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Chinese institutional investors and Kamara’s Monday effect
Gerhard Klinga
a
University of Southampton
THIS IS NOT THE FINAL (POST-REVIEW) VERSION
YOU FIND THE FINAL VERSION HERE:
Kling, G. (2005) Chinese institutional investors and Kamara’s Monday effect,
Journal of Emerging Markets 10(3), 40-47
Mondays exhibit lower stock returns than Fridays, which is known as the Monday
effect. Kamara (1997) argued that the Monday effect disappeared due to institutional
trading and the introduction of derivative instruments. My paper tests this hypothesis
using Chinese data. As institutional investors are unimportant and arbitrage
possibilities limited, the Monday effect should not disappear – but I find the opposite.
Modeling the conditional expected utility of an individual investor, I show that the
trading strategy, “sell on Monday and buy next Friday”, yielded positive outcomes.
Hence, trading incentives existed and led to the disappearance of the Monday effect in
China.
JEL classifications: K22, G28, C22
Keywords: Monday effect, China, anomalies, institutional investors
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I. Introduction
Since Fama (1970) proclaimed the Efficient Market Hypotheses, a great deal of
research was devoted to investigate the randomness of stock price movements to
confirm market efficiency. One strand of the literature focused on all kinds of
calendar anomalies in stock market returns: the January effect and the Monday effect
are the most prominent examples of this research. In particular, French (1980) showed
that the S&P 500 Index exhibited higher returns on Fridays than on Mondays during
the period from 1953 to 1977. Gibbons and Hess (1981) and Smirlock and Starks
(1986) reported similar results. The day of the week effect was also confirmed for
other stock markets. Jaffe and Westerfield (1985) examined the Australian, Canadian,
Japanese and UK stock exchanges and uncovered that in Japan and Australia stock
returns were lowest on Tuesdays. Solnik and Bousquet (1990) demonstrated a strong
and persistent negative return on Tuesdays in the case of the Paris Bourse, and Barone
(1990) found largest declines in Italian stock prices on Tuesdays.
When market returns follow seasonal patterns, the assumption of weak market
efficiency is violated, as by observing past returns future price movements become
predictable, and investors could make extraordinary profits. Kamara (1997) stated that
seasonal effects like the Monday effect disappeared over time due to the introduction
of derivative instruments that facilitated arbitrage and the increasing importance of
institutional investors. The Chinese example offers the possibility to test Kamara’s
hypothesis, for institutional investors were nearly unimportant and derivative
instruments were not developed. If Kamara’s hypothesis were true, the Monday effect
should not disappear in China. Haugen and Jorion (1996) provided an alternative
explanation for the disappearance of calendar effects. They argued that market
participants could learn from past experience and exploit seasonal patterns. Due to
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such arbitrage strategies, seasonal effects should break down. As derivative
instruments were lacking in China, true arbitrage (simultaneous trade on spot and
futures market) was not possible – but risky trading strategies that exploit seasonal
patterns could exist.
My paper is organized as follows: first, I briefly describe the importance of
institutional investors and derivative trading in China; second, descriptive statistics
show daily patterns of returns; third, a modified version of Kamara’s regression model
determines the time trend of the Monday effect. To evaluate whether the trading
strategy “sell on Monday and buy next Friday” promised positive outcomes, I derive
the conditional expected utility of a risk-averse investor. An extended GARCH
approach reveals that this trading strategy was successful and could contribute to the
disappearance of the Monday effect in China.
II. Institutional investors and derivatives in China
There are several authorized closed-end investment funds, and open-end funds were
recently introduced. Yet other forms of institutional investment like pension funds or
managed portfolios of insurance companies are nearly negligible. Generally, one can
state that institutional investors in China play a minor role compared to other stock
markets. The relation between institutional investors’ assets to gross domestic product
can be regarded as proxy concerning the relevance of institutional trading. Based on
World Bank data for 2001, Chinese institutional investors’ assets reached 19% of
GDP; this figure was lower compared to Hungary (26%), Czech Republic (32%), and
further developed Asian market, i.e. South Korea (82%). Consequently, even in
smaller stock markets (in terms of market capitalization), institutional investors are
more relevant than in China. Furthermore, Chinese stock exchanges reopened just
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about fifteen years ago; hence, institutional investors are in an infant stage compared
to their foreign counterparts who could accumulate experience and gain importance
over several decades.
Derivative markets are underdeveloped in China – but this might change soon,
as the Chicago Mercantile Exchange (CME), the largest U.S. futures exchange, and
the Shanghai Stock Exchange (SSE) announced on 2nd March 2005 that they signed a
“Memorandum of Understanding” to share information regarding the development of
derivatives in China. Even prior to this agreement, the CBOE started trading China
Index Futures in October 2004. However, Chinese investors hardly had access to
these hedging tools. Consequently, derivative instruments could not be used to benefit
from seasonal patterns in stock returns.
III. Data and descriptive findings
The SSE was founded on 26th November 1990 and began operations on 19th
December 1990. The SSE is the largest stock market in terms of the number of listed
companies and market capitalization in China and it is a non-profit-institution
governed by the China Securities Regulatory Commission (CSRC). To analyze daily
effects in stock returns, I use the market index of the SEE (A-share market) from
December 1990 to December 2002. Accordingly, the dataset consists of about 630
observations for every day of the week. Table 1 shows descriptive statistics for the
five trading days and highlights that Friday was the most successful trading day with
an average index return of 0.36%. Contrarily, Tuesdays and Mondays were weak days
and exhibited a decline of 0.12% and 0.02% respectively. Negative returns on
Tuesdays are in line with former empirical research1 – but to ensure comparability
1
I refer to Barone (1990), Solnik and Bousquet (1990), and Westerfield (1985).
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with Kamara’s Monday effect, I focus on the difference between Mondays and
Fridays, albeit results concerning the comparisons between Tuesdays and Fridays are
similar.
IV. Empirical analysis
Kamara’s regression model with modifications
To detect the Monday effect, Kamara (1997) regressed index returns on a set of
dummy variables for every day of the week. I modify this approach slightly by using
the difference of market returns on Fridays and Mondays Rf-m as dependent
variable.2 A positive value indicates that the Monday effect exists, as returns on
Mondays are higher than on the following Fridays. The advantage of this modified
regression is that the time trend t of the return difference can be estimated directly.
Kamara’s (1997) specification with five day-dummies does not allow a simple
regression approach and would require a huge set of interaction terms, which might
cause multicollinearity. To determine the order of the polynomial (the time trend), I
run different specification and carry out Ramsey RESET tests.3
p
R f m  R f  Rm      j t j  et
(1)
j 1
Table 2 shows the outcomes of regression (1), and Ramsey RESET tests indicate that
a time trend with p equal to four should be assumed; thus, a linear time trend is not
able to capture the systematic change of the Monday effect over time. Breusch-Pagan
2
This follows Wingender, Lucey, and Pettengill (2005); however, they supposed a linear time trend,
which can be generalized by allowing an arbitrary polynomial with respect to time t.
3
Ramsey RESET tests are applied to uncover omitted variable bias – but are also very useful to detect
non-linearities in regression models.
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tests detect heteroscedasticity, and hence table 2 reports robust p-values based on the
Huber-White sandwich estimator. To test for first-order autocorrelation in residuals, I
apply Durbin-Watson tests, which do not confirm serial dependencies. As Ramsey
RESET tests cannot reject the specification of the model with p equal to four, I select
this specification of the time trend, and figure I depicts the predicted course of the
Monday effect over time. To illustrate whether the predicted time trend is significant,
figure I plots the 95% confidence interval. The results suggest that the Monday effect
existed only shortly after the reopening of the SSE – but disappeared in 1994. As
institutional trading or access to derivative instruments did not play a role in China
during this period, I cannot support Kamara’s hypothesis. In contrast, Haugen and
Jorion (1996) argumentation that investors learn over time to exploit anomalies might
fit better to the Chinese market.
Arbitrage incentives of a Chinese risk-averse investor
The Monday effect can be exploited by a simple trading strategy, namely sell stocks
on Monday and by them back on Friday after four days. Due to the time gap between
both transactions, one cannot call such a strategy real arbitrage, as investors have to
take risk, i.e. political events might occur between Monday and Friday, which could
make the strategy obsolete. I construct a simple stylized model to assess whether
Chinese investors could use such a trading strategy to exploit the Monday effect. If I
cannot find evidence that such a strategy was profitable for a risk-averse investor,
Haugen and Jorion (1996) learning argument could not be confirmed, as investors
would not benefit from the Monday effect. The vNM utility function of a risk-averse
investor is supposed to be a negative exponential utility function with the coefficient
of absolute risk aversion a. When I assume that returns are normally distribution, it is
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straightforward to show that by applying the expectations operator, investors
maximize their expected utility by maximizing the expected return of the trading
strategy and minimizing its variance.4 Justified by my finding that the correlation
coefficient between returns on Mondays Rm and Fridays Rf is 0.0684, I can assume
that both returns are uncorrelated with each other. As the Monday effect changed over
time, distributions and moments of returns are conditional variables that depend on
time t. Moreover, I account for transaction costs c. The conditional expected utility of
a risk-averse investor that sells on Mondays and buys on Fridays can be written as
follows.
1
Et U ( R f  Rm   Et R f  Rm   c  a  Vart R f   Vart R f
2
Covt R f , Rm   0

R f  Rm  N t  t ,  t2

(2)
(3)

(4)
Thus far, I model the impact of time on the mean equation (see equation 1) and
predicted the conditional mean t over time. To discuss whether the expected utility is
positive, and thus an incentive to exploit the Monday effect existed, I also have to
quantify the impact of time on the conditional volatility t2. Accordingly, I estimate a
two equation model consisting of the mean equation (1) and the following extended
GARCH (p, q) model that accounts for time trend up to order l.5 Maximum likelihood
4
By assuming that returns are normally distributed and investors have a negative exponential utility
function, one obtains a mean-variance optimizing behavior. This simple model allows estimating the
expected utility by maximum likelihood.
5
The model fit reaches highest values when I assume a GARCH(1,1) specification and time trend with
order four (l=4).
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estimation provides estimates of this system of equations; all coefficients of the
conditional variance equation are highly significant with p-values of 0.000.
Vart R f   Vart R f         k t   t k    t k   t
p
q
k 1
k 1
l
2
t
k
k 1
(5)
Based on predicted conditional moments, one can derive values of the conditional
expected utility. Figure II depicts the conditional expected utility and shows that
trading incentives existed for reasonable values of a, the absolute coefficient of risk
aversion.6 When transaction costs enter the mean equation, the trading incentives are
lower; however, expected utility is still positive for the Monday-Friday strategy for
alleged costs of 0.5%. As Tuesdays exhibited lowest average returns, one could also
consider the Tuesday-Friday trading strategy. In this case, transaction cost could reach
0.8%, and trading incentives would still exist.
V. Conclusion
In spite of the low importance of institutional investors in China and the lack of
derivative instruments that could facilitate arbitrage, I confirm that the Monday effect
disappeared over time. My findings reject Kamara’s hypothesis that the disappearance
of the Monday effect is related to the increasing importance of institutional trading
and the introduction of derivative instruments. Although derivative instruments were
not available for Chinese investors, they could have used a simple trading strategy to
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Gertner (1993) and Metrick (1995) provided estimates of the coefficient of absolute risk aversion that
depend on income. Using gross national income figures (IMF data) from 1993 to 2003, suggested
values for the coefficient a can be derived. Gertner’s (1993) estimates are in the range from 0.29 and
0.42 – but Metrick’s (1995) predictions are much lower (from 0.06 to 0.09). As both studies did not
focus on China, I use 0.5 as an upper bound of the coefficient a. Hence, my estimates do not overstate
expected utility.
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benefit from the Monday effect, namely “sell on Mondays and buy on the following
Friday”. Due to the time gap, this strategy comes with a cost, namely risk measured
by the volatility of this strategy. By assuming a risk-averse investor with a negative
exponential utility function and normally distributed daily stock returns, I derive the
conditional expected utility of this trading strategy. The predicted conditional
expected utility exhibited positive values and hence indicated that investors could
have used this trading strategy to benefit from the Monday effect. Based on my
empirical findings, I confirm that Chinese investors had incentives to exploit the
Monday effect and were hence responsible for the disappearance of this stock market
anomaly.
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VI. References
Barone, E., 1990, “The Italian stock market: Efficiency and calendar anomalies,”
Journal of Banking and Finance 14, 483-510.
Fama, E.F., 1970, “Efficient capital markets: A review of theory & empirical work,”
Journal of Finance 25, 383-417.
French, K., 1980, “Stock returns and the weekend effect,” Journal of Financial
Economics 8, 55-69.
Gertner, R., 1993, “Game shows and economic behavior: Risk taking on `Card
Sharks’,” Quarterly Journal of Economics 108, 507-521.
Gibbons, M. and P. Hess, 1981, “Day of the week effects and asset returns,” Journal
of Business 54, 579-596.
Haugen, R. and P. Jorion, 1996, “The January effect: Still there after all these years,”
Financial Analysts Journal 52, 27-31.
Jaffe, J. and R. Westerfield, 1985, “Patterns in Japanese common stock returns,”
Journal of Financial and Quantitative Analysis 20, 261-272.
Kamara, A., 1997, “New evidence on the Monday seasonal in stock returns,” Journal
of Business 70, 63-84.
Metrick, A., 1995, “A natural experiment in `Jeopardy!’,” American Economic
Review 85, 240-253.
Smirlock, M. and L. Starks, 1986, “Day of the week and intraday effects in stock
returns,” Journal of Financial Economics 17, 197-210.
Solnik, B. and L. Bousquet, 1990, “Day of the week effect on the Paris Bourse,”
Journal of Banking and Finance 14, 461-468.
Wingender, J., Lucey, B., and G. Pettengill, 2005, “Testing Kamara’s Monday effect
with international data,” working paper.
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Table 1: Descriptive statistics
This table shows average market returns, standard deviations, extreme values, and the
number of observations for every trading day.
Monday
Tuesday
Wednesday
Thursday
Friday
Mean
-0.0002
-0.0012
0.0019
0.0022
0.0036
Standard deviation
0.0309
0.0233
0.0270
0.0494
0.0236
Minimum
-0.1308
-0.1639
-0.1071
-0.1064
-0.0718
Maximum
0.3346
0.1179
0.2990
1.0527
0.2137
Observations
629
633
635
636
628
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Table 2: Regression results for different time trend specifications
The regression (1) is estimated with different specifications concerning the time trend
(values of p). To correct for heteroskedasticity, I report robust p-values in parentheses.
Shaded cells indicate significant coefficients on the 5% level of significance.
Constant
t
t2
t3
t4
t5
p=1
p=2
p=3
p=4
p=5
0.0087
0.0093
0.0047
-0.0045
-0.0104
(0.030)
(0.351)
(0.381)
(0.264)
(0.032)
-0.0000
-0.0000
0.0001
0.0004
0.0006
(0.011)
(0.799)
(0.248)
(0.027)
(0.016)
-
9.09e-9
-3.34e-7
-2.42e-6
-5.51e-6
(0.011)
(0.216)
(0.022)
(0.040)
-
3.64e-10
5.52e-9
1.86e-8
(0.159)
(0.022)
(0.083)
-
-4.10e-12
-2.75e-11
(0.024)
(0.136)
-
1.49e-14
-
-
-
-
-
-
(0.192)
Adjusted R2
0.00
0.00
0.00
0.01
0.01
Observations
627
627
627
627
627
Ramsey RESET 1.81
2.23
2.16
1.81
2.08
(0.144)
(0.084)
(0.091)
(0.143)
(0.101)
87.82
78.79
173.26
205.60
159.95
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
2.542
2.533
2.385
1.920
1.782
(0.111)
(0.112)
(0.123)
(0.166)
(0.182)
Breusch-Pagan
Durbin-Watson
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Figure I: Predicted Monday effect over time
Based on regression (1), this figure plots the 95% confidence interval for the predicted
time trend of the return difference between Fridays and Mondays. If upper and lower
boundaries are positive, a significant Monday effect exists, as returns are higher on
Fridays than on Mondays.
0.025
0.02
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
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Figure II: Predicted conditional expected utility
Based on two-equation maximum likelihood estimation, I predict the conditional
expected utility for a risk-averse investor that sells on Monday and buys on Friday.
Even if transaction costs are assumed, the expected utility stresses the existence of
trading incentives.
0.006
0.004
0.002
0
-0.002
-0.004
-0.006