An investigation of the day-of-the-week effect and month effect in the stock markets of the Asia-Pacific Region

Introduction

Market efficiency refers to the potential of a stock market to assimilate accessible information and reflect it in the stock prices in a short span of time. Efficient market theory presupposes that asset prices behave randomly and investors have no opportunity to earn abnormal returns. Early studies found that the Dow Jones Industrial Average Index in the US market shows signs of a weak form of efficiency. But empirically, it has been proven that the reality is not in line with the maintained theories of asset-pricing behaviour. This shows that inefficiencies may also be a characteristic of the stock market and anomalies might exist. This violates the hypothesis of the weak form of market efficiency because if the markets are efficient, then calendar anomalies such as the day-of-the-week effect should not exist. However, the existence of calendar anomalies is evident with the likelihood of stock prices showing certain patterns at specific times of the calendar.

Calendar anomalies such as the day-of-the-week, turn-of-the-year, weekend, monthly and pre-holiday effect are the oldest forms of calendar anomalies (1973). The day-of-the-week-effect anomaly has been broadly empirically studied in developed countries. Sias and Starks (1995) found that the Monday anomalies are persistent and as compared to Friday, Monday returns falls off. Golder and Macy (2011) established a positive connection between changes in the mood of the investors and returns on Mondays and Fridays. The month-of-the-year effect is an unexplored anomaly. Elango and Pandey (2008) found The January anomaly in Sensex where they observed negative significant returns in January along with March and April.

Previous researchers have used different GARCH family models to measure the volatility to understand the impact of calendar effects. Berument et al. (2010) applied EGARCH to find volatility in S&P500 (NASDAQ). Zhang et al. (2017) used GARCH (1,1) modelling to probe the day-of-the-week effects in SHC index of the Shanghai Stock Exchange.

Calendar effect anomaly occurs owing to different periods and conditions existing in a country. With the same view, our study aims to investigate the existence of the day-of-the-week and monthly effect on five stock exchanges of the Asia-Pacific region viz. India, Hong Kong, Australia, China, and Singapore for the period ranging from January 2010 to September 2023. Our study aims to find and analyze the presence of calendar anomalies in emerging markets such as India and China, and developed stock markets viz. Singapore, Hong Kong, and Australia. The existing literature lacks a comprehensive view of the existence of anomalies in prominent developed and emerging markets.

The present study focuses on testing calendar anomalies not just for return but also for market volatility by fitting the EGARCH model. Subsequent sections of the study are as follows: the second section delineates the methodology and data analysis. The third section spells the findings, while the fourth section comprehends conclusion.

Methodology and Data Analysis

Our study focuses on finding calendar anomaly in stock market returns and stock volatility in five Asia-Pacific region stock exchanges viz, NIFTY, National Stock Exchange (NSE) from India, Hang Seng Index (HSI) from Hong Kong, S&P ASX200 Australian Stock Exchange (S&P) from Australia, Shanghai Stock Exchange Composite Index 000001 (SSEC) from China and Straits Time Index (STI) from Singapore. The present study is based on the data from January 2010 to September 2023 which was extracted from Thompson Reuters.

Day of the Week Effect

For the calculation of daily return, the formula R_dT = ln (I_t / I_t-1) was applied; where, ln denotes the natural logarithm, I_t is the closing index value at day, and ‘t’ I_t-1 is the closing index value at day before ‘t’.

The presence of the day-of-the-week effect was analysed through the following regression equation:

Where R_dT is the index return of the day, D_Tu to D_F represents the dummy variable from Tuesday to Friday, and e_T is the error term. This equation will help us to analyse if there exists significant market returns for any day of the week.

Also, to explore the day-of-the-week effect on the index volatility, the study models volatility using EGARCH (1,1). Literature supports that incorporating the asymmetric volatility through EGARCH yields more adequate results. To overcome the problem of symmetry assumption, the EGARCH model was established to ascertain the asymmetric negative or positive effects in the model. It has been supported by numerous empirical studies that the pessimistic news of the previous day has the ability to influence present day’s volatility than the positive news. This situation refers to the leverage effect, wherein today’s level of risk for investors increases due to the bad news from yesterday. The asymmetric volatility is represented by negative and significant γ (i.e. γ < 0). Therefore, γ represents the leverage effect, and the higher the leverage effect, the higher would be the volatility clustering and vice versa. The equation of the EGARCH models is as follows:

The above equation allows ε_t to have positive and negative values and impact volatility differently. The daily return mean equation to model EGARCH (1,1) is the following:

Where α₁ is the coefficient of lag daily returns and μ is the error term. The lag term i is determined on the basis of the significant ACF and PACF terms.

The impact of index volatility on the day-of-the-week anomaly was checked by running the following regression equation:

This equation shows that today’s volatility depends on the previous day’s volatility and the day-of-the-week effect, if it exists. The EGARCH model is applicable in the presence of heteroskedasticity only. Therefore, the ARCH LM test was run on data in question to check the fitness of the model.

Day of the Month Effect

To calculate the monthly index value, an average of the last day index value of the month, the index value of the preceding and succeeding trading day has been taken. To calculate the monthly index returns, the following formula was used:

R_mT = ln(I_mt / I_mt-1) where, ln denotes the natural logarithm, I_mt denotes the index value of the month ‘t’, and I_mt-1 is the index value of the previous month.

The following regression is run to check the presence of the month effect in the monthly return series:

Where R_mT is the index return of the month, D_FEB to D_DEC represents the dummy variable from February to December, and ε_mT is the error term. Equation (5) detects the presence of significant return in applicable particular month, if applicable.

Findings

Table 1 and 2 gives an account of the descriptive statistics for the daily and monthly index returns respectively. The mean value of the daily returns of all the five markets is near zero. The value of standard deviation reveals that volatility is higher than the STI market for all other markets. The negative value of skewness confirms the presence of asymmetric distribution.

However, a high value of kurtosis shows the presence of thicker tails and a leptokurtic distribution. The high value of Jarque-Bera or JB statistics is an indication that the data of all five stock exchanges do not follow normal distribution.

The monthly index return of NIFTY, STI, and S&P ASX is near zero but HSI and SSEC are showing negative returns. The high value of standard deviation shows the presence of clustering around the mean and less dispersion. The negative skewness value indicates an absence of normal distribution. The proximity to leptokurtic distribution is connected to the high value of skewness. The JB statistics also indicate that the monthly data of all five stock exchanges shows a clear departure from normality.

The ADF test was run to confirm the non-stationarity of return series. Table 3 and Table 4 contains the results of the ADF tests of stationarity.

The prob. values of all indices given in Table 3 and Table 4 are less than 1%, indicating the rejection of the null hypothesis. Hence, it is suitable for EGARCH modelling. EGARCH (p,q) modelling is an autoregressive process where the dependent variable is dependent on its own previous values or lag term.

The next step is to check the autocorrelation among daily and monthly returns. Autoregressive processes usually have an exponentially declining ACF and spikes in the first one or more lags of the PACF. The order of autoregression depends on the number of spikes in ACF and PACF.

From the autocorrelation function (ACF) and partial autocorrelation function (PACF) of daily returns (Figures 1 to 10), the probability value becomes significant after lag 6 for NIFTY; for Hong Kong (HSI), it becomes significant at lag 23; for SSEC, it becomes significant from lag 6; for S&P ASX, it becomes significant from lag 1; and for STI, it becomes significant from lag 11. The return equation for modelling EGARCH volatility terms is set in accordance with the significant lag terms.

The findings for the day of the week effect in daily returns are presented in Table 5.

*Significant at 1% level

The day-of-the-week effect examines if there exists any significant difference between the returns generated by one specific day of the week as opposed to rest of the days.

Table 5 shows that in NIFTY, Tuesday and Friday have positive and significant returns. STI has a negative but significant return pattern on Monday, and positive and significant returns on Tuesday and Wednesday. Conversely, HSI, S&P ASX, and SSEC do not reflect the presence of defined patterns in return generation, indicating an absence of the day-of-the-week anomaly.

In the absence of heteroskedasticity, the EGARCH modelling is not advisable. Therefore, the ARCH LM test was run on all five return series before fitting the EGARCH model. The ARCH LM test assumes the absence of the arch effect. However, our results from the ARCH LM test supported the signs of heteroskedasticity in the daily return series only. Therefore, the EGARCH modelling was applied on the daily data series to capture the volatility on day-of the-week. The absence of heteroskedasticity makes it unfeasible to apply EGARCH on the monthly data series.

Table 6 shows if the daily market volatility has any significant impact on certain days of the week. The daily return findings are supported by the daily volatility results. NIFTY and STI are facing significant volatility on Tuesday’s return. For HSI and SSEC, the market volatility is going through significant impact on Monday but no significant volatility in S&P ASX on any days of the week.

Next, the study computes the month effect on the market returns. Table 7 shows the results of monthly returns and if a month of the year has any significant impact on it. The findings presented in Table 7 depict clear absence of month-effect in all the five markets. It confirms that no month is giving significant greater returns to the investors as compared to rest of the months.

Conclusion

This study is an unprecedented attempt to explore the calendar anomaly and presence of volatility in the Asia-Pacific region between the emerging and developed markets.

The study of Plastun et al. (2019) also supports that markets evolve over time and shift from being inefficient to efficient in a manner where it is not possible for investors to find holes in the price dynamics to earn abnormal gains in the short run.

The outcomes of the study assert that for an emerging country like India, the markets can move towards abnormal profits, whereas for developed markets like Australia and Hong Kong, investors using an anomaly would not be a good idea.

This study is relevant from the perspective of investment manager as it gives insight into profitable investing strategies. The policy makers get an understanding of the relevant policy decisions that can be taken to strengthen the markets further.