INTRODUCTION
The Efficient Market Hypothesis (EMH) argues that prices on any stock market fully reflect all available information at any particular time.Thus, no investor can obtain abnormal profits by using market related information.But the existence of asymmetries in stock returns, known as calendar effects (weekend effect and day of the week effect) , has been extensively investigated in an array of academic studies examining the validity of the Efficient Market Hypothesis (Cross, 1973;French, 1980;Lakonishok and Levi, 1982;Jaffe and Westerfield, 1985;) .
The first scholar to research these“anomalies”in the stock market was Fields (1931) , but it was Cross (1973) who called greater attention to these“anomalies.”After that, a variety of markets were investigated:the developed equity market, the emerging equity market, theforeignexchange market, futuresmarketsanddebtmarkets (Glassman, 1987;Corhy, 1995;Berument, 2007) .Most importantly, Jaffe and Westerfield (1985a) pointed out that the existence of predictable market inefficiencycouldprovideinvestorswith opportunities to generate abnormal returns.
The search for abnormal returns is what makes the Chinese stock market so interesting.The Chinese stock market has many characteristics—institutional frameworks, investment behavior, cultural background—that make it unique.Because these characteristics differ from those of western markets, any investigation of the Chinese equity market’s“anomalies”requires a continued search beyond the existing set of plausible candidates.
LITERATURE REVIEW
Despite evidence of the day of the week effect in both developed and emerging stock markets, the results differ dramatically and controversially as to the days on which abnormal returns are significant.Ingeneral, earlierempiricalstudiesfounda“negative Monday effect”and a“positive Friday effect”in the United States and the United Kingdom (see Cross[1973];French[1980]) .But scholarlyworkpublishedlaterdocumenteda gradual change in the calendar effect for the U.S.stock market.
Berument and Kiymaz (2001) demonstrated a day of the week effect present in the S&P 500index.The study indicated that Monday returns were highest among the weekday and Wednesday returns were lowest.The study of Choudhary and Choudhary (2008) showedsignificantlyhigher positive returns on Thursday in the equity markets of Australia, the U.S, Japan, Switzerland and Korea.A unique comparative study of Bear and non-Bear markets for the U.S indexes, including the Dow Jones Industrial Average and the S&P 500, shows that the day of the week effect was present in both sampled markets (Boudreaux et al., 2010) .
Recently, a growing number of scholars have suggested that the day of the week effect has disappearedinmostsecuritiesmarkets.For example, Gonzalez-PerezandGuerrero (2013) , investigating the U.S market for the period from2004 to 2011, found no evidence of the day of the weekeffect.Confirmativefindingswerealso reported by Carlucci (2013) who examined the main stock exchange indexes of Canada and the U.S.for the 2002-2012 period and found no evidence of the day of the week effect.
In contrast, the day of the effect in Asian and emerging stock markets presents another form of the negative“Tuesday effect”on returns in general (see Aggrawal and Rivoli[1989]) .Other recent cross-country studies indicate that asymmetry, and especiallymarketvolatilityasymmetry, wasa common characteristic in the common European market index;however, the results also presented diversified patterns (Nghiem et al., 2012) .
But, to be fair, there is no universally accepted explanation of the calendar effect either.The existing literature that does proffer an explanation tends to focus on the cost of capital (see Caporale and Gil-Alana[2011]) , information disclosure (see Dellavigna and Pollet[2009]) or influence from futures market (see Faff and Mc Kenzie[2002]) .
Research studies on the Chinese stock market in this area are relatively few, and the conclusions from those studies are inconsistent.In fact, no day of the week effect pattern has been proven across all models.
Empirical investigations by Friedmann and Sanddorf-Kohle (2002) for volatility dynamics in the Chinese equity market applied different GARCH models.Theyfoundthatitisthemarket segmentation in A-share and B-share market that causes the different dynamics and that the number of non-trading days has a significant influence on volatility.Also, volatility decreased when the price change limit was introduced.However, this finding was significant for the daily return on A-shares, but somewhat mixed for B shares.
By applying a dummy regression model, Singh (2014) investigated four emerging stock markets of Brazil, Russia, India and China (BRIC) for the period 1 January 2003 to 15 June 2013.Singh’s article documented the results of a statistically significant negative return on Tuesday for the Chinese stock market.
An empirical research by Bohl, Schuppli and Siklos (2010) indicated that the appearances of the weekday effect seems to have decreased since the deregulation of the B-share markets in Shanghai and Shenzhen during the sample period of 1997through 2001.They concluded that the Tuesday effect in the Chinese markets might not correlate with transmitted Monday effects from the U.S.marketsbutcouldcorrelatewithownership structure.
As can been seen from the previous literature concerning the day of the week effect on returns and volatility, the day of the week effects are a local, country specific phenomena.The estimation method and the data play a significant role in the results (Connolly, 1989) .On March 31, 2010, the Chinese securities market began to implement the margin trading mechanism, which changed the traditional unilateral transaction pattern.With margin trading, investors can buy stocks on leverage and sell stocks they do not own.Transactions can be fulfilled based on the expectation of investors.Given this important regulatory change, it is necessary toexaminethecalendareffectby considering margin trading.The literature review indicates that a number of scholars have studied the Chinese stock markets but scholars hadn’t really studied the effects of the 2010 change to margin trading.
This paper uses the Modified AR-GARCH model to investigate the calendar effect for both returns and volatility.Also, this paper compares the weekday effect before and after the introduction of margin trading and offers an explanation for the reasons behind such phenomena.The overall sample period begins on January 5, 2004and ends on June 23, 2016, setting the time of the introduction of margin trading as the split date.
THEORETICAL MODEL
A Modified AR-GRACH model was used for this paper.Most studies test the day of the week effect on returns by simply employing the Ordinary Least Square (OLS) methodology (Singh, 2014, p.25;Cinko, 2015, p.101, for example) .The OLS modelconsidersdependentdailyreturnsand independent measures of weekday dummy variables (French, 1980) .Kiymaz andBerument (2003) argued that this kind of methodology, however, has two major drawbacks.First of all, the probability of autocorrelation lying in the error terms of the model might result in uncorrected interference.Secondly, the error variances in the model assume a constant variance, which may also lead to inefficient estimations.
Engle (1982) modeled the conditional variance by allowing the forecasted variance of returns to vary systematically over time.The conditional variance depends upon the squared lagged value of the error term from the previous periods of stock return.ThisisknownastheAutoregressive Conditional Heteroskedastic model (q) [ARCH (q) ].Bollerslev (1986) developed the generalized version of the ARCH (q) and expressed the conditional variance as an extended function of lagged values ofεt2and ht2.The extended function of the ARCH model is known as General Autoregressive Conditional Heteroskedasticity (GARCH model) .The GARCHmodelscancapturethethreemost prominent and empirical properties of stock return data:leptokurtosis, skewnessandvolatility clustering.
Kiymaz and Berument (2003) included values of the return variable in the GARCH model to eliminate autoregression.Following Kiymaz and Berument, thispaperusedthemodified AR-GRACHmodelaccountingforboth autoregression and GARCH effects.
METHODOLOGY
Four major indexes, namely, CSI300 (ShanghaiShenzhen 300 Index) , SZSE (Shenzhen Component Index) , SCI (Shanghai composite index) and SSE50 (Shanghai 50 Index) were used in this paper to test the weekly patterns.All data used in this paper were downloaded from the Wind financial terminal.The empirical analyses were carried out using Eviews 6.0.In this paper, the logs of the daily closing prices of indexes were used.The data of dailyreturnswereconstructedasthefirst differences of the logarithmic prices of the stock market index multiples 100.The sampled period ranges from 5 January 2004 to 23, June 2016, with3028 observations in total for each index.
A set of empirical studies added weakly exogenous variables (see, Bohl, Schuppli and Siklos[2010]) to explain the-day-of-the-week effect in both return and volatility.Engle (2001a, 2001b) claims that“GARCH (1, 1) is the simplest and most robust of the family of volatility models, ”and is the most widely applied estimation.Following these studies, the paper allowed exogenous variables to influence conditional variance of stock returns.
In the above equations, Where Rtis the returns on a selected index, , εtis an error term, Mt, Tt, Wtand Htare binary dummy variables for Monday, Tuesday, Wednesday and Thursday at time t.the coefficients aM, aT, aW, aH, and aFrepresent the size and direction of the weekday effect on Rt.The Friday dummy is excluded from the regression to avoid the dummy variable trap or the multi-collinearity problem.AR is the autoregression aggregation with i represents the lag order of autoregressive variables and ai stands for the corresponding coefficients.
The coefficients VM, VT, VW, VH, VCand represent the size and direction of the weekday effect on ht.This specification allows that volatility varies with lagged shocks (ε2t-i) but also includes the momentum in the system that influenced by ht-1.Vccaptures the long-term average value, V1a representsthecoefficientontheARCH (q) component, which was used to measure the impact on volatility from the new news.V1bis the stand inforthecoefficientoftheGARCH (q) component, which could measure the impact on volatility from old news (shock) .This model requires that V1a+V1b<1 for non-explosiveness of the conditional variance and that each of Vc, Vjaand Vjb.The dummy variable takes the value of 1 for a given day of the week and 0 otherwise.
In this article, the Augmented Dickey-Fuller (ADF) tests were used to check the time-series property and the stochastic structure of the data series.Moreover, Levene’s test was employed to test the equality of variance and variation across the day of the week.
RESULTS
The null hypothesis of a unit root tested in ADF tests for all four indexes returns series were unambiguouslyrejectedatthe1%levelof significance, suggesting all these sampled index returns were stationary.The results of the Levene’s test also rejected the null hypothesis that those variances were identical through each day of the week for all index series.
Table 1 reports results from the Modified AR-GARCH (1, 1) specification that investigated the weekday effect in stock returns and volatility for the period before the introduction of margin trading.The statistical results show that only the positive coefficient of Monday and Wednesday were statisticallysignificant.Thecoefficientsof Wednesday were significant at a 5%level among all indexes, and the SSE50 showed somewhat weaker evidence at the 10 per cent level on that day.The positive Monday returns were statistically significant for three of the sampled indexes but not for SSE50.The results could suggest that a positive“Monday effect”and“Wednesday effect”of return existed in Chinese stock market.The positive Mondayeffectmightbeconsistentwiththe hypothesis (e.g.French, 1980) that the highest volatilityonMondaymightreflectthe over-the-weekend-break shocks.
[Table 1]
Whenexamining thecalendareffecton volatility, CSI300 had the highest volatility on Wednesday, which was consistent with the highest required return on that day.By contrast, statistically significantvaluesof thelowestvolatility on Tuesday could only be found in SZSE and SSE50index series.The ARCH coefficient and GARCH coefficient were significantly positive (at the level of 1%) for all equations, suggesting that the volatility of index return was highly persistent.
Taking the CSI300 from the pre sub period as an example, (V1a+V1b) 30=0.994430=0.8450 the impact on the stock price will remain 84.50 per cent even after 30 tra ding days.Therefore, the abnormal fluctuation on the stock market from any shock could be very difficult to eliminate.As presented in Table1, all coefficients in the Ljung-Box Q statistics test and Engle’s ARCH-LM tests provided strong support fortheabsenceofautocorrelationand heteroscedasticity.
Table 2 displays the investigation of the calendar effect for the period after the introduction of margin trading.In fact, the positive“Friday effect”and the negative“Thursday effect”were both statistically significant in all four indexes.For the estimated coefficients for Thursday, CSI300, SZSE and SCI were statistically significant at the1%level, and the critical value was 5%for SSE50.For the estimated coefficients of Friday, the critical level of Friday was statistically significant at 5%for CSI300, SZSE and SCI;SSE50 had a relatively stronger value at the 1%level.
This means the introduction of margin trading certainly changed the calendar effect in the Chinese stock market.This finding is also interesting because only a few instances of the significant lowest Thursday effect have been documented in previous studies of either the Shanghai or Shenzhen Stock Exchanges.For example, Bohl, Schuppli and Siklos (2010) , while investigating stock return seasonality in B-share markets for the period 1994to 2007 for Shenzhen A-shares and Shanghai A-shares, observed a significant Thursday effect only in the Shenzhen B-share market.
Interestingly, the risk averse assumption and the required return compensation were not reflected in the stock market with respect to volatility.According to the results of calendar effect tests on volatility, none of the indexes had the statistically significant lowest volatility on Thursday when it hasthelowestreturn.Moreover, statistically significant negative Tuesday volatilities were found in CSI300, SCI and SSE50, but not in SZSE.The SSE50 also had significant negative volatility on Wednesday and significant positive volatility on Friday.It seems that only the highest volatility of SSE50 on Friday could explain the risk averse theory.
Another result in Table 2 shows the two parameters of the ARCH coefficient and the GARCH coefficient were less than one in all cases;both were positive and statistically significant.In fact, the sum of the two parameters is smaller than that found in the pre sub period.The impact on the stock price remained 0.986230=0.6591 after 30trading days.This suggests that the stock market may have responded and reacted more efficiently towards the shock and news than it would have before the margin trading era.
[Table 2]
CONCLUSIONS
In conclusion, the implementation of margin trading affected the pattern of the weekday effect on returns.Before the introduction of margin trading, there was a positive Monday effect and a positive Wednesday effect in the Chinese securities market.After the implementation of margin trading, bad information could be dealt with completely through margin trading.
The market not only reacted quickly towards bad information but it also showed a higher connection with international securities.In fact, the Chinesestockmarketgraduallymanifesteda weekday effect of“negative Thursday and positive Friday”that was widespread in the international securities market.
It is important that both regulators of, and investors in, the stock market focus on the weekday effect and develop corresponding regulations and trading strategies.Based on the findings in this paper, investors should pay more attention to trades on Friday but avoid trading on Thursday.Moreover, investors should pay more attention to index series trends rather than individual stocks when market risk, transaction costs and observation errors need to be taken into consideration.
APPENDICES
Table 1.The weekday effect test from modified AR-GARCH (1, 1) for pre sub period
Table 2.The weekday effect test from modified AR-GARCH (1, 1) model (posterior sub period)
Note:Standard errors are reported in parentheses and p values are reported in brackets Significance level:a=1%level, b=5%level, c=10%
Note:Standard errors are reported in parentheses and p values are reported in brackets Significance level:a=1%level, b=5%level, c=10%
摘要：过去的研究表明, 中国股市的运行效率受到政府监管与干预并存在非对称交易的现象。2010年3月31日, 中国股票市场实行了融资融券交易试点, 允许投资者进行双边交易。本文显示了中国股票市场的融资融券交易如何影响20042016年间中国股市的日历效应。本文通过修正的AR-GARCH模型进行检验, 发现收益与波动率在融资融券推出前后期间都存在显著的日历效应。在融资融券交易实施前, 中国证券市场的收益率出现了显著的“正星期一”和“正星期三”效应。然而, 在融资融券推出后, 中国证券市场显示出显著的“负星期四”效应和“正星期五”效应。数据检验结果还表明, 信息传递和市场效率在融资融券交易推出后有一定程度的提高。文章在最后针对此现象提出一些指导性决策原则。
关键词：日历效应,融资融券,修正AR-GARCH模型,中国证券市场,有效市场假说
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