Revisiting Calendar Anomalies in Asian Stock Markets
Using a Stochastic Dominance Approach
Hooi Hooi Lean, Russell Smyth and Wing-Keung Wong
RMI Working Paper No. 07/09
Submitted: January 23, 2007
Abstract
Extensive evidence on the prevalence of calendar effects suggests that there exist abnormal
returns. Some recent studies, however, have concluded that calendar effects have largely
disappeared. In spite of the non-normal nature of stock returns, most previous studies have
employed the mean-variance criterion or CAPM statistics. These methods rely on the
normality assumption and depend only on the first two moments to test for calendar effects.
A limitation of these approaches is that they miss important information contained in the data
such as higher moments. In this paper we use a stochastic dominance (SD) test to test for the
existence of day-of-the-week and January effects. We use daily data for 1988 to 2002 for
several Asian markets. Our empirical results support the existence of weekday and monthly
seasonality effects in some Asian markets, but suggest that first-order SD for the January
effect has largely disappeared.
Keywords: Stochastic dominance, Calendar anomalies, Asian markets.
Hooi-Hooi Lean
NUS Risk Management Institute and
School of Social Sciences
Universiti Sains Malaysia
USM, Penang 11800
Malaysia
Tel: (604) 6532663
Fax: (604) 6570918
E-mail: learnmy@gmail.com
Russell Smyth
NUS Risk Management Institute and
Department of Economics
Monash University
Caulfield East, Victoria 3145
Australia
Tel: 61 3 9903 2134
Fax: 61 3 9903 1128
Email: russell.smyth@buseco.monash.edu.au
Wing-Keung Wong
NUS Risk Management Institute and
Department of Economics
National University of Singapore
Block S16, Level 5, 6 Science Drive 2
Singapore 117546
Tel: (65) 6874-6014
Fax: (65) 6775-2646
Email: rmiwwk@nus.edu.sg
© 2007 Wing-Keung Wong. Views expressed herein are those of the author and do not necessarily
reflect the views of the Berkley-NUS Risk Management Institute (RMI).
1. Introduction
A large literature exists that studies day-of-the-week and January effects. Several
studies have found evidence of day-of-the-week and January effects in United States
(U.S.) and international capital markets (see Pettengill, 2003 for a review of the day-ofthe-week effect literature). However, recent studies, which have mainly used data for
the 1990s, reveal a weakening and/or disappearance of calendar effects. Most of the
existing literature has employed the mean-variance (MV) criterion or CAPM statistics.
Both approaches use parametric statistics that rely on the normality assumption and
depend only on the first two moments to test for calendar effects. However, the presence
of both positive and negative skewness in individual and portfolio stock distributions is
well documented (Beedles, 1979; Schwert, 1990). The MV and CAPM approaches have
the limitation that they depend only on the first two moments to test for calendar effects,
which results in missing important information contained in higher moments.
To address these shortcomings, some recent studies have applied a non-parametric
stochastic dominance (SD) approach to examine calendar effects. The SD approach
differs from traditional parametric approaches in that comparing portfolios using the SD
approach is equivalent to the choice of assets by utility maximization. It endorses the
minimum assumptions of the investor’s utility function and studies the entire
distribution of returns directly. The advantage of SD analysis over parametric tests
becomes apparent when the stocks return distribution is non-normal as the SD approach
does not require any assumption about the nature of the distribution and therefore it can
be used for any type of distribution. In addition, SD, revealing the entire distribution,
recovers all information from the distribution while traditional parametric tests,
depending on the mean and variance, omit all information from higher moments. As
2
such, the SD approach is superior and less restrictive than the traditional parametric
statistics for analyzing investment decision-making under uncertainty.
In this study, we employ the SD test proposed by Davidson and Duclos (2000)
(hereafter the DD test) to examine the presence of day-of-the-week and January effects
in Hong Kong, Indonesia, Japan, Malaysia, Singapore, Taiwan and Thailand using daily
data for the period 1988 to 2002. We apply the DD test to investigate the characteristics
of the entire distribution for calendar effects, instead of only considering the mean and
standard deviation, which is the approach in most of the existing literature.
2. Previous studies
The day-of-the-week effect was first observed by Fields (1931) who pointed out that the
U.S. stock market consistently experienced significant negative returns on Mondays and
significant positive returns on Fridays. Explanations for the existence of a day-of-theweek effect include statistical errors, micro market effects, information flow effects and
order flow effects (Pettengill, 2003). There is a large empirical literature for U.S. equity
markets that document a day-of-the-week effect with low returns on Monday. French
(1980), Gibbons and Hess (1981), Keim and Stambaugh (1984) and Linn and
Lockwood (1988) found statistically significant differences in returns across weekdays
and a statistically significant negative return on Monday. Lakonishok and Smidt (1988),
Bessembinder and Hertzel (1993) and Siegel (1998) found day-of-the-week effects in
U.S. equity markets using daily data for long time periods and sub-periods.
Several studies have corroborated the findings for U.S. equity markets and other
developed markets. Jaffe and Westerfield (1985) documented day-of-the-week effects
with significantly negative Monday returns for the Australian, Canadian, Japanese and
U.K. markets. Other studies which have found day-of-the-week effects in multi-country
3
studies for developed markets are Condoyanni et al. (1987), Dubois and Louvet (1996)
and Tong (2000). However, Chang et al. (1993) only found evidence of a day-of-theweek effect in 13 out of 23 countries and their results were sensitive to the choice of
statistical testing procedure. Davidson and Faff (1999) concluded that the day-of-theweek effect has largely disappeared in the Australian equity market.
Among studies for Asian markets, Aggarwal and Rivoli (1989) found a day-of-the-week
effect in four emerging Asian markets with strong negative returns on Monday and
Tuesday. Ho (1990) found a day-of-the-week effect in 10 Asia-Pacific markets
including Hong Kong, Malaysia, the Philippines, Singapore, Taiwan and Thailand. Koh
and Wong (2000) found that equity markets in Hong Kong, Malaysia, the Philippines
and Singapore have negative returns on Monday and Tuesday and positive returns on
Wednesday to Friday. Agrawal and Tandon (1994) considered day-of-the-week effects
in 18 equity markets including India, Malaysia and the Philippines for which Monday
had the lowest negative return and Friday had the highest positive return.
The January effect is the anomaly that common stock returns are larger in January than
in other months. Wachtel (1942) was the first to observe a January effect in the Dow
Jones Industrial average for the period 1927 to 1942. The first rigorous empirical study
of the January effect for U.S. markets was made by Rozeff and Kinney (1976) who
found stock returns for January to be significantly higher than the other 11 months for
several indices for NYSE stocks spanning 1904 to 1974. Of the studies for emerging
Asian markets, Nassir and Mohammad (1987) and Pang (1988) found support for the
existence of a January effect in Malaysia and Hong Kong respectively. Ho (1990) found
that six of eight emerging Asian markets exhibited a January effect. However, Cheung
and Coutts (1999) found no evidence of a January effect for the Hong Kong market.
4
3. Data and Methodology
This study uses daily stock indices for the period January 1, 1988 to December 31,
2002. The indices are the Hang Seng Index for Hong Kong, Jakarta Composite Index
for Indonesia, Kuala Lumpur Composite Index for Malaysia, Nikkei Index for Japan,
Straits Times Index for Singapore, Taiwan Stock Exchange Index for Taiwan and the
SET Index for Thailand. 1 All data used in this paper were obtained from Datastream.
The daily log-return, Rit, is calculated based on the closing values of the stock index i on
days t and t-1 respectively. In our study for the day-of-the-week effect, we exclude any
week with fewer than five trading days. This approach is consistent with that employed
by Wingender and Groff (1989) and with the approach in previous studies on the dayof-the-week effect. Similarly, in our test for the January effect we only examine returns
for the first twenty calendar days so as to fulfil the requirement of equal sample size.
The portfolio of each weekday (month) is formed by grouping the returns of the same
weekday (month) over the entire sample period. Following grouping, a pair-wise
comparison is performed using the SD approach for all portfolios in the study.
The commonly used techniques in the comparison of prospects are the MV model and
the CAPM. For any two investments with variables for profit and return Yi and Y j with
means μ i and μ j and standard deviations σ i and σ j respectively, Y j is said to
dominate Yi by the MV criterion if μ j ≥ μ i and σ j ≤ σ i . The MV and CAPM criteria
depend on the existence of normal return distributions and quadratic utility functions
and are not appropriate if return distributions are not normal or if investors’ utility
functions are not quadratic (Feldstein, 1969; Hakansson, 1972).
1
Where a country had multiple stock indices we chose the index most commonly used in the previous
empirical literature on day-of-the-week and January effeects. For other studies that use the same indices
as us see Aggarwal and Rivoli (1989), Agrawal and Tandon (1994), Brooks and Persand (2001), Cheung
and Coutts (1999) and Kiymaz and Berument (2003).
5
The most common SD rules are first-order SD (FSD), second-order SD (SSD) and
third-order SD (TSD). Letting F0 = f and G0 = g be the probability density functions
(PDF) and F1 = F and G1 = G be the cumulative distribution functions (CDF) of
returns for portfolios X and Y with common support [a, b] where a < b, we can define:
x
H s ( x ) = ∫ H s −1 ( t ) dt for H=F, G and s = 1, 2, 3 .
a
(1)
The three basic SD rules (see, eg. Hadar and Russell, 1969; Whitmore, 1970) are:
1) Portfolio X dominates portfolio Y by FSD, denoted X f1 Y or F f1 G , if and only if
F1 (x ) ≤ G1 (x ) for all possible returns, x, with strict inequality for at least one value
of x.
2) Portfolio X dominates portfolio Y by SSD, denoted X f2 Y or F f2 G , if and only if
F2 (x ) ≤ G2 ( x ) for all possible returns, x, with strict inequality for at least one value
of x.
3) Portfolio X dominates portfolio Y by TSD, denoted X f3 Y or F f3 G , if, and only
if, μ F ≥ μ G and F3 ( x ) ≤ G3 (x ) for all possible returns, x, with strict inequality for at
least one value of x.
Let U be the utility function. Investigating SD among different investments is
equivalent to examining the choice of investments by utility maximization:
Theorem 1:
1.
All non-satiated investors (prefer more to less) with utility functions U ' ( x ) ≥ 0 will
prefer X to Y, and will increase their wealth and utility by shifting their investments
from Y to X, if and only if X f1 Y .
6
2.
All non-satiated and risk-averse investors with utility functions U ' ( x ) ≥ 0 and
U " (x ) ≤ 0 will prefer X to Y, and will increase their utility by shifting their
investments from Y to X, if and only if X f2 Y .
3.
All non-satiated and risk-averse investors with decreasing absolute risk aversion,
such that utility functions U ' ( x ) ≥ 0 , U " (x ) ≤ 0 and U ' " (x ) ≥ 0 (prefer positive
skewness), will prefer X to Y and will increase their utility by shifting their
investments from Y to X, if and only if X f3 Y .
SD implies a hierarchy: FSD implies SSD, which in turn implies TSD. However, the
reverse is not true and, as such, we traditionally only report the lowest dominance order.
4. The Davidson and Duclos (2000) test
As shown in Tse and Zhang (2004) and Lean et al. (2006), the DD test is one of the
most powerful and simplest yet least conservative SD test statistics. Let {mi, oi}, i = 1,
2… N be pairs of observations drawn from the population of Monday (or January) and
non-Monday (or non-January) portfolios with CDF, F ( x ) and G ( x ) respectively.
For a grid of pre-selected points x1, x2… xk , the s-order DD statistic is:
Ts ( x) =
Fˆs ( x) − Gˆ s ( x)
for s = 1, 2 and 3;
ˆ
V ( x)
s
where Vˆs ( x) = VˆFs ( x) + VˆGs ( x) − 2VˆFGs ( x),
Hˆ s ( x ) =
N
1
( x − hi ) +s −1 ,
∑
N ( s − 1)! i =1
N
⎤
1⎡
1
VˆH s ( x) = ⎢
( x − hi ) +2( s −1) − Hˆ s ( x) 2 ⎥ , H = F , G; h = m, o;
2 ∑
N ⎣ N (( s − 1)!) i =1
⎦
N
⎤
1⎡
1
s −1
VˆFGs ( x) = ⎢
( x − mi )+s −1 ( x − oi )+ − Fˆs ( x)Gˆ s ( x) ⎥ .
2 ∑
N ⎣ N (( s − 1)!) i =1
⎦
7
Because it is empirically impossible to test the null hypothesis on the full support of the
distributions, following the approach proposed by Bishop et al. (1992), we test only a
pre-designed finite number of values x for the following hypotheses:
H 0 : Fs ( xi ) = Gs ( xi ) , for all xi , i = 1, 2,..., k ;
H A : Fs ( xi ) ≠ Gs ( xi ) for some xi , but F f/ s G, F p/ s G;
H A1 : Fs ( xi ) ≤ Gs ( xi ) for all xi and Fs ( xi ) < Gs ( xi ) for some xi ;
H A 2 : Fs ( xi ) ≥ Gs ( xi ) for all xi and Fs ( xi ) > Gs ( xi ) for some xi .
In the above hypotheses, H A is set to be exclusive of both H A1 and H A2 , which means
that, if the test accepts H A1 or H A2 , it will not be classified as H A . H A is accepted if
F ( x ) < G ( x ) for some x and F ( x ) > G ( x ) for some x. Under the null hypothesis,
Davidson and Duclos (2000) showed that Ts ( x) is asymptotically distributed as the
Studentized Maximum Modulus (SMM) distribution (Richmond, 1982) to account for
joint test size. To implement the DD test, a test statistic at each grid point is computed
and the null hypothesis H0 is rejected if the largest test statistic is significant. The SMM
distribution with k and infinite degrees of freedom at the α% significant level denoted
by M ∞k ,α is used to control for the probability of rejecting the overall null hypothesis.
The following decision rules are based on the 1-α percentile of M ∞k ,α tabulated by
Stoline and Ury (1979):
1. If Ts ( xi ) < M ∞k ,α for i = 1,..., k accept H 0 .
2. If Ts ( xi ) < M ∞k ,α for all i and − Ts ( xi ) > M ∞k ,α for some i accept H A1.
3. If − Ts ( xi ) < M ∞k ,α for all i and Ts ( xi ) > M ∞k ,α for some i accept H A 2 .
4. If Ts ( xi ) > M ∞k ,α for some i and − Ts ( xi ) > M ∞k ,α for some i accept H A.
If H0 or HA is accepted, there is no SD of one particular weekday (month) over another.
On the other hand, if H A1 or H A2 is accepted for order one, a particular weekday
(month) stochastically dominates the other weekday (month) at the first-order. If H A1 or
8
H A2 is accepted for order two or three, a particular weekday (month) stochastically
dominates the other weekday (month) at the second- or third-order.
Based on the findings in Tse and Zhang (2004) and Lean et al. (2006), the DD test
works well for 10 grid points. Too few grids will miss information on the distributions
between any two consecutive grids (Barrett and Donald, 2003), and too many grids will
violate the independence assumption required by the SMM distribution (Richmond,
1982). In order to make more detailed comparisons without violating the independence
assumption we follow Fong et al. (2005) and make 10 major partitions with 10 minor
partitions within any two consecutive major partitions in each comparison, and show the
statistical inference based on the SMM distribution for k=10 and infinite degrees of
freedom. This allows us to examine for consistency in both the magnitude and sign of
the DD statistics between any two consecutive major partitions. The critical value of
SMM (M) for n = ∞ and k = 10 at the 5% level is 3.254.
5. Results
5.1. Day-of-the-week effect
Table 1 presents the mean return, standard deviation, skewness, kurtosis and
Kolmogorov-Smirnov (K-S) test statistic of the returns for each day of the week and for
each country. It shows a tendency for the lowest mean return to be on Monday and the
highest mean return on Friday, consistent with most previous studies for the day-of-theweek effect. In contrast to the mean returns, the standard deviation of returns generally
decreases as the week progresses as the volatility tends to be highest on Monday and
lowest on Friday in all countries except Indonesia. While not reported, pair wise t-tests
indicated that some weekdays have statistically higher mean returns than others. Fstatistics showed that some standard deviations are statistically different at the 5% level.
9
----------------------Insert Table 1
-----------------------While we are primarily interested in the results of the DD test, for comparative
purposes, we first applied the MV approach. Taking Hong Kong as an example, from
Table 1 it can be seen that in Hong Kong, Monday’s mean return is -0.0801%, which is
lower than all other weekdays (significant at 10% except Tuesday and Thursday) and its
standard deviation is 2.15%, which is significantly higher than all other weekdays.
Hence, applying the MV criterion, Monday is dominated by Tuesday, Wednesday,
Thursday and Friday. On the other hand, Friday’s mean return is 0.1054%, which is
higher than returns on Monday and Thursday (significant at 10%) and its standard
deviation is 1.51%, which is significantly lower than these two weekdays. Thus, we
conclude that Friday dominates Monday and Thursday for Hong Kong using the MV
rule. The results using the MV approach are summarized in Table 2. All results in
Table 2 use a 5% significance level. We find that Monday is dominated by four other
weekdays for Hong Kong, Japan, Malaysia, Singapore and Thailand.
However,
Monday is dominated by Friday for Taiwan only and is dominated by Tuesday and
Wednesday for Indonesia. Friday also dominates other weekdays for each of the
countries in the sample except Japan and Indonesia. In Japan, Friday is dominated by
Tuesday and Thursday. Overall, the findings from the MV criteria are inconsistent with
a diminishing weekday effect that has been suggested by recent studies.
----------------------Insert Table 2
-----------------------However, if normality does not hold then the MV rule may lead to paradoxical results.
Table 1 shows that weekday returns in the countries under consideration are nonnormal, as evidenced by higher kurtosis than normal and the highly significant K-S
10
statistics. Moreover, on the basis of the findings using the MV criterion, we cannot
conclude whether the investor’s preference between portfolios will lead to an increase in
wealth or, in the case of risk-averse individuals, whether their preference will increase
their utility without an increase in wealth. The SD approach can be used for this
purpose. To illustrate, we plot the CDFs of Monday and Friday returns in Figure 1 for
Indonesia and in Figure 2 for Malaysia. The CDF plots show that there is no FSD
between the Monday and Friday stock returns for Indonesia as their CDFs touch. For
Malaysia, the CDF plot for Friday is below that of Monday, thus Friday FSD Monday.
---------------------------Insert Figs. 1 & 2 here
---------------------------To verify this inference formally we apply the DD test to the series. Recall that the DD
test rejects the null hypothesis if none of the DD statistics is significantly positive and at
least one of the DD statistics is significantly negative (Davidson and Duclos, 2000). In
some situations, X dominates Y in a small range, but most risk-averse individuals prefer
Y to X. In this case, it is said that Y almost stochastically dominates X (Leshno and
Levy, 2002). Thus these DD test decision rules are too restrictive. To minimize a Type
II error of finding dominance when there is none, and to take care of the almost SD
effect, a conservative 5% cut-off point is used in this study. Using a 5% cut-off point, a
particular weekday is said to dominate the others if at least 5% of Ts are significantly
negative and no portion of Ts is significantly positive.
---------------------------Insert Figs. 3 & 4 here
---------------------------Figures 3 and 4 show the values of the first three orders DD statistics over the entire
distribution of returns in Indonesia and Malaysia respectively. These figures give a
visual representation of the DD test results. The plots show that in general the first-order
11
DD statistics, T1, moves from negative to positive along the distribution of returns. This
implies that Friday FSD Monday in the lower range of returns (negative returns) while
Monday FSD Friday in the upper range (positive returns). However, the difference
could be significant or insignificant. From the figures we found that no T1 is
significantly negative and positive for Indonesia while 10% of T1 is significantly
negative and no T1 is significantly positive for Malaysia. All second- and third-order
DD statistics (T2 and T3) are negative along the distribution of returns. Most are found
to be significant at the 5% level for Malaysia (50%-SSD, 63%-TSD) but not for
Indonesia (0%-SSD, 0%-TSD). Thus we conclude that Friday dominates Monday for
the first three orders for Malaysia but not for Indonesia at the 5% SMM significance
level. This infers that any risk-averse investor will prefer Friday to Monday in the
Malaysian stock market as they will increase their wealth as well as their expected
utility, subject to trading costs, by switching their investments from Monday to Friday.
------------------Insert Table 3
-------------------Table 3 shows the dominance among different weekday returns for each country in our
study using the DD test. Our results show that Monday stock returns are stochastically
dominated by at least one of the other weekday returns at the first-order in all countries
except Indonesia and Taiwan. For example, Tuesday returns FSD Monday returns in
Hong Kong, Japan and Singapore; Friday returns FSD Monday returns in Malaysia,
Singapore and Thailand; Thursday returns FSD Monday returns in Singapore and
Wednesday returns FSD Monday returns in Thailand. Moreover, our results also show
that Friday returns FSD both Tuesday and Thursday returns in Thailand. Monday
returns are stochastically dominated by Thursday returns in Japan and dominated by
Wednesday returns in Malaysia and Singapore at second- and third-order. Moreover,
12
Monday returns are dominated by all other weekdays by SSD and TSD in Taiwan. Thus
we conclude that there is a day-of-the-week effect in some Asian markets.
If we compare Tables 2 and 3 the number of cases where pair wise dominance is found
using the MV approach (42 pairs) is much larger than the number of cases where pair
wise dominance is found using the DD approach (17 pairs). Except for Taiwan, each
time that pair wise dominance was found with the DD test, it was also found with the
MV approach. Thus, while sometimes the conclusions drawn from the MV and SD
approaches are the same, there are several instances where they differ. Meyer (1987)
showed that the conclusion drawn from the SD and MV approaches could be the same
when the returns being studied belong to the same location-scale family. However, it is
not surprising that there are several cases where the two approaches give different
results. First, the MV criteria is only applicable when the decision maker's utility
function is quadratic or the probability distribution of return is normal while these
assumptions are not required by the SD criterion. Second, even when all the
distributions of the underlying returns being studied are normal, it is still possible that
the conclusion drawn from the SD approach will be different from that drawn from the
MV approach. Hanoch and Levy (1969) constructed an example in which decision
making based on the MV choice criteria contradicted that based on SD theory. Levy
(1989) showed that the MV efficient set is different from the SD efficient sets.
5.2. January effect
Table 4 presents summary statistics of monthly returns for each country. January returns
are positive, although not necessarily significant, in all countries for our sample except
Hong Kong. However, January does not have the highest returns of the month (except
in Japan and Thailand) and Hong Kong even has very low returns in January. Table 4
suggests that January returns exhibit a high standard deviation. Japan and Thailand are
13
the two countries with the highest mean and standard deviation for January returns. The
higher kurtosis than normal and the highly significant K-S statistics show that January
returns in each of the seven Asian countries in this study are non-normal.
-----------------------Insert Tables 4 & 5
------------------------Table 5 reports dominance between January and non-January returns using the MV
approach at the 5% level. There is no MV dominance for Japan and Thailand because
these two countries have the highest mean and standard deviation for their January
returns. Hong Kong has the most MV dominance pairs (6 pairs) with February, April,
May, July, November and December returns preferred to January returns. Singapore has
the least MV dominance pairs (2 pairs) with returns in February and April preferred to
January returns. For Taiwan, January dominates four months (August, October,
November and December) but is only dominated by February. In Indonesia, January
dominates August, September and October and is not dominated by any months.
-----------------------Insert Table 6
------------------------Table 6 reports the DD test results for January returns with each of the non-January
months for the whole sample period. We find that July returns FSD January returns in
Hong Kong. January returns are dominated by July, November and December at
second- and third-order in Singapore. For other markets, the January returns do not
dominate any of the non-January months and vice-versa by FSD, SSD or TSD. Thus,
we conclude that there is no monthly seasonality effect in the Asian markets except in
Hong Kong. This finding is contrary to Seyhun’s (1993) results for an earlier time
period. One reason why Seyhun (1993) finds a January effect but we do not using a
similar methodology is that our results could reflect the fact that investors have become
more aware of the effect and are timing their trades accordingly. Another reason could
14
be that Seyhun used U.S. data while we test for Asian markets.
Comparing Tables 5 and 6, with the MV approach there are 20 pair wise cases of
dominance while there are only four using the DD approach. While there is no evidence
of dominance for two countries (Japan and Thailand) using the MV approach, there is
no evidence of dominance for five countries (Taiwan, Japan, Malaysia, Indonesia and
Thailand) using the DD approach. July dominates January for Hong Kong using the MV
and DD approaches, but for Singapore, the SSD of July, November and December to
January is not picked up with the MV approach. The possible reasons for the different
results are the same as the day-of-the-week effect that are discussed above.
6. Conclusions
As discussed earlier, some relatively recent studies have suggested a weakening and/or
disappearance of the day-of-the-week effect in non-US markets over the course of the
1990s. However these findings are still tentative due to the differing statistical tools
used in the studies - some of which may have been mis-specified or suffer serious
measurement problems. As stock returns in Asian markets are not normally distributed
by nature, the parametric MV approach is of limited value. Another limitation is that
findings using the MV approach cannot be used to conclude whether investors’
portfolio preferences will increase wealth or, in the case of risk-averse investors, lead to
an increase in utility without an increase in wealth. Thus, this study has used the SD
approach, which is not distribution-dependent and can shed light on the utility and
wealth implications of portfolio preferences through exploiting information in higher
order moments to test for day-of-the-week and January effects in Asian markets.
The findings that Monday returns are dominated by other weekdays and Friday
dominates other weekdays, applying the MV criterion, suggests that the diminishing of
15
a weekday effect claimed by recent studies is questionable. Our DD test results for the
day-of-the-week effect also indicate there is FSD of other weekdays over Monday
returns in the Asian countries studied. Moreover, the existence of SSD and TSD in
some of the markets suggests that risk-averse individuals would prefer (or not prefer)
certain weekdays in some of the Asian markets to maximize their expected utility. The
existence of a weekday effect raises the possibility that investors could exploit this to
earn abnormal returns, although studies documented in Pettengill (2003) suggest that
such returns would typically be outweighed by trading costs. On the other hand, the DD
test results for the January effect suggest that it has largely disappeared from Asian
markets and that only in Singapore is January dominated by some other months at SSD
and TSD. The reason for the re-appearance of the day-of-the-week and disappearance of
the January effects from Asian markets is an interesting topic for future research.
Acknowledgments
We thank an anonymous referee for several helpful suggestions and Fang-Fah Lam for
research assistance. We alone are responsible for any remaining shortcomings.
16
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19
Table 1
Summary statistics of weekday returns for Asian countries (1988-2002)
Mon
Tue
Wed
Thu
Fri
Hong Kong
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
-0.0801
2.15
-2.41
29.31
0.14
0.0944c
1.48
-0.92
17.59
0.08
0.1148c
1.78
1.01
14.68
0.10
-0.0567
1.61
-0.89
5.75
0.09
0.1054c
1.51
0.71
4.29
0.08
Taiwan
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
0.0816
2.62
0.13
2.45
0.06
-0.1152
1.87
0.19
2.71
0.11
0.0013
1.93
-0.26
1.45
0.06
0.0223
1.96
-0.31
2.21
0.09
0.0983
1.90
-0.17
1.90
0.07
Japan
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
-0.1736a
1.60
-0.07
2.97
0.08
0.0382
1.35
1.04
10.93
0.07
0.0208
1.46
0.21
2.81
0.07
0.0189
1.37
-0.04
2.35
0.07
-0.0654
1.41
0.35
3.40
0.08
Malaysia
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
-0.1720a
1.88
1.85
26.28
0.13
0.0250
1.83
-1.30
69.33
0.16
0.1008c
1.42
0.52
8.94
0.09
0.0099
1.43
-1.11
10.42
0.10
0.1020c
1.36
1.13
13.97
0.10
Singapore
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
-0.1477b
1.72
0.34
13.72
0.12
0.0055
1.23
0.21
11.35
0.09
0.0597
1.31
-0.13
5.34
0.08
0.0548
1.25
-0.12
4.77
0.07
0.0916c
1.22
0.32
6.95
0.07
Indonesia
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
-0.0047
1.78
1.93
24.14
0.16
-0.0340
1.42
0.31
9.81
0.13
0.0015
1.73
0.75
18.34
0.13
0.1027
1.84
1.24
28.51
0.16
0.1538c
2.14
9.92
184.96
0.21
Thailand
Mean (%)
Std Dev (%)
Skewness
Kurtosis
K-Sa
-0.2333a
1.95
0.43
5.03
0.12
-0.0860
1.75
0.12
6.21
0.09
0.0936
1.82
-0.52
3.42
0.07
-0.0016
1.77
0.31
4.76
0.08
0.2430a
1.64
0.86
6.52
0.10
Notes: a, b, c denote significance difference from zero at the 1%, 5% and 10% level respectively.
20
Table 2
MV test results of day-of-the-week effect for Asian countries
Hong Kong
Tue>Mon
Wed>Mon
Thu>Mon
Fri>Mon
Tue>Thu
Fri>Thu
Taiwan
Fri>Mon
Fri>Wed
Fri>Thu
Japan
Tue>Mon
Tue>Fri
Wed>Mon
Thu>Fri
Thu>Mon
Fri>Mon
Tue>Wed
Tue>Thu
Malaysia
Tue>Mon
Fri>Tue
Wed>Mon
Fri>Wed
Thu>Mon
Fri>Thu
Fri>Mon
Wed>Tue
Wed>Thu
Singapore
Tue>Mon
Fri>Thu
Wed>Mon
Thu>Mon
Fri>Mon
Fri>Tue
Fri>Wed
Indonesia
Tue>Mon
Wed>Mon
Thailand
Tue>Mon
Fri>Thu
Wed>Mon
Thu>Mon
Fri>Mon
Fri>Tue
Fri>Wed
Notes: Results of the MV test are reported for day-of-the-week effect for seven Asian countries. The
sample period is January 1988 to December 2002. X >Y means X dominates Y by MV rule if μ x > μ y
and
σ x <σ y
at the 5% significance level.
21
Table 3
DD test results of day-of-the-week effect for Asian countries
Hong Kong
Taiwan
Japan
Malaysia
Singapore
Indonesia
Thailand
Tue >1 Mon
Tue >2 Mon
Tue >1 Mon
Wed >2 Mon
Tue >1 Mon
ND
Wed >1 Mon
Wed >2 Mon
Thu >2 Mon
Fri >1 Mon
Wed >2 Mon
Thu >2 Mon
Fri >2 Mon
Thu >1 Mon
Fri >1 Mon
Fri >1 Mon
Fri >1 Tue
Fri >1 Thu
Notes: Results of the Davidson and Duclos (DD) (2000) test of stochastic dominance are reported for
day-of-the-week effect for seven Asian countries. The sample period is January 1988 to December 2002.
The DD test statistics are computed over a grid of 100 daily different weekday portfolio returns. ND
denotes FSD, SSD & TSD do not exist; X >1 Y means X dominates Y at FSD, SSD & TSD; X >2 Y
means that X dominates Y at SSD & TSD at the 5% significance level.
22
Table 4
Summary statistics of monthly returns for Asian countries (1988-2002)
Hong
Kong
Taiwan
Japan
Malaysia
Singapore
Indonesia
Thailand
January
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
-0.0097
1.91
-0.65
3.69
0.13
0.2258c
2.16
0.02
2.20
0.11
0.1122
1.60
0.87
5.02
0.12
0.0502
1.75
0.51
6.10
0.12
0.0700
1.88
-0.12
5.58
0.11
0.1877b
1.73
-0.37
12.34
0.14
0.2685b
2.19
0.72
4.25
0.11
February
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
0.2586a
1.66
1.27
11.60
0.08
0.3400a
1.88
0.35
2.67
0.10
0.0325
1.16
-0.17
1.42
0.06
0.2406b
1.75
4.57
55.99
0.15
0.0924
1.34
3.89
42.83
0.10
0.0017
1.52
1.02
21.51
0.14
-0.0351
2.06
0.23
6.54
0.09
March
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
-0.0169
1.51
-0.57
2.80
0.09
0.0613
1.68
-0.02
1.99
0.06
-0.0314
1.56
0.49
2.37
0.07
-0.0674
1.06
-0.14
2.71
0.06
-0.0592
1.15
0.15
2.24
0.08
0.0711
1.31
1.80
15.49
0.14
-0.0565
1.39
0.06
1.35
0.06
April
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
0.0902
1.43
-0.41
5.35
0.09
0.0206
1.85
-0.15
0.69
0.05b
0.0683
1.49
-0.35
4.67
0.10
0.0780
1.35
-0.36
3.60
0.09
0.1396b
1.21
-1.10
10.23
0.07
0.0191
1.47
-0.77
28.26
0.15
0.1225
1.40
0.90
5.09
0.12
May
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
0.0630
1.66
-1.03
10.75
0.10
-0.1205
1.93
-0.47
1.99
0.09
0.0105
1.13
-0.02
1.75
0.07
0.0224
1.20
0.12
3.59
0.10
-0.0184
0.98
-0.18
1.87
0.08
0.1838b
1.36
0.05
6.32
0.15
-0.0841
1.77
0.26
6.04
0.10
June
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
-0.0082
1.94
-5.62
74.36
0.14
-0.0546
1.88
-0.57
2.54
0.08
-0.0535
1.26
0.15
0.83
0.06
-0.0168
1.16
-0.18
1.94
0.08
-0.0013
1.08
0.29
3.25
0.07
0.0728
1.31
1.96
13.51
0.14
0.0409
1.57
0.40
4.14
0.09
July
Mean (%)
StdDev (%)
Skewness
Kurtosis
0.0781
1.23
0.06
0.55
0.0271
2.12
0.09
1.14
-0.0005
1.31
0.18
1.53
-0.0003
1.14
-0.44
3.05
0.0143
0.96
0.28
1.98
-0.0607
1.07
-0.53
3.80
-0.0710
1.63
0.94
4.31
23
K-Sa
0.045c
0.07
0.07
0.09
0.05b
0.12
0.11
August
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
-0.2061b
1.81
-0.65
5.14
0.10
-0.1424
2.18
-0.15
1.68
0.08
-0.1216
1.58
0.10
2.30
0.07
-0.2115b
1.73
-0.29
5.81
0.15
-0.1824b
1.47
-0.97
4.10
0.11
-0.1331
2.42
-0.39
35.73
0.19
-0.1725
1.96
-0.43
5.66
0.09
September
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
-0.0156
1.62
-0.09
5.41
0.10
-0.2452b
1.87
-0.47
3.32
0.07
-0.1644b
1.54
-0.34
2.15
0.10
-0.1091
2.70
-0.02
33.81
0.22
-0.1290c
1.29
-0.32
7.45
0.11
-0.1995b
1.75
0.27
8.45
0.13
-0.1235
1.82
-0.07
3.70
0.09
October
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
0.2253c
2.22
0.17
17.79
0.14
-0.0936
2.30
-0.08
2.07
0.11
0.0277
1.56
1.47
12.23
0.09
0.0793
1.48
-1.35
16.41
0.11
0.1306
1.64
-0.65
10.43
0.12
-0.0132
1.81
0.18
9.97
0.16
0.0814
1.83
0.41
3.48
0.08
November
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
0.0135
1.47
0.07
1.52
0.08
0.1110
2.25
0.58
5.39
0.09
0.0225
1.46
0.30
3.46
0.09
-0.0050
1.44
-1.40
16.59
0.12
0.1231c
1.24
0.66
4.95
0.09
0.0316
1.56
0.67
7.53
0.15
-0.0681
1.80
-0.29
2.45
0.08
December
Mean (%)
StdDev (%)
Skewness
Kurtosis
K-Sa
0.1053
1.54
-0.56
4.00
0.09
0.1326
2.19
-0.03
2.19
0.09
-0.0369
1.36
-0.11
1.90
0.11
0.2799a
1.40
0.54
14.67
0.12
0.1869a
1.07
0.05
1.18
0.07
0.3573b
3.06
7.42
92.89
0.25
0.1733b
1.43
0.40
3.21
0.10
Notes: a, b, c denote significance difference from zero at the 1%, 5% and 10% level respectively.
24
Table 5
MV test results of January effect for Asian countries
Hong Kong
Taiwan
Japan
Malaysia
Singapore
Indonesia
Thailand
Feb > Jan; Apr > Jan; May > Jan; Jul > Jan; Nov > Jan; Dec > Jan
Feb > Jan; Jan >Aug; Jan > Oct; Jan > Nov; Jan > Dec
ND
Apr > Jan; Oct > Jan; Dec > Jan; Jan > Aug
Feb > Jan; Apr > Jan
Jan > Aug; Jan > Sep; Jan > Oct
ND
Notes: Results of the MV test are reported for January effect for seven Asian countries. The sample
period is January 1988 to December 2002. X>Y means X dominates Y by MV rule if μ x > μ y and
σ x <σ y
at the 5% significance level.
Table 6:
DD test Results of January effect for Asian countries
Hong Kong
Taiwan
Japan
Malaysia
Singapore
Indonesia
Thailand
Jul >2 Jan
Jul >1 Jan
ND
ND
ND
Nov >2 Jan
ND
ND
Dec >2 Jan
Notes: Results of the Davidson-Duclos (DD) (2000) test of stochastic dominance are reported for January
effect for seven Asian countries. The sample period is January 1988 to December 2002. The DD test
statistics are computed over a grid of 100 daily different month portfolio returns. ND denotes FSD, SSD
& TSD do not exist; X >1 Y is X dominates Y at FSD, SSD & TSD; X >2 Y is X dominates Y at SSD &
TSD at the 5% significance level.
25
1.2
1
CDF
0.8
0.6
0.4
0.2
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
Returns
Monday
Friday
Figure 1
CDF of Monday and Friday returns for Indonesia
1.2
1
CDF
0.8
0.6
0.4
0.2
0
-0.1 -0.1 -0.1 -0.1 -0.1
-0
-0
-0
0.01 0.03 0.04 0.06 0.08 0.09 0.11 0.12 0.14 0.16 0.17 0.19
Returns
Monday
Friday
Figure 2
CDF of Monday and Friday returns for Malaysia
26
1.5
1
0.5
DD Statistics
0
-0.5
-0.1 -0.1 -0.1
-0
-0
0.02 0.05 0.08 0.1 0.13 0.15 0.18 0.2 0.23 0.25 0.28 0.31 0.33 0.36 0.38
-1
-1.5
-2
-2.5
-3
-3.5
Re turns
T1
T2
T3
Figure 3
DD statistics of Monday and Friday returns for Indonesia
3
2
DD Statistics
1
0
-1
-0.1 -0.1 -0.1 -0.1 -0.1
-0
-0
-0
0.01 0.03 0.04 0.06 0.08 0.09 0.11 0.12 0.14 0.16 0.17 0.19
-2
-3
-4
-5
-6
Returns
T1
T2
T3
Figure 4
DD Statistics of Monday and Friday returns for Malaysia
27