DAY OF THE WEEK EFFECT IN
SMALL SECURITIES MARKETS
Virgilijus Sakalauskas and Dalia Kriksciuniene
Department of Informatics, Vilnius University, Muitines 8, 44280 Kaunas, Lithuania
Keywords: Day-of-the-week effect, securities markets, return index, Kolmogorov-Smirnov test, Stock Index.
Abstract: In this article statistical investigation of the day-of-the-week effect was explored for the case of small
securities market. By applying statistical analysis of Vilnius Stock OMX Index return data, the effect was
not observed. After rearranging data to the meaningful subsets of return variable the significant difference
among Monday and Friday compared pairwise to the other days of the week, has been observed. The
hypothesis of equality of the higher moments across days of the week could be rejected by indicating that a
weekly pattern on the higher moments exists.
1 INTRODUCTION
Many research studies address the problem of stocks
profitability by using wide variety of methods. One
group of authors use methods of technical analysis
for investigating influence of historical prices
deviations (Achelis, 2000), the others concentrate to
the fundamental analysis of the stock market, aimed
to development of financial indicators, which could
reveal stock price changes (Thomsett, 2006). No
method has any significant preference over the
others, thus some price change phenomena or
anomalies of the stocks can be explained only by
integrative application of both methods groups. One
of such phenomena is the influence of day-of-the-
week for the profitability and risk of investment.
Day-of-the-week effect indicates the anomaly of
the return of stocks, which occurs during the specific
days of the week. The traditional understanding of
return is presented by expression, where return on
time moment t,
t
R
is evaluated by logarithmic
difference of stock price over time interval (t-1,t]:
)ln()ln()ln(
1
1
−
−
−==
tt
t
t
t
PP
P
P
R
,
(1)
where
t
P
indicates the price of financial
instrument at time moment t.
Day-of-the-week effect has attracted attention of
many investigators. Fama (1965) and many other
authors (Jaffe and Westerfield, 1989; Gregoriou et al
2004; Gordon and Tang, 1998) have substantiated
that mean return and variance of investment
significantly differs across days of the week. In these
works the significance of „ Monday anomaly“ was
indicated. This means that the volatility of return of
Mondays is significantly higher, than during the
other days, and the mean return is lower. Other
articles (Syed and Basher, 2006; Tong, 2000) have
verified the hypothesis about the exclusive shape of
the return function at the first and last days of the
week in different financial markets of US, European
and Asia-Pasific exchange. In these research works
the day-of-the-week effect analysis was based on the
first two return distribution moments. Gordon and
Tang (1998), Galai and Kedar-Levy (2005) have
tested the effect of higher moments (e.g. skewness
and kurtosis) of return and concluded that the
hypothesis of equality of the higher moments across
days of the week can be rejected, indicating that a
weekly pattern on the higher moments exists.
The anomalies of the first trading day can be
explained by the influence of institutional traders,
also by the abundance of stock market news during
the weekend, comparing to other days of the week.
The effect of the last trading day can probably be
explained by the psychological factor.
All these investigation have been made in
developed securities markets. Some new research
sources indicate that the influence of day of week
effect is fading (Syed et al, 2006). There is no
research presented, if similar dependencies are still
important in the small securities markets with low
turnover and comparatively small number of market
players.
In this work we shall analyse the day-of-the-
week effect in the small markets with low liquidity.
432
Sakalauskas V. and Kriksciuniene D. (2007).
DAY OF THE WEEK EFFECT IN SMALL SECURITIES MARKETS.
In Proceedings of the Ninth International Conference on Enterprise Information Systems - AIDSS, pages 432-435
DOI: 10.5220/0002383404320435
Copyright
c
 SciTePress

The research methods, used in the article include
traditional analysis, where the differences of first
moments, calculated for the days of the week, will
be investigated, and the methods, based on analysis
of the higher moments.
The research outcomes and conclusions are
presented in section 3. All calculations are made
with the STATISTICA 6.0 for Windows software.
2 DATA AND METHODOLOGY
Data was taken from Vilnius Stock Exchange
information (The Nordic Exchange, 2006). The
OMX Vilnius Stock Index is a capitalization
weighted chain linked total-return index. For the
further calculations in this research we used the
OMX Vilnius Stock Index values of the time
interval from 2003-01-01 to 2006-11-21 on daily
basis (Figure 1).
The OMX Vilnius Stock Index values
0
100
200
300
400
500
600
03.01.01 03.07.01 04.01.01 04.07.01 05.01.01 05.07.01 06.01.01 06.07.01
Figure 1: The OMX Index values.
Return on investment to this index was
calculated by applying formula (1). For analysis of
the day-of-the-week effect the collected return data
has been processed in the following way.
The primary data set was assigned to the variable
RETURN (or R). Then two additional data sets
were derived from it. The first data set RETURN+
(or R+) was combined of those values of data set
RETURN, which had positive return on the prior
trading day. The data set RETURN- (or R-) was
made of RETURN values, which had negative
returns on the prior trading day. The prepared sets of
data, used for the further research consisted of 984
values for variable R; the derived data sets had 580
values of R+ and 382 values of the R- variable.
Similar method for splitting the initial data set was
used by Galai (2005). This method of data
rearrangement more clearly highlighted presence of
the day-of-the-week effect.
The three data sets were initially analysed by
presenting their Summary Statistics (Table 1).
Table 1: Day-of-the-week Summary Statistics (Bold
numbers indicate 5% significance).
From this table we observe that the average
return R+ values exceed significantly the return
values of other variables. One of possible reasons to
explain this effect could be psychological drive for
investment under the conditions of raising market
index. The effect of Friday increase return is
explained psychologically, by good moods of traders
before weekend.
By analysing standard deviation we noticed, that
there is no difference in volatility between days of
the week and among volatility the variables R, R+,
R-. The difference of daily rates of return
distribution from normal distribution is most evident
by analysing high moments (skewness and kurtosis).
Significant difference of skewness and kurtosis from
zero value indicates deviations from a normal
DAY OF THE WEEK EFFECT IN SMALL SECURITIES MARKETS
433

distribution. In the Table 1, the estimations of
skewness and kurtosis were statistically significant
at 5% level (printed in bold numbers) for almost all
weekdays and all three variables. In this way we
had to reject hypothesis about normality of return
distribution.
Further, the day-of-the-week effect was be
explored by applying the t-test for differences
between mean returns for Monday and the other
days of the week.
In the Figure 2 we can see that only the variable
R+ had statistically significant difference between
Monday and Friday mean returns (grey background).
By performing t-test for the other days of the week,
similar results were obtained - only R+ had a
statistically significant difference between Monday
and those on any other day.
Figure 2: T-test between returns on Monday and Friday.
Further for the research of the day-of-the-week
effect we shall use the regression model. Generally it
is defined it with the help of the following equation:
t
ε
,t
Da
,t
Da
,t
Da
,t
Daa
t
R
+++
+
+
+=
4433
2211
(2)
where a estimates the average return on Friday,
i
a
estimates the average difference between the return
on Friday and the i-th (i=1,2,3,4) trading day‘s
return,
ti
D
,
is the dummy variable for the i-th
trading day on date t,
0>
t
ε
is for random
regression error.
The null hypothesis for this model
0
H
stated the
equality of average daily rates of return:
0:
43210
=
=== aaaaH
. The results of
application of the regression model for R and R+
variables are presented Figure 3. The analysis of the
variable R revealed, that only subset the of data for
Friday (grey background) had the statistically
significant difference from other days of the week.
Figure 3: Regression model for R and R+ variables
The R+ indicates the significance difference for
Friday and Monday (grey background). The R- had
no statistically significant difference among those
days. The comparable results for big security
markets can be found in (Kohers et al, 2004, Tong,
2000).
Very similar results we obtained using analysis
of Variance method.
Figure 4: ANOVA results.
As we can see on Figure 4, only the analysis of
variable R+ indicates significant difference between
days of the week. Application of F criteria to R+,
allows us to reject the hypothesis of absence of
average differences among the return of the different
days of the week.
By applying the Kolmogorov-Smirnov test we
tested hypothesis, that two samples were drawn from
the same population. This test is sensitive to the
differences of the general shapes of the distributions
of the two samples (i.e., to differences of variance,
ICEIS 2007 - International Conference on Enterprise Information Systems
434

skewness, kurtosis etc.). It is generally applied for
testing the influence of higher moments for the
distribution (StatSoft Inc., 2006). In our case, for
investigation of the day-of-the-week effect, we
applied Kolmogorov-Smirnov test for different days
of the week. It was defined, that the variable R+ has
significant pairwise difference of the days of the
week only for Monday and Friday, what means, the
value of return index of first and last trading day of
the week differed from the other weekdays. In the
Figure 5, the Kolmogorov-Smirnov test values for
indicating difference among Monday and Tuesday
distributions was presented.
Figure 5: Kolmogorov-Smirnov test.
Similar tendency was valid for the other days of
the week. Even more significant influence could be
observed among Monday and Friday distributions.
By applying Mann-Whitney U test, used to
explore location characteristics of two samples
(means, average ranks, respectively), we also
observed significant difference of variable R+
values of Monday, compared to the other days of the
week.
3 CONCLUSIONS
In this article the statistical analysis of data of the
week effect was explored for the case of Lithuanian
stock market. The application of traditional
statistical analysis methods, such as regression
analysis, t-test, ANOVA, Levene and Brown-
Forsythe test of homogeneity of variances gave the
results, which allowed us to conclude, that only the
data set R+ had a statistically significant difference
between Monday and other days of the week. We
have noticed that the average return of Monday
trading was the lowest, and Friday trading was the
highest during the week. As stock market news flow
during the weekend is generally very low for small
securities markets, it does not influence much the
Monday trading turnover. We could rather conclude
the effects of ‘Monday somnolence’ and ‘Friday
uplift’ for the return of emerging markets.
The application of nonparametric Kolmogorov-
Smirnov test, based on analysis of the higher
moments of return distribution, did not indicate the
day-of-the-week effect for the full set of historical
data (variable R). This effect was indicated only for
the variable R+, where significant difference among
Monday and Friday compared pairwise to the other
days of the week, has been observed.
The differences of the days of the week effect,
studied in this article can advice us for further
research directions: investigation of the differences
between developed and emerging markets and to
research more precisely the derived sets of variables
R+ and R-. This type of research could give us
better insight to the behaviour of return data, and
could lead us to more precise outcomes of analysis.
REFERENCES
Achelis, S.B., 2000. Technical Analysis from A to Z,
McGraw-Hill Professional. 2nd Editon.
Fama, E.F., 1965. The behaviour of stock market prices,
J.Busin. 38, 34-105.
Galai, D. and Kedar-Levy, H., 2005. Day-of-the-week
Effect in high Moments, Financial Markets,
Institutions & Instruments, 14:3, 169-186.
Gordon, Y.N. Tang, 1998. Weekly pattern of exchange
rate risk: evidence from ten Asian-Pasific currencies,
Asia_Pacific Financial Markets, 5, 261-274
Gregoriou, A., Kontonikas, A. and Tsitsianis, N., 2004.
Does the day-of-the-week effect exist once transaction
costs have been accounted for? Evidence from the UK.
Applied Financial Economics, 14, 215–220.
Jaffe, J.F., Westerfield, R. and Ma, C., 1989. A twist on
the Monday effect in stock prices: evidence from the
U.S. and foreign stock markets. Journal of Banking
and finance 13, 641-650.
Kohers, G., Kohers N., Pandey V. and Kohers T., 2004.
The disappearing day-of-the-week effect in the
world’s largest equity markets. Applied Economics
Letters, 11, 167–171.
StatSoft Inc., 2006. Electronic Statistics Textbook. Tulsa,
OK: StatSoft. WEB:
http://www.statsoft.com/textbook/stathome.html.
Syed, A. Basher and Sadorsky, P., 2006. Day-of-the-week
effects in emerging stock markets. Applied Economics
Letters, 13, 621–628.
The Nordic Exchange. Retrieved November 25, 2006,
from http://www.baltic.omxgroup.com/.
Thomsett Michael, C., 2006. Getting started in
fundamental analysis. Wiley, pp.232.
Tong, W., 2000. International evidence on weekend
Anomalies. Journal of fin. research 23:4, 495-522.
DAY OF THE WEEK EFFECT IN SMALL SECURITIES MARKETS
435