9.60***

γ

0.134470.01036

12.98***

δ

0.981480.00232

422.19***(3)The turn-of-the-month-effect in Nikkei 225
Coeﬃcient

Estimate

Standard error

Z-valueb1

0.001400.00093

1.51

Coeﬃcient

Estimate

Standard error

Z-valueb2

0.00032

0.000740.44

b-1-0.001010.00090

-1.13

b-2

-0.00017

0.00080-0.22

c0.000130.000200.64

λ10.286070.11254

2.54**

λ2-0.32257

0.08367-3.86***

λ-1

0.114429

0.124880.92

λ-20.12701

0.980171.3

λ0-0.34434

0.03434-10.03***α-0.11494

0.00590-19.47***γ

0.206120.01265

16.29***

δ

0.960900.00392245.24***(4)The turn-of-the-month-effect in NASDAQCOM
Coeﬃcient

Estimate

Standard error

Z-valueb-30.001290.00075

1.74*

b-4

0.000230.000770.30

c0.000260.000171.55

λ-3-0.06377

0.10832

-0.59

λ-4

0.16477

0.106921.54

λ0-0.29385

0.02457-11.96***α-0.13290

0.00588-22.61***γ

0.157850.01186

13.31***

δ

0.96728

0.00269358.98***(5) The turn-of-the-month-effect in DAX
Coeﬃcient

Estimate

Standard error

Z-valueb1

0.00300

0.000933.20***

b2-0.00198

0.00062-3.21***

b-1-0.00076

0.00067

-1.14

b-2

-0.00056

0.00090-0.62c0.000230.00018

1.25

Coeﬃcient

Estimate

Standard error

Z-value

λ1

0.70909

0.12480

5,68***

λ2-0.54752

0.10592-5.17***

λ-1-0.25627

0.11944-2.15**

λ-20.10337

0.093131.11

λ0-0.22232

0.02184-10.18***α-0.12962

0.00712-18.19***γ0.13562

0.01243

10.91***

δ

0.97455

0.00251388.51***

From Table 10 (1), (2), (3), (4) and (5), under the consideration of time-varying volatility, except Nikkei
225, all the other indexes are also verified with the turn-of-the-month-effect in return. For CSI 300, from
Table 10 (1), the returns on the first day, second day in one month and the last day in one month are higher
than the other days for significant 0.00406, 0.00185 and 0.00175. For HSI, from Table 10 (2), the returns on
the first day in one month is higher than the other days for significant 0.00296. For NASDAQCOM, from
Table 10 (4), the return on two days before last day in one month is higher than the other days for significant
0.00129. For DAX, from Table 10 (5), the return on the first is higher than the other days for significant
0.003 but the return in the second day is lower than the other days for significant -0.00198.
For variance, from Table 10, except NASDAQCOM, other indexes are examined with the-turn-of-themonth-effect in variance. For CSI 300, from Table 10 (1), the return on the first day in one month is morevolatile and the second day is less volatile than the other days for significant 0.59824 and -0.51335. For HSI,
from Table 10 (2), the returns on the first day in one month and the day before last day are more volatile forsignificant 0.53445 and 0.20123. For Nikkei 225, from Table 10 (3), the return on the first day in one monthis more volatile and the return on the second day in one month is less volatile for significant 0.28607 and-0.32257. For DAX, from Table 10 (5), the return on the first in one month is more volatile and the returns
on the second day and the last day in one month are less volatile for significant -0.54752 and -0.25627.
From Table 10, all five indexes are examined with arch and garch effect for significant γ and δ. Except CSI
300, other four indexes have leverage effect that a fall in returns results in greater volatility than an increase
in returns of the same magnitude for significant negative α.
4.6 Day-of-the-week effect
Table 11 shows the mean returns on five weekdays for five indexes.
Table 11 The mean returns on weekdays for five indexes
Note: The returns and standard deviations on five weekdays of five indexes are summarized in this table.
(1) The mean returns for CSI 300
Period
2006-2020

2006-2010

Statistic

MondayTuesday

WednesdayThursdayFridayMean

0.001750.00008

0.00059-0.001100.00107

Sd

0.02127

0.016170.01605

0.01655

0.01593Mean

0.00471-0.00218

0.00179-0.00038

0.00107

Sd

0.026110.02056

0.02179

0.02055

0.01946

Period
2011-20152016-2020

Statistic

MondayTuesday

WednesdayThursdayFridayMean-0.00028

0.00008

0.00095-0.00163

0.00153

Sd

0.019440.01530

0.01458

0.01575

0.01522Mean

0.00108

0.00226-0.00094-0.001300.00062

Sd

0.016120.010850.009210.01232

0.01225

Statistic

MondayTuesday

WednesdayThursdayFridayMean

0.00010-0.00007

0.00047-0.00005

0.00036

Sd

0.017280.01456

0.014470.014360.01385Mean

0.00129-0.00136

0.000610.000960.00028

Sd

0.02356

0.019200.01909

0.01857

0.01814Mean-0.00150-0.00027

0.00083-0.00027

0.00089

Sd

0.01277

0.011850.011810.012400.01085Mean

0.000540.00145-0.00002-0.00083-0.00009

Sd

0.01300

0.011020.01104

0.01095

0.01139(2) The mean returns for HSI
Period
2006-2020

2006-20102011-20152016-2020(3) The mean returns for Nikkei 225
Period
2006-2020

2006-20102011-20152016-2020

Statistic

MondayTuesday

WednesdayThursdayFridayMean-0.00006

0.000150.000410.00053-0.00034

Sd

0.015400.015470.014370.015530.01503

Mean-0.00033-0.00094-0.00079

0.00162-0.00150

Sd

0.01799

0.01835

0.01674

0.01934

0.01818Mean-0.00097-0.00014

0.002070.000390.00096

Sd

0.014130.01458

0.013850.01359

0.01296Mean

0.001260.00142-0.00006-0.00044-0.00047

Sd

0.013480.01295

0.01198

0.01273

0.01329(4) The mean returns for NASDAQCOM
Period
2006-2020

2006-2010

Statistic

MondayTuesday

WednesdayThursdayFridayMean-0.00017

0.001160.000900.000300.00030

Sd

0.01563

0.013850.01335

0.01382

0.01225

Mean-0.00085

0.000450.001150.00023-0.00041

Period
2006-20102011-20152016-2020

Statistic

MondayTuesday

WednesdayThursdayFridaySd

0.018540.017450.015780.01649

0.01336

Mean-0.00048

0.00157

0.000180.000710.00041

Sd

0.011390.010470.01098

0.011400.01015Mean

0.000840.001450.00137-0.00004

0.00022

Sd

0.016020.01271

0.01279

0.013080.01298

Statistic

MondayTuesday

WednesdayThursdayFridayMean

0.000230.000970.00063-0.00040-0.00022

Sd

0.015850.01375

0.013020.01400

0.01309

Mean

0.001310.000280.00061-0.00038-0.00089

Sd

0.018420.015180.01474

0.01487

0.01413Mean-0.00095

0.000800.000620.001200.00000

Sd

0.01391

0.01357

0.01266

0.013360.01310Mean

0.000460.00184

0.00066-0.00202

0.00024

Sd

0.014540.012290.011430.01352

0.01192(5) The mean returns for DAX
Period
2006-2020

2006-20102011-20152016-2020

From Table 11 (1), (2), (3), (4) and (5), it is clear that not all weekdays have the same return level. From
Table 11 (1), CSI 300, the return on Monday seems higher than the other days in one week with 0.00175.
From Table 11 (2), HSI, the return on Wednesday seems higher with 0.00047. From Table 11 (3), Nikkei 225,
the return on Thursday seems higher with 0.00053. From Table 11 (4), NASDAQCOM, the return on
Tuesday seems higher with 0.00116. From Table 11 (5), the return on Tuesday seems higher with 0.00097.
In order to take a deep look, we regress (3). The results of regression (3) are summarized in Table 12.
Table 12 The day-of-the-week-effect in five indexes
Note: This table shows the results of regression:

Rt: the daily returns of stock index
Mt, TUt, Wt, THt, Ft: the dummy variable which equal to 1 when the day is Monday, or Tuesday, orWednesday, or Thursday, or Friday respectively and to 0 when the day is the other days
bi: the coefficients of the-day-of-the-week effect*** means very significant with p value lower than 0.01. ** means significant with p value higher than 0.01
but lower than 0.05. * means a little significant with p value higher than 0.05 but lower than 0.1. No * means
insignificant.
(1) The day-of-the-week-effect in CSI 300

b1

2006-2020

2006-20102011-20152016-2020

0.00175***

0.00471***-0.00028

0.00108

2006-2020

2006-20102011-20152016-2020

b2

0.00008-0.00218

0.00008

0.00226***b30.000590.001790.00095-0.00094b4-0.00111*-0.00038-0.00163-0.00130b50.00107*0.001070.001530.00062

2006-2020

2006-20102011-20152016-2020

b1

0.000100.00129-0.0015*0.00054b2-0.00007-0.00136-0.00027

0.00145**b30.000470.000610.00083-0.00002b4-0.00005

0.00096-0.00027-0.00083b5

0.000360.000280.00089-0.00009

2006-2020

2006-20102011-20152016-2020

b1-0.00006-0.00033-0.00097

0.00126b20.00015-0.00094-0.00014

0.00142**b30.00041-0.00079

0.00207**-0.00006b4

0.000530.001620.00039-0.00044b5-0.00034-0.00150

0.00096-0.00047(2) The day-of-the-week-effect in HSI(3) The day-of-the-week-effect in Nikkei 225(4) The day-of-the-week-effect in NASDAQCOM
2006-2020

2006-20102011-20152016-2020

b1-0.00017-0.00085-0.00048

0.00084b20.00116**0.000450.00157**0.00145*b30.0009*0.001150.000180.00137b4

0.000300.000230.00071-0.00004b5

0.00007-0.00041

0.000410.00022

2006-2020

2006-20102011-20152016-2020

b1

0.000230.00131-0.00095

0.00046b2

0.00097*0.000280.000800.00184**(5) The day-of-the-week-effect in DAX

2006-2020

2006-20102011-20152016-2020

b3

0.000630.000610.000620.00066b4-0.00040-0.00038

0.00120-0.00202**b5-0.00022-0.00089

0.00000

0.00024

From Table 12 (1), (2), (3), (4) and (5), the day-of-week effect exists in all five markets but with different
types. From Table 12 (1), CSI 300, from 2006 to 2020 and sub-period 2006 to 2010, Monday’s return are
higher than the other days. Friday’s return is not as the previous studies, it even shows higher positive returns
form 2006 to 2020 in CSI 300 with significant 0.00107. The return on Thursday is less the the other days
with significant -0.00111 from 2006 to 2020. From Table 12 (2), HSI shows negative return on Monday in
sub-period 2011-2015 with significant -0.0015 and shows positive return on Tuesday from 2015 to 2020 withsignificant 0.00145. From Table 12 (3), Nikkei 225 shows higher positive return on Wednesday and on
Tuesday in sub-period 2011-2015 and 2016-2020, respectively. From Table 12 (4), NASDAQCOM showshigher positive returns almost on Tuesday from 2006 to 2020 and sub-period from 2011 to 2015, which isdifferent from previous studies. From Table 12 (5), DAX, the returns on Tuesday and Thursday are higher
than the other days in sub period 2016-2020. Anyway, all markets exist the day-of-week-effect which issignificant evidence against an efficient market.
We also regress a EGARCH(1, 1) model as follow.
Table 13 The day-of-the-week-effect in five indexes—EGARCH(1,1)
Note: This table shows the result of regression:

Rt: the daily return of stock index
Mt, TUt, THt, Ft: the dummy variable which equal to 1 when the day is Monday, or Tuesday, or Thursday, orFriday respectively and to 0 when the day is the other days
bi: the day-of-the-week-effect in conditional mean function
λi: the day-of-the-week-effect in conditional variance function*** means very significant with p value lower than 0.01. ** means significant with p value higher than 0.01
but lower than 0.05. * means a little significant with p value higher than 0.05 but lower than 0.1. No *means insignificant.
(1)The day-of-the-week-effect in CSI 300
Coeﬃcient

Estimate

Standard error

Z-valueb1

0.001440.00066

2.23**

b2

0.011430.00057

2.00**

b4-0.00089

0.00059-1.5

b5

0.000740.000581.26

c0.00006

0.000410.15

λ10.51480

0.06101

8.44***

λ2-0.30038

0.08501-3.53***

Coeﬃcient

Estimate

Standard error

Z-value

λ40.315110.08617

3.66***

λ50.09869

0.066491.48

λ0-0.18209

0.05220-3.49***

α-0.00746

0.00511-1.46

γ0.15226

0.00900

16.91***

δ

0.99200

0.00152653.38***(2) The day-of-the-week-effect in HSI
Coeﬃcient

Estimate

Standard error

Z-valueb1-0.00039

0.00053-0.74

b2-0.00067

0.00054-1.24

b4-0.00070

0.00052-1.34

b5-0.00055

0.00055-1.01

c0.000710.000381.89*

λ10.23057

0.05989

3.85***

λ2-0.04907

0.06618-0.74

λ40.103810.081091.28

λ5-0.00179

0.05509-0.03

λ0-0.20992

0.04351-4.83***

α-0.06126

0.00659-9.30***

γ

0.13098

0.01037

12.63***

δ

0.98200

0.00223440.31***(3)The day-of-the-week-effect in Nikkei 225
Coeﬃcient

Estimate

Standard error

Z-valueb1-0.00022

0.00083-0.26

b2-0.00010

0.00075-0.14

b4

0.000530.000750.70

b5-0.00028

0.00074-0.37

c0.00006

0.000510.13

λ10.129360.04820

2.68***

λ20.15357

0.03179

4.83***

Coeﬃcient

Estimate

Standard error

Z-value

λ4

0.000410.035880.01

λ5-0.00361

0.04824-0.07

λ0-15.76154

0.06260-251.81***α-0.01112

0.00356-3.12***

γ

0.090810.00392

23.15***

δ-0.86941

0.00632-137.65***(4)The day-of-the-week-effect in NASDAQCOM
Coeﬃcient

Estimate

Standard error

Z-valueb1-0.00061

0.00047-1.28

b2-0.00060

0.00048-1.25

b4-0.00033

0.00048-0.70

b5-0.00026

0.00046-0.57

c0.000670.00034

2.01**

λ1

0.01980

0.075870.26

λ20.05403

0.086160.63

λ40.094270.087141.08

λ5-0.05548

0.07004-0.79

λ0-0.30438

0.05754-5.29***

α-0.13380

0.00644-20.77***

γ

0.15430

0.01219

12.66***

δ

0.968100.00260

372.33***(5) The day-of-the-week-effect in DAX
Coeﬃcient

Estimate

Standard error

Z-valueb1-0.00042

0.00045-0.94

b4-0.00040

0.00044-0.92

b5-0.00024

0.00044-0.53

c0.000410.000241.69*

λ10.19925

0.05866

3.40***

λ4

0.25918

0.07132

3.63***

λ50.018640.05666

0.33

Coeﬃcient

Estimate

Standard error

Z-valueλ0-0.31307

0.03333-9.39***

α-0.12468

0.00731-17.06***γ

0.12875

0.01197

10.76***

δ

0.97499

0.00245397.26***

From Table 13 (1), (2), (3), (4) and (5), under the consideration of time-varying volatility, the day-of-theweek-effect only exists in CSI 300 from 2006 to 2020 in return. From Table 13 (1), the returns on Monday
and Tuesday in a week are higher than the other days for significant 0.00144 and 0.01143. As for variance,from Table 13 (1), CSI 300, the returns on Monday and Thursday are more volatile and the return on Tuesday
is less volatile for significant 0.5148, 0.31511 and -0.30038. From Table 13 (2), HSI, the reruns on Monday
is more volatile for significant 0.23057. From Table 13 (3), Nikkei 225, the returns on Monday and Tuesday
are more volatile for significant 0.12936 and 0.15357. From Table 13 (4), NASDAQCOM, the returns on
every days in a week show the same level of volatility. From Table 13 (5), DAX, the returns on Monday andThursday are more volatile for significant 0.19925 and 0.25918.
From Table 13, all five indexes are examined with arch effect and garch effect with significant γ and δ.
Except CSI 300, other four indexes are found negative leverage effect for significant negative α, -0.06126,-0.01112, -0.13380, -0.12875, which implies that a fall in returns results in greater volatility than an increase
in returns of the same magnitude.
5.Conclusions
This paper examined the market efficiency level in five stock markets with five indexes. The methods fortesting market efficiency are autocorrelation, runs test, specific strategy, January effect, the-turn-of-themonth-effect (the TOM effect) and the-day-of-the-week-effect (the DOW effect). We found that:(1)There isstrong evidence of autocorrelation for CSI 300 and NASDAQCOM. From the viewpoint of autocorrelation,
the most efficient market among five stock markets is the market in Hong Kong. (2) The results of runs tests
do not found evidence against randomness in daily returns for CSI 300, HSI from 2006 to 2020 but find alittle evidence for Nikkei 225, NASDAQCOM and DAX. From the viewpoint of runs test, the higher level of
efficient markets among five stock markets are the markets in China and Hong Kong. (3) The strategy
analyzed here does not find evidence for inefficient market. (4) The January effect did not exist in fiveindexes. (5) All five indexes are characterized with a TOM effect in different level and therefore thehypothesis of efficient market is rejected for five markets. (6) All five indexed are also found the-day-ofweek effect which indicates an inefficient stock market. (7) After the consideration of time-varying volatility,
we found January effect in Nikkei 225. Except Nikkei 225 all the other indexes are verified with the turn-ofthe-month-effect in return and only CSI 300 are verified with the day-of-the-week-effect in return.
In a ward, we conclude that all five markets are not weak form efficient from 2006 to 2020 from theviewpoint of autocorrelation, the-turn-of-month effect and the-day-of-week effect.
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