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The day-of-the-week effect on the Santiago stock exchange of Chile.

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
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Author:Kamath, Ravindra; Liu, Chinpiao
Publication:Journal of International Business Research
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Date:Mar 1, 2011
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