Calendar Anomalies in Stock Markets: Day of the Week Effect

Neetu Chadha*

Assistant Professor, Delhi Institute of Advanced Studies, Rohini, Delhi

ABSTRACT:

Till the late seventies, empirical studies bolstered the view that capital market are informational efficient. Academician and researcher on the concept of informational efficiency of capital markets developed various theoretical security valuation models. However the late seventies and eighties produced the evidences questioning the validity of this theory and illuminated the various anomalies related to the capital market efficiency. These studies demonstrated the possible trading strategies, seasonal anomalies and persistence of technical analysis yielding abnormal returns using the historical data and publicly available information.

Many empirical tests were made in the seventies and eighties to demonstrate the efficiency of stock market. In the nineties and twenties, by contrast much has been written with the aim of demonstrating their inefficiency by identifying systematic variations in stock prices related to the calendar of the year. These systematic variations were named as calendar anomalies. These anomalies occur when there is a meaningful temporal change. This paper is an attempt to analyse and test the calendar anomalies with respect to the Day of the week effect. This study undertook an empirical analysis of the pattern of daily equity returns and the day-of-the-week effect in the Indian stock markets. In the case of the National Stock Exchange over the period, the test of weekend effect shows that returns are negative on Monday and positive on Thursday. So no general comment can be made regarding the presence of day-of-the-week effect in the Indian stock market.

INTRODUCTION:

Calendar anomalies are the systematic variations. These anomalies occur when there is a meaningful temporal change. This may occur yearly, weekly or daily and such phenomenon are well known because they can be easily identified. Some writers consider the result of these studies to be fruit of data mining, while others consider them to be reliable and seek to find rational explanation for the behavior of investors. A further question is regarding the transaction cost. In the event that one could exploit a market anomaly for a profit, the relative transaction costs would erode the profit margin.

Transaction costs can flatten net returns and thus, make it difficult to measure the volatility produced by calendar anomalies. There is large number of growing literature documenting calendar anomalies. These calendar anomalies are the collection of studies which find that on certain trading days, months or times of the year, the market exhibit above average price change. A partial list includes month of the year effect, holiday effect, turn of the year effect etc. The follower of all these anomalies believes that in above mentioned cases there is non–randomness in stock price behavior which shows possibility of extra returns.

Studies on the Indian stock market’s calendar anomalies, especially in the  bull phase of market due to growing economy, wider participation foreign institutional investors and retail investors, are very few. In an attempt to fill this gap, this paper explores the Indian stock market’s informational efficiency in its weak form in the context of calendar anomalies especially in respect of the day of week effect.

DAY OF THE WEEK EFFECT:

Day of the week effect is a phenomenon that constitutes a forum of anomaly of the efficient capital market theory. According to this phenomenon the average daily return of the market is not same for all days of the week, as we would expect on the basis of efficient market theory. The day of the week effect refers to the existence of a pattern on the part of stock returns, whereby these returns are linked to the particular day of the week. Such relation has verified mainly in the U.S.A. The last trading days of the week, particularly Friday are characterized by the positive and subsequently positive returns, while Monday, the first trading day of the week differs from other days, even producing negative returns. The presence of such an effect would mean that equity returns are not independent of the day of the week, evidence against random walk theory. The most satisfactory explanation that has been given for the negative returns on Monday is that usually the unfavorable news appears during the weekends. These unfavorable news influence the majority of investors negatively, causing them to sell on the following Monday. The day of the week effect in Indian market was examined by many researchers like Chaudhary (1991), Poshakwala (1996), Goswami and Anshuman (2000), Chaudhary (2000), Bhattacharya, Sarkar and Mukhopadhaya (2003). In a fascinating study, French examines the returns generated by the SandP 500 index for each day of the week over the time period 1953-1977. Ignoring holidays, the returns for Monday represent a three- calendar- day investment, from the close of trading Friday to the close of trading Monday. Returns for the other days of the week represent a one day period of investment. If expected return is a linear function of the period of investment, measured in calendar time, the mean return for Monday should be three times the mean return for the other days of the week. However, if the process generating returns operates in terms of trading days, the return for all five days of the week should be the same. Regardless of how returns are generated, one would not expect the returns for Monday to be less than the other four days of the week. As it turns out, the returns for Monday have not only been less than those for the other four days of the week, but Monday returns have actually been negative. Since the returns are being compared for the same portfolio at different times of the week, the proper specification of the equilibrium model (single or two factor model etc.) for determining normal returns is not an important issue. As French notes,” It is difficult to imagine any reasonable model of equilibrium consistent with both market efficiency and negative expected returns to a portfolio as large as the standard and Poor’s composite.”

One might be tempted to devise a trading strategy based on the weekend effect, of purchasing the SandP 500 at the close on Monday, sell at the close on Friday, and hold cash over the weekend. Ignoring transaction costs, the trading rule would have generated an average return of 13.4% from 1953 to1977, while a simple buy and hold would have yielded a 5.5% annual return. However, if transaction costs of only 0.25% per transaction were included, the buy- and –hold strategy would have provided a higher return. Nevertheless, knowledge of the weekend effect still is of value. Purchases planned for Thursday or Friday might be delayed until Monday, while sales planned for Monday might be delayed until the end of the week. Thus, the weekend effect provides an interesting counter example to the efficient market hypothesis.

Aggarwal and Tandon (1994) and Mills and Coutts (1995) have done excellent surveys of papers investigating the effects of day-of-the-week and the weekend on stock returns. Among the many studies that have been done are Lakonishok and Levi (1982), Keim and Stambaugh (1984), Jaffe and Westerfield (1985), Rogalski (1984), and Smirlock and Starks (1986). Similarly, Godfrey, Granger and Moregenster (1964), Fama (1965), and Gibbons and Hess (1981) have shown that return variance is higher on Mondays in the US. In other words, these studies claim that the day-of-the week has an effect on the conditional variance of stock returns also. French and Roll (1986) and Foster and Viswanathan (1990) claim that stock return variance should be the highest on Mondays when the informed trader has maximum information advantage. Variance should decline through the week with the arrival of public information and the decrease in the advantage of the private information leads to lower returns variance on Fridays. In the Indian context, few studies done have seen only the day-of-the-week effect in returns. Chaudhury (1991) studied the Bombay Stock Exchange Sensitive Index between June 1988 and January 1990. He found that the average return on Monday is negative and the highest returns are on Friday. Poshakwale (1996), in his study on the Bombay Stock Exchange National Index between January 1987 and October 1994, found that mean returns except for Monday and Wednesday are positive and that weekend effect on returns support the presence of first order auto-correlation. Broca (1992) has used Kruskall-Wallis test on BSE National Index daily returns during the period April 1984 - December 1989 to show that there is evidence of significant variations in stock returns according to the day-of-the-week. Arumugam (1998-99) has comprehensively investigated the ‘day-of-the-week effect’ in Sensex returns during 1979- 1997 and found that Monday returns are significantly positive during a bull market, significantly negative during a bear market, and insignificant otherwise

OBJECTIVES OF THE STUDY:

1.     To study whether stock market is really efficient in its weak form or not.

2.     To study and test the presence of day of the week effect in Indian stock market.

DATA:

The data were obtained from the NSE website for the period of 01.04.2012 to. 31.03.2016. NSE operates many indices to gauge the activities in its stock market. Of these CNX SandP NIFTY Index is used as a proxy for the market portfolio. SandP CNX Nifty is a representative of the Indian stock market, which comprises 50 most liquid individual stocks at the national stock exchange. It is also considered to be an indicator of the performance of the whole economy. Hence, it is more appropriate to conduct a stock market related study in India by using the data for SandP CNX Nifty.  Accordingly study utilizes daily closing of S$P CNX Nifty index.

HYPOTHESIS:

In most of the stock exchanges around the world, trading takes place Monday to Friday. If the return generating process for the stocks operates continuously then, the returns on Monday shall be three times the returns on each of the other days of the week. This is known as the Calendar-time hypothesis. Many researchers have rejected the calendar time hypothesis and proposed an alternative trading-time hypothesis. Trading-time hypothesis postulates that the return generating process is active only during the trading hours and average returns are same for all five trading days of the week.

More formally, our null hypothesis is

H₀: m₁ = m₂ = m₃ = m₄ = 0 against

H₁: At least one of m_j j_e {1,2,3,4} is different from 0.

Our hypothesis is a two-tailed hypothesis and we test this hypothesis at 5 percent significance level.

METHODOLOGY:

The trading time model is used in this paper to test the day-of-the-week effect on the National Stock Exchange. The model postulates that the rate of return for each day is equal. Specifically, the model can be mathematically written as:

R_t = c + m₁X₁ +m₂X₂ + m₃X₃ +m₄X₄ + e_t (1)

Where, t = the time period (t = 1,...,n)

R_t = the return for day t

X₁, X₂, X₃, X₄ = dummy variables and are 1 for trading days Tuesday through Friday,

e_t ~ N (0, )

The intercept term, c, is the return for Monday: the day-of-the-week coefficients, m₁ to m₄, are the difference between the expected return for Monday and the expected return for each of the other trading days. If the expected return is the same for each day of the week in the overall period of this study, the model suggests that the estimated day-of the-week coefficients, m₁ through m₄, will be close to zero, and the t-statistic for individual coefficients should not be significant.

ANALYSIS:

Table: Trading Time Hypothesis Regression Results for Nifty Returns

Regression Results for Nifty Returns on Monday

Regression results for Nifty returns on Tuesday

0.00083

Regression results for Nifty returns on Wednesday

-0.00083

Regression results for Nifty returns on Thursday

-0.00458

Regression results for Nifty returns on Friday

EMPIRICAL RESULTS:

Table 1 reports the estimated parameters of the trading time regression model and the associated statistics. The parametric t-test indicates that the average return of Nifty on Tuesday is negative and average return on Thursday is positive. The returns on other trading days can not be separated from zero. The results are consistent with the observations from the other markets, which show that, in general, daily returns are negative on first two days of the week and are positive on latter 3 days of the week. In the regression analysis, the intercept term ‘c’ is significantly negative implying that the Monday returns are on average negative. Also, the Thursday return premium over Monday return is significantly positive. Thus we reject the trading-time hypothesis that the returns are equal on all days of the week. Since the results of the test for trading-time hypothesis indicate that the returns on Monday are negative and the return on Thursday is positive, the trading-time hypothesis is rejected. A slight modification can be incorporated in the regression model to test whether the returns on any of the other weekdays are different from zero. The regression equation retains its form but the variables need to be redefined for this purpose. For example, if we want to test whether the returns on Friday are significantly different from zero then we should define the intercept ‘c’ as the returns on Friday, and the dummy variables X₁ through X₄ should be defined as 1 for Monday through Thursday respectively. The coefficients m₁ through m₄ are return premiums over Friday return for Monday through Thursday. The results of the regression analysis using the modified equations validate the findings from the parametric t-test. The results have been presented in Tables 2, 3, 4 and 5 for Tuesday, Wednesday, Thursday and Friday respectively. The parametric t-test indicates presence of significantly positive returns on Thursday and zero return on the other days of the week. The (modified) regression equation however indicates that returns on all days are insignificant. The regression output shows presence of a negative Friday premium over the Monday returns. The trading-time hypothesis that the returns are equal on all days of the week is thus rejected. These observations are inconsistent with the observation from the other markets, which show that, in general, daily returns are negative on first two days of the week and are positive on the latter 3 days of the week. In the case of the National Stock Exchange over the period, the test of weekend effect shows that returns are negative on Monday and positive on Thursday.

CONCLUSION:

Null hypothesis i.e. there exists no difference in the returns between the days of the week is clearly rejected as m₁ ≠ m₂ ≠ m₃ ≠ m₄. From the tables and analysis it is clear that returns on Monday are negative and on Thursday it is positive. Hence the Indian stock market cannot be treated as fully efficient till now.

This study undertook an empirical analysis of the pattern of daily equity returns and the day-of-the-week effect in the Indian stock markets. No general comment can be made regarding the presence of day-of-the-week effect in the Indian stock market. In the case of the National Stock Exchange, the test of weekend effect shows that returns are negative on Monday and positive on Thursday. Monday is generally the most volatile day of the week. The most obvious possible reason for the weekend effect is that news that de-presses stock prices tends to come at the weekend and on the other days when the stock exchange is closed. However, if this were so, an efficient market would discount the prices of securities appropriately during the week an anomalously high rate of change in stock prices on Friday, before the weekend closure.

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Accepted on 28.12.2016          © A&V Publications all right reserved