Literature review
Literature Review On Day Of The Week Effects
Efficient Market Hypothesis (EMH) claims that financial markets are “informationally efficient” Fama (1970). In other words, financial markets reflect all known information and according to stock prices rapidly adjust to any new information (Reilly and Brown, 1997), so the current price already reflects all known information about the stock. Therefore, according to this theory, it would be impossible to earn excess returns and beat the market on a regular basis unless it is through luck.
The EMH was initially expressed by Bachelier (1900) in the form of random walks (Bachelier, 1900 cited in Fama, 1965). The random walk theory is explained by prices that are unpredictable and that future stock prices cannot be forecasted using prior information (Lo &Mackinlay, 1988). Bachelier (1900) concluded that commodity speculation was a “fair game”. This meant that investors could not make abnormal profits as the existing price of a share was a fair estimate of its future price. However this theory was ignored until Samuelson (1965) developed the theoretical framework for the random walk. This theory created by Samuelson (1965), combined with empirical findings from other researchers including Fama (1965) formed the foundation to the development of the EMH. The theory of EMH was finally proposed by Fama (1970).
Fama (1970) states that three different levels of market efficiency exist when based on what is meant as available information. These include the weak-form, which asserts that security prices reflect all historical information, meaning that abnormal profits cannot be gained by using trading strategies based on past information. In other words if the market is set to be weak-form efficient, then it follows a random walk. The second level of efficiency is called semi-strong-form, which asserts that security prices reflect all publicly available information. Therefore prices will immediately adjust for all public announcements. And finally the third level is known as strong-form and states that all information including private and public is reflected in the stock prices. All three forms of efficiency are transparent, meaning that if a stock market is strong-form efficient, it would also mean it is efficient in the weak-form.
However in recent years the EMH has come under scrutiny and many market analysts have argued for market inefficiency, at least in its weak-form (Malkiel, 2003). Since the EMH is based on the assumption that investors are rational, researchers have found that some investors sometimes take irrational approaches to decision making opposed to the conventional rational or logical thinking. In recent years, Behavioural Finance has emerged as one of the key explanations into why and how markets may be inefficient.
Some of the explanations that behavioural finance proposes include feedback mechanisms which describe why short-run serial correlation was not zero found by Lo &Mackinlay (1999). Long-run return reversals has also been established as an explanation as to why markets may not be efficient as DeBondt&Thaler (1985) found that investors were subject to waves of optimism and pessimism which causes stock prices to deviate from their fundamental true value and later to experience a concept known as mean reversion. The concept of mean reversion is a contradiction to the EMH as it follows a trend. This is also consistent with the behavioural decision theory proposed by Kahneman&Tversky (1979) in which they claimed that investors may be overconfident in their ability to forecast future stock prices. The day of the week effect as proposed earlier has been identified as one of the key violations to the EMH and is discussed further in section 2.2.
2.2 – Review of Literature on Day of the Week Effects
The phenomenon of day of the week effects has been extensively researched over the last few decades. By definition, an anomaly is an incident that cannot be explained by a prevailing theory (Al-Loughani, Al-Saad and Ali, 2005). In the case of stock markets, anomalies are occurrences that dispute the Efficient Market Hypothesis (Brooks and Persand, 2001:155).
Existence of anomalies in stock markets can be attributed to several factors, such as variations in seasons or the weather, or changes in liquidity preferences before vacations or holidays.Another possible explanation isthe so called measurement error. There are many times that measurementerror is considered to be the cause of day of the week effectphenomenon, mostly because this phenomenon appears to be stronger forcompanies with low capitalization. The stock returns tend to underperform in the summer compared to winter months, and to do better on sunny compared to rainy days. Investors sell their securities towards holidays or vacations for liquidity reasons (see Bouman and Jacobsen, 2002; Cao & Wei, 2004; Kamstra, Kramer and Levi, 2003). Anomalies can also be attributed to tax-loss selling late in the financial year (Grinblatt and Markowitz, 2003).
The most famous anomalies include, among others, the January effect, first identified by Rozeff and Kinney (1976) using data from the New York Stock Exchange (see also subsequent studies by Bhardwaj and Brooks, 1992; Bhabra, Dhillon and Ramirez 1999; Maxwell, 1998); the Weekend effect, also known as the day-of-the-week effect, the Monday effect or the Monday seasonal; the Holiday effect; the turn-of-the-month effect; the Small firm effect; the Weather effect; and the Price/earnings ratio effect.
The existence of these anomalies in stock markets may indicate the presence of profitable trading strategies and, most importantly, the inefficiency of the stock markets in quickly incorporating information (whether public or private information) into the price of stocks if trading costs are ignored.
One anomaly that has often been studied extensively in several developed stock markets is the Weekend or day-of-the-week effect (Basher and Sadorsky, 2006:2). This refers to the tendency for stocks to exhibit relatively large returns on Fridays compared to those on Mondays. Some empirical investigations have reported compelling evidence that there are day-of-the-week (Weekend) effects in US stock returns. Mean returns on Mondays have been reported to be negative (Smirlock and Starks, 1986) compared to Fridays. A weekend effect in the mean return distribution of several stock markets was also identified (Jaffe and Westerfield, 1985).
The aim of this study is to ascertain whether the day-of-the-week effect is present in the UCITS Hedge Fund Index for the period beginning January 2011 and ending late July 2016.
The rest of the paper is organised as follows: Section 2 describes the data and methodology to be used in this study. The results of the empirical work are presented and discussed in Section 3. Section 4 concludes this study and gives suggestions for further research).
2.3 – Evidence from Developed Markets
The day-of-the-week effect was first observed and documented by M.F.M. Osbomc,
the physicist who applied the concept of Brownian motion to the stock market in 1959
(Osbome, 1959). Since Osbome’s discovery in 1959, Cross (1973), French (1980),
Gibbons and Hess (1981), Lakonishok and Levi (1982), Keim and Stambaugh (1984),
andRogalski (1984) amongst others have confirmed that there are differences in the
distributions of stock returns in each of the week days. The results of these studies
indicate that the average return on Mondays is considerably less than the average return
during the other week days.
Although these studies have been performed on the equity markets in the US., the dayof-
the-week effect has been investigated for both international equity markets and
intcmational non-equity financial markets. Jaffe and Westerfield (1985a, 1985b) found
significant negative mean returns on Mondays in the US., Canada and the UK stock
markets, and significant negative Tuesday returns in the Japanese and Australian stock
markets. Agganval and Rivoli (1989) studied the emerging markets of East Asia and
observed lower mean returns on Mondays and Tuesdays in thc stock returns of Hong
Kong, Singapore, Malaysia and the Philippines, from September 1976 to June 1988.
Kato and Schallheim (1985), Chang, Pinegar and Ravichandran (1993), Athanassakos
and Robinson (1994), and Dubois (1986) showed that the distributions of stock returns
also vary by the week days internationally. The day-of-the-week effect is also detected
in the commodity and stock futures markets (Cornell, 1985; Dy1 and Maberly, 1986;
Gay &Kim, 1987), the Treasury bill market (Flannery &Protopapadakis, 1988), and in
the foreign exchange market (Corhay, Fatemi, & Rad, 1995).
While the focus of the above studies has been the seasonal pattern in mean returns,
there are several other empirical studies investigating the time-series behaviour of stock
prices in terms of volatility by using variations of the GARCH models (French et al.
(1987), Akgiray (1989), Baillie and DeGennaro (1990), Hamaoet al. (1990), Nelson
(1991); Campbell and Hentsche1(1992), and Ogum, Nouyrigat and Beer (2002)). These
studies report that the expected returns in stock markets are time-varying and
conditionallyheteroskedastic.
Studies researching the day-of-the-week effect have been performed with good reason.
The existence of predictable seasonal behaviour in stock returns may lead to profitable
trading strategies, and in tum, abnormal returns. If a day-of-the-week effect is present
within a particular market, investors will be in the position to take advantage of
relatively regular shifts in the market by designing trading strategies, which account for
such predictable patterns.
Even though these trading strategies may not be able to generate desired profits,
(because of factors such as transaction costs) they may still provide insights for
investors. Since the rational financial decision-maker contemplates both the retums and
the timing of the investment, the knowledge of a day-of-the-week effect in mean
retums will be most helpful in ensuring healthy profits.
Further, should investors be aware of a day-of-the-week effect in volatility patterns,
they will be in the position to avoid making key investmcnts on days with high
volatility. Since hedge fund managers are responsible for managing their fund’s
portfolios according to a specific mandate, day-of-the-week patterns are of critical
importance to their managers. Simply, if investors can thus identify a certain pattern in
volatility, more profitable investment decisions could be made based on both rcturn and
risk factors. Ultimately, this would give investors another tool to design profitable
strategies.
Fama (1965) examined the behaviour of stock prices and discovered that there was evidence of abnormality in stock returns. This brought forward the theory of stock prices being influenced by non-trading days. Therefore, Fama (1965) established that anticipation of economical events that occur during non-trading days have a continuous effect on stock prices. He tested the hypothesis that Monday’s variance is three times greater than the other trading days in the week because of the accumulation of variances over the non-trading days. He found that the variance was approximately 20% higher than the other trading days which fell short of his hypothesis. As this was an opening study into this field, there was bound to be limitations and short-comings which may have compromised the accuracy of his results. As the day of the week effect was a secondary focus in his paper only a small sample of stocks were used. In addition, he considered only variances to determine the effect which only describes the spread of the returns, however had he used mean returns in addition, it would have explained the day of the week better as one can confirm by how much the return differs between each day of the week. Nevertheless, this was an introductory study and if it wasn’t for this paper, the issue of day of the week effects may not have been picked up as early as it was.
French (1980) extended Fama’s (1965) contribution in which he examined whether the process of generating stock returns operates continuously or during active trading days only. This was done on S&P 500 stock returns with the following two methods. The Calendar-time hypothesis [1] and the Trading- time hypothesis [2] , in which the returns are only generated during the active trading days of the week. Therefore if the alternative hypothesis was rejected, the returns for each day of the week should be identical since any of the returns represent only one trading day.
French (1980) found that during 1953-1977, the daily returns from the S&P 500 portfolio were inconsistent with both the Trading day model and the Calendar time model. The average returns on the Mondays were negative compared to the other four positive trading day returns. This was an unusual finding which led others to examine this anomaly further.
Gibbons & Hess (1981) investigated further into French’s (1980) research as they examined the S&P 500 index and the equal weighted index from 1962-1978 for the day of the week affect on asset returns. They considered the delay between trading and settlements in stocks and measurement errors as possible explanations for the day of the week effect. They found a similar result to French (1980) however Mondays were not the only day found to give significantly low mean returns. Tuesday appeared to also have low returns, and Wednesday and Friday had higher mean returns than Tuesday and Thursday. In the overall analysis, the annual mean return on a Monday ranged from -33.5% (S&P 500) to 26.8% (equally-weighted index). The hypothesis of the equality of means was rejected in each of the sub-periods run. The inclusion of the sub-periods was very valuable as it gave a different perspective of the market at different time periods.
Following on from Gibbons & Hess (1981), Rogalski (1984) developed his understanding of Monday returns further as he set out to examine the Dow Jones Industrial Average index (DJIA) in terms of trading day and non-trading day returns. This study was different from the previous papers as it distinguished between trading and non-trading day returns, in which the examination from Friday close to Monday close was decomposed into two parts. First one being from Friday close to Monday open; second one was from Monday open to Monday close. He found that all of the average negative returns from Friday close to Monday close occur during non-trading hours and that the actual returns during Monday trading hours are positive.
Keim and Stambaugh (1984) extend the study of the day-of-the-week effect by
extending the total research period to 55 years. They also examine additional stocks,
such as those of small firms (low capitalisation) and those traded OTC. Keim and
Stambaugh (1984) make use of S & P Composite index returns and reassert the fact
that the data exhibits a weekend effect.They continue, by hypothesising that the higher-than-average stochastic disturbance
(error) terms of their model on Fridays, tend to produce lower-than-average returns on
Mondays. This behaviour implies a lower correlation between a Friday’s return and
Monday’s return, than between returns on other successive days. They once again
prove a Monday effect in the U.S. market.
Smirlock& Starks (1986) proposed a further analysis into the nature and timing of the day of the week effect on the Dow Jones Industrial Average. The use of hourly returns for a 21 year period was justified as a more efficient and thorough manner as the likes of Rogalski (1984) and others had used disparate time periods. For the empirical analysis, the total sample period was divided into three sub-periods. The first sub-period was from 1963-1968, second was from 1968-1974, and the most recent sub-period was from 1974-1983. In the pre 1974 periods, results showed that the hourly returns on Monday were significantly lower than the other trading days in the week. However, in the post 1974 period, there was nothing odd about Monday returns compared to the other trading days. To break this down further, the first sub-period showed that returns from Friday close to Monday open were positive. These returns were eliminated by the negative returns that occurred all day during Monday, resulting in a negative return for the entire day. In the second sub-period, the non-trading weekend returns were vaguely negative. This affected the opening hours of Monday in a negative manner and although the Monday returns did recover with the rest of the day showing positive returns, the returns for the entire day were significant and negative. For the most recent sub-period, the non-trading weekend returns were significantly negative, however, after noon the Monday hourly returns were positive, yielding no weekend effect in trading time, thus, concluding that the weekend effect was ‘moving up in time’. The results from this latter period are consistent with that of Rogalski (1984).
As many researchers had focused primarily on the U.S. stock market for these anomalies, Jaffe &Westerfield (1985) decided to expand this research area and found evidence of this phenomenon in four other developed economies. They demonstrated that this irregularity wasn’t just an element of the U.S. stock market.
Jaffe &Westerfield (1985) found that along with the US, Canada, UK, Japan and Australia had shown evidence of day of the week effects. US, Canada and UK exhibited the lowest mean returns on a Monday which is consistent with the literature so far. Contrary to the negative Monday returns, the lowest returns for Japan and Australia were found on Tuesday. This was an unexpected twist in their study which led them to investigate further into this matter. They also confirmed that measurement errors and settlement periods were not the cause of the day of the week effect. They tested whether the anomalies found in the other four economies was a result of the seasonality found in the US stock market. Results showed that there may have been some evidence of a one day time lag between the US and Australia. The time zone theory or the spill-over effect may have explained some of the seasonality in the Australian stock market.
More International evidence was documented by Condoyanni et al. (1987) as they found results which concur with Jaffe &Westerfield’s (1985). Condoyanni et al. (1987) tested for day of the week effects in six National stock exchanges which include Australia, Canada, France, Japan, Singapore& U.K during the periods 1969-1984. Canada and U.K was found to exhibit the conventional negative Monday returns, whereas, negative Tuesdays were found for Australia, France, Japan & Singapore. They discovered that not all markets in the same continent behave identically as France and U.K had contrasting day of the week effects.
A study by Mehdian& Perry (2001) claimed that day of the week effects in the U.S. have been reducing over time. They studied three major stock indices during the period 1964-1998 and although they found negative Monday returns for the the entire period; when analysing sub periods, they found that the negative sign for Monday had switched to a positive one from 1987 onwards. This is consistent with findings by Smirlock& Starks (1986) as they too found that the sign for the Monday coefficient had changed as time went on.
This theory of disappearing day of the week effects was also agreed by Kohers et al. (2004) who studied whether the increase in market efficiency over the previous 22 years had caused the day of the week seasonality to decline over time. They inspected the world’s largest economies and found clear evidence of the presence of this anomaly during the 1980’s. However from 1990 onwards, they concluded that the day of the week effects were fading away as the markets had become more efficient.
Most of the literature reviewed so far has used the OLS regression to investigate the day of the week effect. However there is a major drawback to this method. The error variance are assumed to be constant through time and does not take into account the time varying volatility that stock returns have.
Berument and Kiymaz (2001) introduced a new method for testing the day of the week effect by incorporating stock market volatility. As previously stated, the OLS regression has a major limitation as it assumes a constant variance. They employed Bollerslev (1986)’s generalised version of Engle (1982)’s ARCH model, called the GARCH(1,1) [3] . They used three models to examine the S&P 500 for the day of the week effect in return and volatility equation. The three models were the OLS Regression, which assumes a constant variance through time; GARCH(1,1), which incorporates heteroscedasticity and the Modified GARCH, which permits the constant term of the conditional variance to alter for each trading day.
Results from the OLS and the GARCH(1,1) were quite similar as both found Mondays to produce the lowest return and Wednesdays to perform the highest. The result from the Modified GARCH showed that Fridays were the most volatile and Wednesdays were the least volatile.
Clearly, there has been extensive literature expressing the day of the week anomaly in the more developed economies of the world. However, the same cannot be said for the emerging economies. There has been inadequate and inconclusive evidence of the day of the week effect in different emerging markets around the globe.
Brooks &Persand (2001) found that during 1989-1996 both Thailand and Malaysia exhibited significant positive Monday returns and Negative Tuesday returns. They also found Taiwan to display negative Wednesday returns.
Yalcin and Yucel (2006) examined 20 emerging economies for the day of the week effect and found that only 3 of the countries hold for the anomaly in returns. India’s lowest return was found on Tuesdays and highest on Wednesdays between 1996-2005.
4.3.11 Conclusion
The various studies detailed investigate the day-of-the-week effect by testing seasonal
patterns in stock returns, volatility, various markets and a variety of financial
inshuments. The majority of the studies investigating the day-of-the-week effect in
stock returns employ the standard ordinary least-squares (OLS) methodology by
regressing the returns on five daily dummy variables (Chang eral., 1993; Cornell,
1985; Keim&Stambaugh, 1984, and Gibbons and Hess, 1981).
OLS regression analysis is based on several statistical assumptions. One key
assumption is that the errors are independent of each other. Using time-series data,
however, has two major drawbacks. The first is that the errors in the model may be
autocorrelated and the second is that error variances may be time-dependent as opposed
to being constant, thus implying heteroskedasticity. If the error term is autocorrelated,
the efficiency of OLS parameter estimates is adversely affected and standard error
estimates are biased.
In order to address the issue of autocorrelation, lagged values of the dependant variable
can be included in the equation (Bemment&Kiymaz, 2001:3). Such a model assumes
that returns (as dependant variable) have the following stochastic process:
whereR, represents returns; M,, Tu,, Thu,. andFri, are the dummy variables for Monday,
Tuesday, Thursday, and Friday at time t. M, = 1, if day I’ is a Monday and 0 otherwise;
Tu, = 1, if day t is a Tuesday and 0 otherwise, etc. The stochastic disturbance (error)
term is indicated by E,.
In order to address the problem of heteroskedasticity in error terms, variances of errors
are allowed to be time-dependent, so as to include a conditional heteroskedasticity that
captures time variation of variance in stock returns. Hence, error terms now have a
mean of zero and a time changing variance ofa: (E, – (0, D:)). To achieve this, the data
can be modelled with a conditional heteroskedastic model (Berument&Kiymaz,
2001:9).
The literature suggests various conditional heteroskedasticity models. As previously
mentioned. the prominent two are the ARCH and GARCH models. Engle et a[.(1987)
also introduce the ARCH-M methodology, which allows the conditional standard errors
(or variance) to affect returns. French et al. (1987) make use of a GARCH-M model to
test the relationship between stock returns and stock market volatility. In recent studies,
GARCH(1,l)-M was decided upon as an appropriate model for financial data
(Litterman, 2003:245).
Nelson (1991), however, finds various shortcomings with the general GARCH(l.l)
models (see section 4.3.9). Firstly, because GARCH models assume that only the
magnitude and not the positivity or negativity of unexpected excess returns determines
featurecr:, they rule out the possibility of a negative correlation between current rcturns
andfuture returns volatility. Secondly, GARCH models impose parameter restrictions
which are often violated by estimatrd coefficients; this may unduly restrict the
dynamics of the conditional variance pmcess. Thirdly, with GARCH models it is often
difficult to assess whether or not shocks to conditional variance persist. Ogumeia/.
(2002) make use of the EGARCH models developed by Nelson (1991) in order to
examine the autorcgressive behaviour of conditional volatility on the NSE (Kenya). By
making use of Nelson’s model, Ogum et al. (2002) manage to el~mlnate the major
shottcomings of typical GARCH models.
This dissertation, therefore takcsLhcfindings of Nelson (1991) into consideration in
deciding upon a final model in order to determine the day-of-the-week effect, In the
next section the data modelled is discussed and thc process followed in deriving the
final model is detailed.