Day-of-the-week effect in the Taiwan Interbank Call Loan Market
Chin-Shan Hsieh1
Department of International Business
Kao Yuan University
No.1821, Chung-Shan Rd., Lu-Chu County, Kaohsiung County 821
Taiwan (R.O.C.)
Cheng-Te Chen2
Department of Management information System
Far East University
No.49, Chung Hua Rd., Hsin-Shih, Tainan County 744
Taiwan (R.O.C.)
Abstract
This study uses stochastic dominance theory with and without risk-free asset, which is distribution-free, to
examine whether the day-of-the-week effect exists in the Taiwan Interbank Call Loan Market. The main results
in our study indicate that the Tuesday returns in the all various maturities dominate on all the other trading days
of the week. Our particular finding in Taiwan interbank call loan market is that Monday returns of one week and
two weeks of maturity are dominated by all non-Monday returns. These results imply that financial institution
can decide an optimal proportion of investment in risky assets and risk-free assets.
JEL classification: F31; G14; G15
Keywords: Stochastic Dominance theory; Day-of-the-week effect
1. Introduction
In the last several decades of financial research, one of the particular return patterns of
financial assets is the day-of-the-week effect. That is, returns of equity assets shown to be
lower on Monday as compared to other days of the week (Cross, 1973; French, 1980; Harris,
1986). Ritter and Chopra (1989), Lakonishok and Maberly (1990), DeFusco et al. (1993),
Al-Loughani and Chappell (2001) and Tonchev and Kim (2004) find the negative average
Monday return in the US and some emerging stock markets. Similarly, Stickel (1982) and
Roll (1983) study in futures prices and Gibbons and Hess (1981) investigate in Treasury bills
returns show that the day-of-the-week effect.
McFarland et al. (1982) have first documented the day-of-the-week effect in the foreign
exchange market. Their empirical results show that Monday and Wednesday offer higher
average returns than Thursday and Friday, a finding also later confirmed by So (1987) and
1
2
u9327901@ccms.nkfust.edu.tw
nike@cc.feu.edu.tw
Cornett et al. (1995)
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exchange markets are generally higher on Tuesday and Wednesday and lower on Friday.
Yamori and Kurihara (2004) find that the day-of-the-week effect exists in the 1980s for some
currencies, but disappears for almost all currencies in the 1990s in the New York foreign
exchange market. Recently, Ke, Chiang and Liao (2007) indicate that higher returns appear on
the first three days of the week across different trading-day regimes in the Taiwan foreign
exchange market.
An earlier literature in interbank call loan market, including papers by Spindt and
Hoffmeister (1988), Griffiths and Winters (1995), and Hamilton (1996), that demonstrated
calendar day effects in brokered fed funds related to the maintenance period for reserve
requirements and also to holidays and quarter ends. Griffiths and Winters (1997) found such
effects in the interest rate on repurchase agreements on general Treasury collateral. Lee
(2003a) found that the overnight Eurodollar bid rate exhibits day-of-the-maintenance-period
effects similar to but smaller in magnitude than those in the brokered federal funds rate in
1984–1997. Cyree et al. (2003) identified calendar day effects using the overnight London
interbank offer rate in the 1991–1995, but not in the previous five years when Eurodollar
borrowings were subject to a 3 percent reserve requirement. More recently, Demiralp,
Preslopsky and Whitesell (2006) investigates the overnight interbank markets for brokered
federal funds, Eurodollars, and repurchase agreements by developing a new time series
importantly representing direct trades of federal funds. The result in contrast to Lee (2003a,b),
they do not find significant end-of-maintenance-period effects in Eurodollars.
The goal of the study is to investigate if there is day-of-the-week effect in the Taiwan
interbank call loan market. We use daily data on various three maturities from 2005 through
2008. Earlier studies use the regression model to test whether the day-of-the-week effect
exists in the interbank call loan market (e.g., Lee, 2003a; Cyree et al., 2003; Demiralp,
Preslopsky and Whitesell, 2006). We are the first to study and employ the stochastic
dominance (SD) theory to examine day-of-the-week effect in the interbank call loan market.
The first important feature of SD is that it is distribution-free. SD rules are distribution-free in
the sense that the distribution of returns can be any type of distribution. Second, the advantage
of SD is that it makes minimum assump
t
i
onso
fi
nve
s
t
or
’
sut
i
l
i
t
yf
unc
t
i
on.Fore
xa
mpl
e
,
first-degree stochastic dominance (FSD) and first-degree stochastic dominance with risk-free
assets (FSDR) assume only that investors prefer more return to less; i.e., investor utility
function thus can be concave, linear or convex. In contrast, many asset pricing models, like
the well-known capital asset pricing model (CAPM), are derived on the assumption that the
investor utility function must be concave or on the normality assumption of returns. In
addi
t
i
on,SD me
t
hodol
ogyi
se
nt
i
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si
ta
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owspa
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tofi
nve
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’mone
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e
di
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the stock portfolio (risky assets) and part of their money to be invested in the risk-free assets.
That is, our methodology utilizing SD theory enables financial institution to have a better tool
for assets allocation.
The main results in our study indicate that the Tuesday returns in the all various
maturities dominate on all the other trading days of the week by the third-order SD with or
without risk-free assets. Our particular finding in Taiwan interbank call loan market is that
Monday returns of one week and two weeks of maturity are dominated by all non-Monday
returns. These results imply that financial institution can decide an optimal proportion of
investment in risky assets and risk-free assets. The rest of this paper is organized as follows:
Section 2 brief introduction of Taiwan interbank call loan market. Section 3 describes the data
and methodology. Section 4 presents and explains the empirical results. The final section is
the conclusions.
2. Brief Introduction of Taiwan Interbank Call Loan Market
In October 1991, the Taiwan Interbank Call Loan Center was reorganized into the
Interbank Money Center with broadened membership that includes investment and trust
companies, bills finance companies, the Postal Savings Bureau and credit cooperatives. At the
same time, the business scope of the Interbank Money Center was enlarged to include the
dealing of short-term financing with maturity till 180 days. As of December 31, 2006, the
total annual trading value of inter-bank call loan market reached NT 20,238.3 billion.
In addition to the trading of short-term bills, inter-bank call loans also play a major role
in Taiwan’
s money market. The Bankers Association of the Republic of China formally
established the Inter-Bank Call Loan Center to deal with the brokerage of call loan
transactions in 1980. The call loan market was mainly supplying liquid funds for margin
borrowing on the stock market.
3. Data and methodology
Call loan rate returns are defined as Rt = (Pt –Pt-1)/ Pt-1, where Pt is the Taipei Interbank
offered rate. Daily data of three maturities consisting of one week, two weeks and one month
are taken from the Taiwan Interbank Call Loan Center. The sample period contains 685
trading days from October 2005 to June 2008.
Table 1 shows the means and standard deviations on the various maturities by day of the
week. The highest returns appear on Tuesday for all maturities, and the lowest returns
appear on Thursday for most maturities. In addition, the highest standard deviation appears on
Tuesday for all maturities, and the lowest on Wednesday for all maturities. The results imply
day-of-the-week effect in the Taiwan interbank call loan market.
We also investigate the normality of the daily returns assumption for the various
maturities using the Kolmogorov-Smirnov (K-S) test. The results show that the daily returns
within the week do not follow a normal distribution4. As a result, it is more appropriate to use
the SD theory to examine the day-of-the-week effect.
Table 1
Means and Standard Deviations in Parentheses (in percent) for Daily Returns
on the various maturities
Monday
Tuesday
Wednesday
Thursday
Friday
One week
0.0592%
(2.4371)1
0.3419
(4.1216)
0.0072
(0.8300)
-0.0259
(0.8431)
0.0706
(2.5901)
Two weeks
0.0661
(2.5700)
0.3894
(4.2682)
-0.0244
(0.4567)
-0.0115
(0.7693)
0.0310
(2.2488)
One month
0.1757
(2.2884)
0.2867
(2.7361)
-0.0110
(0.5670)
-0.0380
(0.7529)
-0.0113
(1.8122)
1. The standard deviation of returns is reported in parentheses.
The stochastic dominance (SD) theory provides a simple method of selecting risky
alternatives5. Suppose an investor has to choose between two risky assets, A1 and A2, and the
return on asset A1 always exceeds that on asset A2. Then, as long as investors prefer more
returns to less, no investor would choose asset A2 because asset A1 would always provide a
higher return. Further, denote by Ui for i = 1, 2, 3 the utility function class, where U1
includes all u, with u' > 0; U2 includes all u with u'> 0, and u" < 0; and U3 includes all u with
u'> 0, u" < 0 and u"' > 0. This illustration is a special case of the first-degree stochastic
dominance (FSD). Generally, asset A1 dominates asset A2 by FSD, if the cumulative density
function (CDF) of A1 lies, roughly speaking, to the right of the CDF of A2. That is, with the
distribution of G1 (asset A1), the chance of earning a higher return is always greater than with
the distribution of G2 (asset A2), regardless of whether investors like or dislike risks.
Formally, the first-degree stochastic dominance (FSD) means that when all the all i
nve
s
t
or
s
’
utility function belongs to U1, if and only if:
G1 ( x) G2 ( x)
for all possible x
The preference when G1 a lies entirely to the right of G2 is obvious.
(1)
When two CDFs
cross, the other factor must be considered to establish the successive dominance. If investors
are risk-averse then second-degree stochastic dominance (SSD) can be adopted. Formally,
the second-degree stochastic dominance (SSD) means that when all the all investors utility
function belong to U2, if and only if:
x
[G (t ) G (t )]dt 0
2

where
x
G (t )dt

2
1
x
G (t )dt
and
1

for all possible x
(2)
are the areas under G1 and G2, respectively.
Hence,
SSD allows CDFs to cross by some amounts as long as the area under the G1 is always less
than that under G2. Figure 1 shows that, when the conditions of equation (2) are met, G1 lies
far enough to the right of G2 that asset A1 is preferred to asset A2, because the expected utility
gain from the positive area to the left of x1 exceeds the reduction in the expected utility loss
between x1 and x2. Finally, third-degree stochastic dominance (TSD) means that when all the
all investors utility function belong to U3, if and only if: 3
x
t
[G ( z) G ( z )]dzdt 0
 
where
x
t
G2 ( z)dzdt
 
and
2
1
x
t
G1 ( z )dzdt
 
for all possible x
are the areas under
x
G (t )dt , respectively.

1
Figure 1. G1 preferred to G2 with risk aversion
. Figures 1 and 2 are slightly modified from Levy (1998, p. 146-47).
3
(3)
x
G (t )dt

2
and
When borrowing and lending at the risk-free rate is permitted, much stronger rules,
called stochastic dominance with risk-free asset rules (SDR), can be employed.
Consider a
portfolio of one risky asset and one riskless asset, with % of the i
nve
s
t
or
’
s money is
invested in the risky asset A1 and (1 %) is borrowed or lent at the riskless rate; the
portfolio return,
Rp ,
is then computed as the weighted sum of two assets:
R p (1 )rf A1 , where r f is the riskless rate.
distribution function of R p .
Furthermore, let F be the cumulated
Next, compare the two distributions G1 and G2 as shown in
Figure 2. Clearly, neither G1 nor G2 dominates the other by FSD.
Nevertheless, it is
possible rotate G1 about the point ( r f , G1 (rf ) ) and obtain G1 which dominates G2 by FSD;
therefore G1 dominates G2 by first-degree stochastic dominance with riskless rate (FSDR).
Formally, let G1 and G2 be the CDFs of two risky assets, A1 and A2.
CDF of R p , where : R p (1 )rf A1 and  is a constant.
Also, let G1 be the
Then, G1 dominates G2 by
FSDR if and only if
G1( x) G2 ( x)
for all possible x
(4)
Similar to SSD, G1 dominates G2 by second-degree stochastic dominance with riskless rate
(SSDR) if and only if:
x
[G (t ) G (t )]dt 0
2

1
for all possible x
(5)
Similar to TSD, G1 dominates G2 by third-degree stochastic dominance with riskless rate
(TSDR) if and only if:
x
t
[G ( z) G ( z )]dzdt 0
 
2
1
for all possible x
(6)
G2
G1
G1ω
Figure 2. G1 and to G2 intersect but G1,β dominate G2
4. Empirical results
This study uses SD rules to examine the day-of-the-week effect. That is, we test the null
hypothesis that returns on all weekdays are equal. The empirical study uses a version of the
stochastic dominance algorithm introduced and developed by Levy and Kroll (1979), Levy
and Sarnat (1985) or Levy (1992). That is, the FSD, SSD, TSD, FSDR, SSDR and TSDR
criteria are employed to test the day-of-the-week effect. The annual risk-free assets return
during our study period was ranging from 1.89% to 2.735%, which is used to conduct the
FSDR, SSDR and TSDR tests.
Using the weak assumption ( U 
>0)oni
nve
s
t
or
s
’p
r
e
f
e
r
e
nc
e
s
,t
hepe
r
f
or
ma
nc
eofthe
weekdays cannot be distinguished, i.e., the FSD (without lending and borrowing at a risk-free
interest rate) efficient sets for one week. Allowing investors to borrow and lend money at a
risk-free interest rate although can reduce the size of the FSDR efficient sets, but the
performance of Tuesday, Wednesday and Friday still cannot be distinguished when the FSDR
rule is used to test the dominance relationship between them for the one week of maturity.
Thus, sharper decision rules are required to distinguish among weekdays for the one week of
maturity. The FSD, SSD, TSD, FSDR, SSDR and TSDR efficient sets of various maturities
are shown in Table 2.
Table 2
The day-of-the-week effect for the various maturities
one week
FSD2 SSD TSD
+1
Tuesday
+
Wednesday +
Thursday
+
Friday
+
Monday
- + +
+ +
- - -
two weeks
one month
FSDR SSDR TSDR
FSDR SSDR TSDR
FSDR SSDR TSDR
FSD SSD TSD
FSD SSD TSD
rf 1%3 rf 1% rf 1%
rf 1% rf 1% rf 1%
rf 1% rf 1% rf 1%
+
+
-4
-5
+
+
-
+
-
- - + + +
+ + +
+ + + - -
+
-6
-7
+
+
-
+
-
- - + + +
- - - - + - -
+
+
+
-
1. Efficient sets (winner) marked by "+", inefficient sets (loser) marked by "-".
2. FSD: first-degree stochastic dominance, SSD: second-degree stochastic dominance, TSD: third-degree
stochastic dominance, FSDR: first-degree stochastic dominance with risk-free asset, SSDR: second-degree
stochastic dominance with risk-free asset, TSDR: third-degree stochastic dominance with risk-free asset.
3. r f is the annual returns on risk-free assets.
4. Tuesday dominates Wednesday at annual risk-free rate, rf 1% in one week.
5. Tuesday dominates Thursday at annual risk-free rate, rf 1% in one week.
6. Tuesday dominates Wednesday at annual risk-free rate, rf 1% in two weeks.
7. Tuesday dominates Thursday at annual risk-free rate, rf 1% in two weeks.

Assuming risk aversion ( U 
> 0 and U 
< 0), which most economists accept, different
findings are revealed: the performance of Tuesday and Wednesday dominate returns on all the
other trading days of the week for the one week of maturity efficient set when the SSD rule is
used to examine the dominance relationship among weekdays. The other maturities also show
the Tuesday is an efficient set. For example, the returns on Tuesday dominate the returns on
all the other trading days of the week for the SSD efficient sets of the one month of maturity.
The results are much stronger when investors are allowed to borrow and lend money at
a risk-free interest rate. As noted above, rf denote the risk-free interest rate. The results of the
SSDR efficient set for various maturities exhibit that Tuesda
y
’
sr
e
t
ur
nsout
pe
r
f
or
mthe returns
on all the other trading days of the week. Note that the size of SSDR efficient set is a function
of risk-free interest rate. For rf > 1%, the SSDR efficient sets of the one and two week of
maturities display that Tues
da
y
’
sr
e
t
ur
nsoutperform the returns on all the other trading days
of the week.



Assuming investor’
s expected utility function belongs to U 
> 0, U 
< 0 and U 
>0,
the performance of Tuesday and Wednesday dominate returns on all the other trading days of
the week for the one week and two weeks of maturity efficient set when the TSD rule is used
to examine the dominance relationship among weekdays. On one month of maturity, the
returns on Tuesday dominate the returns on all the other trading days of the week for the TSD
efficient sets.
+
-
5. Conclusions
This study employs the distribution-free stochastic dominance theory to examine the
day-of-the-week effect of three types of maturity in the Taiwan Interbank call loan market for
the period, 2005–2008. Our findings can be summarized as follows.
First, our findings indicate that the Tuesday returns in the all various maturities
dominate on all the other trading days of the week. Secondly, our particular finding in Taiwan
Interbank call loan market is that Monday returns of one week and two weeks of maturity are
dominated by all non-Monday returns. Thirdly, the results also show that allocating part of
financial institution’fund in risk-free assets is useful in distinguishing returns among various
trading days of the week. These results imply that financial institution can decide an optimal
proportion of investment in risky assets and risk-free assets.
References
Al-Loughani, N., Chappell, D. (2001). Modelling the day-of-the-week effect on the Kuwait
Stock Exchange: A GARCH representation. Applied Financial Economics 11 (4),
353–359.
Ay
dog
˘
a
n,K.
,Boot
h,G.
G. (2003). Calendar anomalies in the Turkish foreign exchange
markets. Applied Financial Economics 13 (5), 353–360.
Cornett, M.M., Schwarz, T.V., Szakmary, A.C. (1995). Seasonalities and intraday return
pattern in the foreign currency futures market. Journal of Banking and Finance 19 (5),
843–869.
Cross, F. (1973). The behavior of stock prices on Fridays and Mondays. Financial Analysts
Journal 29 (6), 67–69.
Cyree, K., Griffiths, M., & Winters, D. (2003). On the pervasive effects of Federal Reserve
settlement regulations. Economic Review, 27–46, Federal Reserve Bank of St. Louis.
DeFusco, R.A., McCabe, G., Yook, K.C. (1993). Day of the week effect: A test of the
information timing hypothesis. Journal of Business Finance & Accounting 20 (6),
835–842.
Demiralp, S., B. Preslopsky and W. Whitesell (2006), Overnight interbank loan markets,
Journal of Economics and Business 58, 67–83.
French, K. (1980). Stocks returns and the weekend effect. Journal of Financial Economics 8
(1), 55–69.
Gibbons, M.R., Hess, P. (1981). Days of the week effects and asset returns. Journal of
Business 54 (4), 579–596.
Griffiths, M., & Winters, D. (1995). Day-of-the-week effects in federal funds rates: further
empirical findings. Journal of Banking and Finance, 19, 1265–1284.
Griffiths, M., & Winters, D. (1997). The effect of Federal Reserve accounting rules on the
equilibrium level of overnight repo rates. Journal of Business Finance and Accounting,
24(6), 815–832.
Hamilton, J. (1996). The daily market for federal funds. Journal of Political Economy, 104,
26–56.
Harris, L. (1986). A transaction data study of weekly and intradaily patterns in stock returns.
Journal of Financial Economics 16 (1), 99–117.
Ke, M. C., Y. C. Chiang, T. L. Liao (2007). Day-of-the-week effect in the Taiwan foreign
exchange market. Journal of banking and finance 31, 2847-2865.
Lakonishok, J., Maberly, E. (1990). The weekend effect: Trading patterns of individuals and
institutional investors. Journal of Finance 45 (1), 231–243.
Lee, Y.-S. (2003a). The federal funds market and the overnight Eurodollar market. Journal of
Banking and Finance, 27, 749–771.
Lee, Y.-S. (2003b). Intraday predictability of overnight interest rates. Working paper,
University of Nottingham.
Levy, H. (1992). Stochastic dominance and expected utility: Survey and analysis.
Management Science 38 (4), 555–593.
Levy, H. (1998). Stochastic Dominance: Investment Decision Making Under Uncertainty.
Kluwer Academic Publishers, US.
Levy, H., Kroll, Y. (1979). Efficiency analysis with borrowing and lending: Criteria and their
effectiveness. Review of Economics and Statistics 61 (1), 125–130.
Levy, H., Sarnat, M. (1985). Investment and Portfolio Analysis. Wiley, New York, pp.
178–231.
McFarland, J., Pettit, R., Sung, S. (1982). The distribution of foreign exchange price changes:
Trading day effects and risk measurement. Journal of Finance 37 (3), 693–715.
Ritter, J.R., Chopra, N. (1989). Portfolio rebalancing and the turn-of-the-year effect. Journal
of Finance 44 (1), 149–166.
Roll, R. (1983). Orange Juice and Weather, Manuscript, UCLA.
So, J.C. (1987). The distribution of foreign exchange price changes: Trading day effects and
risk measurement –A comment. Journal of Finance 42 (1), 181–188.
Spindt, P., & Hoffmeister, J. (1988). The micromechanics of the federal funds market:
implications of day-of-the-week effects in funds rate volatility. Journal of Financial and
Quantitative Analysis, 23(4), 401–416.
Stickel, S. (1982). Empirical Tests of Future Prices. Manuscript, University of Chicago.
Tonchev, D., Kim, T.-H. (2004). Calendar effects in Eastern European financial markets:
Evidence from the Czech Republic, Slovakia and Slovenia. Applied Financial Economics
14 (14), 1035–1043.
Yamori, N., Kurihara, Y. (2004). The day-of-the-week effect in foreign exchange markets:
Multi-currency evidence. Research in International Business and Finance 18 (1), 51–57.