The day-of-the-week effect on the Santiago stock exchange of Chile.
Kamath, Ravindra ; Liu, Chinpiao
INTRODUCTION
Finance literature offers extensive evidence of the day-of-the-week
effect in both, developed and developing markets. The Monday returns for
the equity markets have been found to be the lowest of the week and
often negative. Simultaneously, the Friday returns have been documented
to be the highest of the week. Several recent studies have questioned
the day-of-the-week effect results uncovered by relying on the OLS
methodology (see for example, Connolly (1989), Chang, et al. (1993) and
Dubois and Louvet (1996)). And yet, the use of the more robust
econometric techniques has not always led to disputing the OLS method
based findings regarding the presence of the anomalous effect. For
example, while Alexakis and Xanthakis (1995) and Kamath, et al. (1998)
have reported that the evidence on the anomalous effect in their studies
was methodology independent, the Chen, et al. (2001) paper concluded
that their findings were both, the estimation methodology specific as
well as the sample period specific.
The objectives of this study are to determine if there is evidence
of the day-of-the-week effect on the emerging equity markets of Chile
and to ascertain if the findings on "the effect" are sample
period specific. Bollerslev's GARCH methodology is utilized in this
study of the Santiago Stock Exchange of Chile. To meet the stated
objectives, we utilize the daily data of the Selective Stock Price
Index, IPSA (Indice de Precios Selectivo de Acciones) over the most
recent 68-month period from January, 2003 through August, 2008.
PREVIOUS RESEARCH
Numerous studies of seasonal anomalies in the equity markets can be
found in finance literature. The empirical evidence on the presence of
the day-of-the-week effect occupies a central role in these studies. The
well known articles by French (1980), Gibbons and Hess (1981), Keim and
Stambaugh (1984), among others have indicated that the market returns
tend to be dependent on the day of the week. Lakonishok and Smidt (1988)
found that such an anomalous effect was present in the Dow Jones dating
back to 1897. In an overwhelming majority of the older studies, the OLS
methodology was utilized to detect :the effect. Connoly (1989) was one
of the first researchers who argued that the return distributional
characteristics of stock markets did not advocate the use of the OLS
method. Connolly's findings suggested that the intensity of the
day-of-the-week effect had weakened considerably after 1975. The results
of the post-1975 sub-periods of Keim and Stambaugh (1984), Rogalski
(1984), Smirlock and Starks (1986) and Condoyanni, et al. (1987) in fact
showed a much reduced intensity of the anomalous effect.
Following Connolly (1989), studies by Chang, et al. (1993) and
Dubois and Louvet (1996) also presented evidence which questioned the
presence of "the effect". Chang, et al. (1993) noted that the
day-of-the-week effect had become insignificant in the post-1986 period
in the U.S., Belgium, Denmark and Germany even though such an effect was
very much present in Canada, Hong Kong and seven European markets.
Dubois and Louvet (1996) documented that "the effect" had
vanished in the post-1985 sub-period in the U.S., Canada, Japan, Germany
and Australia. Wilson and Jones (1993) study however found "the
effect" to be glaringly present in four U.S. market indices even
after making corrections for the non-normality of the data.
The day-of-the-week effect has been examined for equity markets
around the world. Kamath, et al. (1998) present findings on this effect
in 20 national markets in a tabulated form. The said effect has been
investigated for the markets of Canada, Finland, France, Germany,
Greece, Italy, the Netherlands, Spain, Sweden, Switzerland, Turkey, the
U.K., Australia, Hong Kong, China, Japan, South Korea, Malaysia, New
Zealand, Philippines, Singapore, Thailand, Taiwan, Israel, Argentina,
Brazil, Chile, Columbia, Mexico, Peru and Venezuela. With some
exceptions, a persistent day-of-the-week effect has been reported in
most markets. The papers by Ho (1990), Lee, et al. (1990) and Wong, et
al. (1992) found the returns to be positive on all days of the week as
was found by Lauterback and Unger (1992) in Israel. In many cases, the
findings for certain markets are not consistent either because of the
methodological differences or because of the sample period differences
or both. For example, in case of Spain, Santemases (1986) found absence
of "the effect" while Chang, et al. (1993) found a robust
presence of "the effect" during the 1986-1992 period. Hui
(2005) found evidence of the said effect in Singapore but not in South
Korea, Hong Kong and Taiwan. Tong (2000) concluded that a Monday effect
existed in the U.S. and fifteen markets outside the U.S. A recent study
by Mazumdar, et al. (2008) found that the day-of-the-week effect
patterns exist even for ishares of 17 countries. They conclude that
trading based on "the effect" "outperforms a buy-and-hold
strategy for most ishares" (p 714).
In a 2001 study of the said effect in China, Chen, et al. conclude
that, "The evidence of the day-of-the-week anomaly in China is
clearly dependent on the estimation method and sample period" (p
139). In the present study we attempt to evaluate if the findings on the
anomalous effect in Chile are in fact sample period specific. In the
case of South Korea, Kamath and Chusanochoti (2002) found such an effect
to be rather robust in the decade of the 1980s but to have completely
disappeared in the decade of the 1990s regardless of the methodology
used. Easton and Faff (1994) for Australia, Alexakis and Xanthakis
(1995) for Greece and Kamath, et al. (1998) for Thailand documented that
their conclusions regarding the presence of "the effect" were
unaffected by the methodology used for detecting it.
DATA AND METHODOLOGY
This investigation utilizes the daily closing index prices of the
IPSA, the equity market index of the Santiago Stock Exchange of Chile,
from January, 2003 through August, 2008. This data gave rise to a total
of 1411 daily rates of return. The IPSA is a value weighted index made
up of the 40 most actively traded stocks. The composition of the IPSA is
revised quarterly. This index has been computed since 1977. The Santiago
Stock Exchange is open from Monday through Friday except for holidays.
The information on the closing prices of the IPSA and the daily
returns are summarized in Table 1. The IPSA began the year 2003 at 1008
and on the last trading day of August, 2008, it closed just over 2,895.
Accordingly, IPSA rose 189 percent over the 68-month period. The Chilean
market gained in each of the five full calendar years covered by the
study. The ending index in August, 2008 was about 605 points below the
2007 high closing of almost 3,500. The daily returns were calculated
using equation (1) in which [R.sub.t] is the daily return on the index,
IPSA, and [P.sub.t] and [P.sub.t-1] are the index closing prices on day
t and t-1, respectively.
[R.sub.t] = (([P.sub.t]/[P.sub.t-1])-1) x 100 (1)
Descriptive statistics of the daily returns on the IPSA are
summarized in Table 2. This table displays the relevant statistics for
the overall 68-month period covered in this study as well as for the two
34-month sub-periods. An inspection of Table 2 reveals some interesting
facts. First, the mean daily returns are positive in all three periods.
Second, even though the mean daily return in the second sub-period is
about one half of the same in the earlier period, it is accompanied by a
much larger standard deviation. Accordingly, the coefficient of
variation of daily returns (risk per unit of return) can be computed to
be 20.76 in the second period as compared to a value of 7.49 in the
first period (not shown in the table). Third, the median return is
actually larger in the second period than in the first. Fourth, the
distributions of daily returns are found to be negatively skewed in all
three periods. Moreover, the kurtosis values noted are considerably
larger than 3.0 in the overall and the second period and thus exhibiting
fatter tails than the normal distribution. To further emphasize this
distinction, we present a comparison of the distributional
characteristics of the IPSA with the theoretical normal distribution in
Table 3. The Jarque-Bera test statistics shown in Table 2 reject the
normality hypothesis at the 1 percent level for the IPSA returns in all
three study intervals. These distributional findings of the Chilean
stock market index are comparable to those of numerous international
markets in studies by Chang, et al. (1993), Corhay and Rad (1994),
Easten and Faff (1994), Kamath, et al. (1998), Chen, et al. (2001) and
Hui (2005).
Table 2 also contains the Box-Pierce Q (23) statistics of the three
rates of return series. These statistics are found to be significant in
all three study intervals thereby indicating that significant linear
dependencies exist in all three return series. However, when the Q (23)
measures are adjusted for heteroskedasticity, the resulting measures,
Adj Q (23), are found to be insignificant in both sub-periods. The
[Q.sup.2] (23) figures, the values of the Box-Pierce statistics for the
squared return series are found to be significant in all three test
intervals which suggest the rejection of the null hypothesis of
conditional homoskedasticity.
The non-normal distributional attributes of the IPSA discussed
above do not recommend the use of the Ordinary Least Squares (OLS)
method which was the method of choice in an overwhelming number of
studies conducted to detect the day-of-the-week effect prier to the
1990s. Therefore, we rely on a methodology which can capture the time
dependence of return variability. Bollerslev's Generalized
Autoregressive Conditional Heteroskedasticity (GARCH) model (1986) is
our choice of methodology in the present study. The GARCH (p, q) model
is given by equation (2) in which [[epsilon].sub.t] is the regression
error term conditional on the information set [phi] at t-1, and
[h.sub.t] is the conditional variance dependent on past squared errors
(return shocks).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
To ascertain the presence of the day-of-the-week effect in the
Chilean stock market, we utilize the GARCH (1,1) model suggested by
French, et al. (1987) and Corhay and Rad (1994), among others for the
study of equity market returns. The precise model relied upon in this
study is depicted by equation (3). In this equation, [R.sub.t] is the
daily return, and [d.sub.1] - [d.sub.4] are the dummy variables for
Monday through Thursday, respectively, and d0 is the dummy variable for
Friday.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
EMPIRICAL FINDINGS
The means and standard deviations of the returns of each day of the
week on the IPSA for the overall period and two 34-month sub-periods are
contained in Table 4a. The Wednesday mean returns are found to be
significantly different from zero in all three study intervals. While
the Monday mean returns are found to be significantly negative in the
overall period and in the second sub-period, the Friday mean returns are
found to be significantly positive in the overall period and in the
first sub-period. Table 4a indicates that the Monday mean returns are
consistently the lowest returns of the week and that the Wednesday mean
returns are the highest returns of the week.
We further examine the mean daily returns in Table 4b in which the
percentage of times the IPSA returns were positive on each day of the
week are presented. In the overall study period, the Monday return was
positive in less than 50 percent of the time while the Friday return was
positive in more than 60 percent of the time. In the second sub-period,
the Monday return was positive on less than 42 percent of the time while
the Wednesday and the Friday returns were positive more than 61 percent
of the time.
Since the distributional characteristics of the Chilean Stock
market index were found to be non-normal and exhibited both, linear and
non-linear dependencies, we present the evidence on serial correlation
in this index in Table 5. The tabulated results indicate that the IPSA
returns are significantly correlated with the previous day's
return. The Q (23) statistics pertaining to the OLS errors from the
first order autoregressive model are found to be significant in two of
the three study intervals. Yet, when these errors are adjusted for
heteroskedasticity, the resulting Adj Q (23) statistics are
insignificant in all three study intervals. The tabulated results also
indicate that the [Q.sup.2] (23) statistics pertaining to the square of
the error terms are very much significant in all three periods. These
findings support our decision to utilize the GARCH methodology in this
investigation which can account for the heteroskedasticity in the return
data.
The results of the GAPCH (1, 1) estimation are summarized in Table
6. Several observations can be made from these tabulations. First, the
daily returns in the Chilean equity market are more dependent on the
returns of the previous day than on the day of the week itself ([beta]).
In the first 34-month sub-period as well as in the overall period, there
is evidence of the day-of-the-week effect on the IPSA attributable to
the negative Monday returns and the positive Friday returns. Third, in
the second 34-month sub-period, the day-of-the-week effect is still
present but not because of Monday or Friday. In this sub-period, the
Wednesday's returns are the cause of "the effect." Thus,
even though we have detected a persistent presence of the
day-of-the-week effect on the Santiago Stock Exchange over the recent
68-month period, the underlying findings are sample period specific. In
this respect, our findings echo the sentiments expressed by the Chen, et
al. study (2001). Fourth, the likelihood ratios (LR) which measure the
relative fit of the GARCH model as compared to that of the OLS model
indicate the significantly superior fit of the GARCH (1,1) model
utilized in this study. Fifth, in all three estimations of Table 6, the
parameters [[alpha].sub.1] and [[alpha].sub.2] are found to be
statistically significant at the one percent level. The additions of
these two parameters are found to equal 0.973, 0.960 and 0.984 in the
overall period, in the first sub-period and in the second sub-period,
respectively. These sums which are near 1.0 suggest that the shocks to
volatility tend to persist over time.
SUMMARY
The objective of this study was two fold: first, to ascertain if
the returns on the Santiago Stock Exchange of Chile exhibited the
day-of-the-week effect and second, to determine if the uncovered
evidence on the said effect was sample period specific. To meet these
objectives, this investigation examined the daily data on the Selective
Stock Price Index, IPSA over the two recent 34-month sub-periods from
January, 2003 through August, 2008. Over this 68-month period, the
Chilean Stock market gained about 190 percent.
The findings of the study revealed that the day-of-the-week effect
was present during both sub-periods of the study. However, different
days of the week were responsible for the detected effect. Specifically,
in the first 34 months of the study, the said effect was found to exist
because of the negative Monday returns and the positive Friday returns
as has been reported for numerous equity markets around the world. In
the second 34 months of the study, the presence of the day-of-the-week
effect was neither attributable to Mondays nor Fridays; instead, it was
caused by the significantly positive returns on Wednesdays. Thus, even
though the said effect has persisted over the entire study period, our
conclusions in this respect are sample period specific. Moreover, both
the GARCH (1,1) formulation as well as the first order autoregressive
formulation indicated that yesterday's return in the Chilean stock
market is a significant determinant of today's return. In other
words, the lagged return effect was more significant than the
day-of-the-week effect.
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Ravindra Kamath, Cleveland State University
Chinpiao Liu, Cleveland State University
Table 1: Raw Data of the Santiago Stock Exchange Index (IPSA) of
Chile, 1/2003-8/2008
Time Period 1/1/2003- 1/1/2004- 1/1/2005-
12/31/2003 12/31/2004 12/31/2005
Highest Index 1,585.78 1,825.34 2,214.07
Close Date 10/21/03 12/22/04 08/02/05
Lowest Index 982.17 1,390.63 1,710.07
Close Date 01/27/03 05/10/04 01/12/05
Last Day Index Close 1,484.80 1796.48 1,964.47
Return for the year % 46.43 20.99 9.35
Time Period 1/1/2006- 1/1/2007- 1/1/2008
12/31/2006 12/31/2007 8/31/2008
Highest Index 2,712.81 3,499.50 3,096.11
Close Date 12/27/06 07/03/07 05/29/08
Lowest Index 1,939.60 2,689.19 2,427.11
Close Date 01/02/06 01/02/07 01/21/08
Last Day Index Close 2,693.36 3,051.83 2,895.25
Return for the year % 37.10 13.31 (5.13)
Table 2: Summary Statistics of Daily Stock Index (IPSA) Returns in
Chile, 1/2003-8/2008
N Mean Median Max. Min. Std.dev.
Period % % %
1/2003-8/2008 1411 0.08 0.106 5.804 -5.03 0.97
1/2003-10/2005 711 0.106 0.094 2.819 -3.044 0.794
11/2005-8/2008 700 0.054 0.124 5.804 -5.03 1.121
Coeff. Jarque-
Coeff. of of excess Bera Q(23)
Period Skewness Kurtosis test statistic
1/2003-8/2008 -0.33 6.33 678.7 ** 72.7 **
1/2003-10/2005 -0.14 3.49 9.3 44.3 **
11/2005-8/2008 -0.35 6.24 321.2 ** 47.0 **
Adj. [Q.sup.2]
Q(23) (23)
Period statistic statistic
1/2003-8/2008 42.1 * 631.7 **
1/2003-10/2005 34 135.5 **
11/2005-8/2008 31.5 275.9 **
** and * represent significance levels of 1 and 5 percent, respectively
Table 3: A comparison of Santiago Stock Index Return Distributions
with the Normal Distribution, 1/2003-8/2008
Normal
Distribution 1S.D. 2S.D. 3S.D. 4S.D. 5S.D. >5S.D.
Interval 0.6826 0.9545 0.9973 0.9999 0.9999 0.0000
1/2003-8/2008 0.7392 0.9546 0.9887 0.9943 0.9972 0.0028
1/2003-10/2005 0.6850 0.9536 0.9930 1.0000 1.0000 0.0000
11/2005-8/2008 0.7543 0.9500 0.9871 0.9943 0.9986 0.0014
Table 4a: Means and Standard Deviations of Chilean Stock Index
Returns Across the Days of the Week, 1/2003-8/2008
Period 1/2003-8/2008 1/2003-10/2005 11/2005-8/2008
Day Mean Std. Mean Std. Mean Std.
Dev. Dev Dev.
Monday -0.119 * 0.921 -0.037 0.853 -0.203 * 0.982
Tuesday 0.007 1.112 0.128 0.851 -0.119 1.324
Wednesday 0.220 ** 0.959 0.173 ** 0.759 0.267 ** 1.126
Thursday 0.147 * 0.980 0.091 0.777 0.204 * 1.147
Friday 0.134 ** 0.819 0.169 ** 0.711 0.099 0.914
** and * represent significance levels of 1 percent and 5 percent,
respectively
Table 4b: Percentage of days the Chilean stock index returns were
positive, 1/2003-8/2008
Period 1/2003-8/2008 1/2003-10/2005 11/2005-8/2008
Monday 48.70 55.47 41.67
Tuesday 51.22 55.78 46.43
Wednesday 59.09 56.94 61.27
Thursday 56.25 53.47 59.03
Friday 60.14 58.99 61.27
Table 5: Autoregressive model: statistics of daily residual series of
the Santiago Stock Exchange of Chile returns, 1/2003-8/2008
[R.sub.t]=[[alpha].sub.(0)] + [R.sub.t-1] + [[epsilon].sub.t]
Q(23) Adj. [Q.sup.2]
Statistic Q(23) (23)
Period [alpha.sub.0] [alpha.sub.1] statistic Statistic
1/2003 0.068 ** 0.149 ** 41.0 * 28.8 668.6 **
-08/2008 (2.66) (5.65)
1/2003 0.085 ** 0.196 ** 17.3 15.6 101.6 **
-10/2005 (2.89) (5.31)
11/2005 0.046 0.123 ** 35.1 * 25.7 293.2 **
-08/2008 (1.09) (3.28)
** and * represent significance levels of 1 and 5 percent, respectively
Table 6: Day/of/the/week effects on the Santiago Stock Exchange of
Chile: Garch (1, 1) results (a,b,) 1/2003-8/2008
Period [d.sub.0] [d.sub.1] [d.sub.2] [d.sub.3] [d.sub.4]
1/2003 0.129 ** -0.179 ** -0.03 0.081 -0.015
-8/2008 (2.75) (-2.72) (-0.48) (1.28) (-0.22)
1/2003 0.158 * -0.245 ** 0.005 -0.008 -0.066
-10/2005 (2.39) (-2.80) (0.05) (-0.09) (-0.73)
11/2005 0.084 -0.076 -0.072 0.198 * 0.054
-8/2008 (1.27) (-0.74) (-0.77) (2.16) (0.53)
Period [beta] [a.sub.0] [a.sub.1] [a.sub.2] LL
1/2003 0.161 ** 0.031 ** 0.170 ** 0.803 ** -1770.5
-8/2008 (5.78) (3.18) (7.02) (28.4)
1/2003 0.184 ** 0.026 * 0.118 ** 0.842 ** -798.2
-10/2005 (4.77) (1.98) (3.69) (20.69)
11/2005 0.133 ** 0.041 * 0.227 ** 0.757 ** -964.0
-8/2008 (3.23) (2.34) (5.84) (19.17)
Period LR
1/2003 320.4 **
-8/2008
1/2003 54.2 **
-10/2005
11/2005 185.7 **
-8/2008
(a.) LL: Log likelihood value and LR: likelihood ratio.
(b.) ** and * represent significance levels of 1 and 5 percent,
respectively
