Day of the Week Effect Anomaly and Efficiency: A Recent Study on Indian Stock Market

INTRODUCTION

We see a continuous momentarily variation in stock prices or Indices (e.g. Nifty, Sensex) of a stock market in both the directions. It is very difficult to anticipate the direction for very short period of time or its value at an instance of time. Even it is difficult to estimate for long time horizon. But with the help of extensive research on historical data we can somehow find the trend and maturity value of Index up to some extent. This tendency of stock market makes it highly volatile and risky for investment purpose. Stock Market Efficiency and market Anomaly have been two major things which have been a matter of concern for investor as well as for researcher. A better understanding of both makes safe for stakeholder to take correct decision and parking of capital in more efficient manner. The term ―Efficient Market Hypothesis (EMH)‖ has been widely used in stock market and extensive researches have been carried out in both developed and emerging market. In contrary of this, stock market anomaly has also been observed in different forms.

A market theory proposed by Eugene Fama in 1960. His theory states that it is impossible to beat the stock market because at any point of time security prices reflect all available information in the market. Stocks are traded at their fair value. It is impossible to to trade in under or overvalued securities. Investor can earn abnormal return only by way of speculation through investment in riskier securities. There are three type of EMH which are as follows: The weak form of EMH assumes that current stock price fully reflect all security related information. Historical price data has no bearing on the future movement of stock price and hence therefore it is impossible to earn excess return with the help of technical analysis. The semi-strong form of EMH assumes that current stock prices adjust rapidly to the release of all new public information. Security price incorporates both public and private available market information. Excess returns cannot be achieved using fundamental analysis. The strong form of EMH assumes that current stock prices fully reflect all public and private information. Public, private and inside market related information, all are reflected in the stock price and no one has significant access to relevant market information. Thus in a perfect market it is impossible to earn excess return consistently over a period of time. Thus we can see that there is little possibility to earn excess return in inefficient market but not in efficient one on the basis of available information. One can beat the market even in efficient market only on the basis of his skill or by chance. Now if we talk about the stock market anomaly, so it can be defined as distortion in the pattern of price regulatory action, behavioral biasness by traders and agents or calendar effect such as January effect or day of the week effect. Several researches have been carried out on different market anomalies in which Calendar anomaly has been studied for past two decades. ―The day of the week effect‖ has been studied extensively in developed and emerging market. The day of the week effect refers that average return on an Index on a particular day of the week shows a particular pattern. Studies have shown that distribution of stock returns varies according to the day of the week (Cross 1973, French 1980; kin and Stambaugh 1984; Rogalski 1984; Aggarwal and Riyoli 1989) The focus of our research is to test the Weak form of Market Efficiency of Indian stock market and study on ―The day of the week effect‖.

The day of the week effect has been extensively investigated in different stock markets. Several studies showed that the distributions of stock returns differ with days of the week (Cross 1973; Lakonishok and Levi 1982; Keim and Stambaugh 1984; Rogalski 1984; Harris 1986). They documented that The last trading day i.e. Friday is characterized by substantial positive returns. Most of the studies carried out in USA stock market. Similar Day-of-the-week effect also found in Canadian stock market (Jaffe and Westerfield 1985; Dubois and Louvet 1996; kiymaz and Berument 2003). In other developed stock markets like France, Germany and UK Austria and Netherland. It is found that average negative return on Monday and average positive return on Friday (Condoyanmi et al 1987; Jaffe, Jeffrey F, Westerfield and Ma 1989; Kiymaz and Berument 2003). In Contrary to US and Canadian stock market, lowest mean return is found on Tuesday in Japanese and Australian stock market (Dubios and Louvet 1996;) Italy stock market showed the same anamoly with lowest mean return on Friday (Barone 1990). The Day-of –the-week effect also shown in other international stock market ( Solnik and Bousquet 1990; Barone 1990;Balaban 1995 and Agarwal and Tandon 1994). In Taiwan stock market, the mean negative return found Tuesday and Wednesday for two different periods (Choudhary 2000, Brooks and Persand 2001). South korea market showed no strong evidence of seasonal anomaly. In china, positive mean return found on Thursday and Friday (Mookerjee and Yu 1999). India showed positive return on Friday (Choudhary 2000). Similar result found in most of the Asian markets like Thailand, Indonesia, Malaysia etc. (Choudhary 2000; Kamnath 2002; Lian and Chen 2004). (2010) has done detailed empirical study on European Stock Market. He took UK, Germany, France, Spain, Greece and Portugal for his study for the period of 1993 to 2007. His finding revealed that only Germany and Spain stock market are weak form of efficient market and rest of the markets are inefficient market. For the period of 1995 to 2000, three most developed countries- Czech, Hungary and Poland showed weak form of efficient market (Gilmore and McManus; 2003). Two major Chinese stock markets Shanghai and Shenzhen were tested for the period of 1992-2005 and result showed that both the markets are not the weak form of efficient (Chung; 2006). Dhaka Stock market showed the weak form of market efficiency (Mollik and Bepari; 2009). Gupta and P. Basu (2007) did his empirical research on both of the Indian Stock Markets NSE and BSE for the period of 1991 to 2006 and revealed that both of the markets do not show the weak form of market efficiency.

To proceed with this research, daily closing value of CNX Nifty from year April 2009 to Mar 2018 is made available from the official website: www.nseindia.com. Further this data is segregated day wise i.e.; Monday to Friday. To find the daily return on Nifty, following formula is used: Where Rt is the daily percentage return on CNX Nifty on day t, It and It-1 are closing values of the stock index on days t and t-1 respectively. So in this way, we have returns on CNX Nifty for each Monday, Tuesday, Wednesday, Thursday and Friday from April 2009 to Mar 2018 separately. To proceed further, first we check that how data would be treated either through Parametric or Non parametric test. Once, it is confirmed then we use different tools under that test to achieve our objective.

To check the applicability of either Parametric or Non parametric test, we first check the validity of its assumptions. For parametric test, two most important assumptions are: (i) Data should be normality distributed and (ii) equal variances of populations from which samples are drawn.

normality distributed. H1: The distribution of returns for each day is not normality distributed. Now we find the Kolmogorov-Smirnov statistic at 95% confidence level whose result as follows: As we are seeing that P value is almost ZERO for each day, so our null hypothesis is rejected and hence the returns for each day are not normally distributed. As data do not follows the first assumption of parametric test so there is no need to go for validity check of other assumptions and we can conclude that data would be processed under non parametric test.

To take an overview of data, we find the different descriptive statistics as per the given table. Here we can see range of returns is highest for Monday with lowest positive return and highest variance. While the mean return on Thursday is lowest and negative with lowest variance. But this information is not sufficient for making any conclusion. We proceed with further analysis

To check correlation among the returns on each day, we find the Spearman‘s correlation coefficients which tell us that how return on a day is affected by the return on other day. As from the table we can see that correlation coefficient between Monday- lowest between Monday-Friday (-ve sign) with very high significance.

As in Parametric test there is no direct way to check the equality of variances of more than two populations. So in that situation we use the Non parametric Leven‘s test. Our hypothesis is as follows: Ho: Variances of returns of each day are equal H1: Variances of returns of each day are not equal The table shows the result as follows. Here we can see the F statistics for equality of variances among each day‘s return is significant with value of 0.548(P>0.05). Our null hypothesis would be accepted and we can conclude that variances of returns of each day are equal.

As we have more than two related variables (return on each day), we would use Friedman‘s test in alternative of repeated measures ANOVA in parametric test. Our hypothesis would be as follows: Ho: There is no significant difference among returns of each day H1: There is significant difference among the returns of each day As per the result shown in given table we can see that the Chi-Square statistics is 0.539 with returns on each day.

For investigating the randomness in shares price movement Wald-Wolfowitz Runs Test is used. For a given sequence of observations, run test examines the dependence of consecutive observations and tells whether one observation influences the values taken by later observations. The total number of runs with a level of significance shows whether the observations are random or not. Here our hypothesis would be as follows: Ho: Returns of a particular day is random. H1: Returns for a particular day is not random The result of Run test is shown in the given table. Here we can see that there are sufficient number of runs for each of the day with sufficient level of significance (p>0.05). Hence we accept the null hypothesis and conclude that returns for a particular day is random i.e. returns on either Monday or Thursday is independent from other returns on the same day. Here the cut point is taken as median because for non parametric test, median is best estimate for central tendency.

This test is widely used for testing the weak form of Efficient Market Hypothesis (EMH) in stock market. The Serial Correlation Coefficient measures the relationship between the values of a random variable independence of random variable in time series data. Our hypothesis would be as follows: Ho: There is no first order correlation present in series i.e. weak form of EMH exists. H1: There is first order correlation exist in series i.e. weak form of EMH does not exist. Here data are not segregated day wise. It is taken as it is available in continuity with time. Now from figure we can see that auto correlation coefficients exist in the 1st lag, 2nd lag and 6th lag which suggest the serial dependence among returns. Therefore we reject the Null Hypothesis and conclude that weak form of EMH does exist in Indian stock market.

After testing the data set of daily return on CNX Nifty with several statistical tools, we can say that the average return or pattern of distribution of returns over all five week days are same as well as their variances of returns for all days are same. As far as correlation of returns among any two days is concerned, we get no strong evidence. So day of the week effect is not observed in Indian stock market. Analyses also suggest that Indian stock market is not even weakly efficient which requires several corrective measures by regulatory body and government to make it strongly efficient. Although Week of the Day Effect not observed but several other anomaly may exist which may cause the Indian stock market inefficient in even weak form.

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Assistant Professor, St. Xavier‘s College of Management & Technology, Patna