Modern Economy, 2011, 2, 597-601
doi:10.4236/me.2011.24067 Published Online September 2011 (http://www.SciRP.org/journal/me)
Copyright © 2011 SciRes. ME
Is the Tokyo Foreign Exchange Market Efficient from Two
Perspectives of Forward Bias and Anomaly?
Department of Economics, Aichi University, Aichi, Japan
Received April 23, 2011; revised June 13, 2011; accepted Ju ne 23, 2011
This paper examines the efficiency of the Tokyo Foreign Exchange Market from two perspectives. One is
whether or not forward bias in this market has existed and the other is the effect of interventions in the mar-
ket with a focus on whether or not a day-of-the-week anomaly exists in it. Empirical results show that for-
ward exchange rates are a biased predictor of future spot exchange rates; however, there are some anomalies
in the market. The findings suggest the conclusion that this market has not been completely efficient.
Keywords: Anomaly, Exchange Rate, Foreign Exchange Market, Intervention
Many papers have investigated foreign exchange markets
and exchange rates not only from the view of theoretical
aspects but also from empirical ones. Above all, market
efficiency has received much attention and many analy-
ses have been conducted. This paper focuses on 1)
whether or not forward bias has existed and 2) anoma-
lous (day-of-the-week) effects produced by interventions
in the market.1
For interest rate parity, many researchers have tackled
the problem of the forward bias or forward premium
puzzle along with the condition of covered or uncovered
interest rate parity. Their results have not been inclusive;
however, most studies have concluded that covered in-
terest rate parity (CIP) holds in most recent cases but that
uncovered interest rate parity (UIP) does not. Evidence
and findings have been mixed. For example, Fatum and
Hutchison (2003)  and Fatum and Pederson (2009) 
supported this view but Aguilar and Nydalh (2000) 
did not. Recent studies have examined th e reason that the
condition does not hold.
Louis et al. (1999)  showed that forward markets
that have been tested have become efficient in the sense
that CIP holds well. Cook (2009)  found little or even
a negative relationship between expected excess returns
on exchange rates for adjusted U.S. money market rates.
Batten and Szilagyi (2010)  indicated that evidence of
declining deviations from equilibrium is consistent with
a more efficient trading environment. Fong et al. (2010)
 showed that CIP arbitrage deviations include com-
pensation for liqu idity and credit risk.
The hypothesis for the formation of exchange rate ex-
pectations may be one reason that interest rate parity,
especially UIP, does not hold. Exchange rate expecta-
tions are usually assumed to be adaptive or rational.
However, in the real world, exchange rate forecasters are
heterogeneous. Much attention has been paid to this het-
erogeneity. Heterogeneity in exchange rates seems to be
a major source of volatility. Smith and Pitts (2006) 
empirical results suggested strong conditional het-
eroskedasticity, as well as contemporaneous correlation,
in the mean-corrected volume measure. Kim and Sheen
(2006)  and Chari (2007)  suggested an asym-
metric volatility in central bank threshold effects. Bertoli
et al. (2011)  showed that the relationship between
exchange misalignment and forecast heterogeneity is
important for the so-called coordination channel of in-
tervention. It should be noted that recent papers about
central bank intervention seem to shed light on hetero-
geneity for policy tools.2
Almost all of the aforementioned articles have shown
that forward premium is inversely related to future ex-
2Shah et al. (2009)  showed the same results in the case of Pakistan
Breedon and Vitale (2010)  suggested that the strong contempora-
neous correlation between order flow and exchange rates is largely due
to portfolio-balance effects. Marsh (2010)  also indicated that
strong contemporaneous correlation between order flows and exchange
rate changes essentially disappears on days when the Bank of Japan
1Yamori and Kurihara (2006)  examined day-of- the week anoma-
lies in foreign exchange markets in 1980 s and 1990 s.
change rate changes or excess returns, as shown by Fama
(1984) . Recently, Lyons (2001)  showed a rea-
son for the occurrence of the forward premium puzzle.3
Lyons noted that the forward bias in foreign exchange
markets does not attract speculative funds until the trad-
ing strategy is expected to bring an excess return that
exceeds that of other trading strategies. This indicates a
band of inaction in which the forward bias will continue
until it is large enough to attract speculative fu nds. Sarno
et al. (2006)  supported this idea by employing
nonlinear models that inco rporated the band of inaction.
Few recent studies have analyzed this forward bias,
especially in the Tokyo market. Forward bias is accepted
rejection of the UIP, which indicates that forward ex-
change rates are a biased predictor of future spot ex-
change rates. After an examination of this perspective,
this article addresses anomaly, namely day-of-the-week,
and the effects of interventions.
This paper also focuses on foreign exchange market
interventions and examines their effectiveness in the
market. Marsh (2010)  indicated that strong contem-
poraneous correlation between order flows and exchange
rate changes essentially disappear on days when the
Ministry of Finance (Bank of Japan) intervenes. Kim and
Le (2010)  suggested that interventions conducted
during periods of oral intervention were in general more
effective in moving the exchange rate in the desired di-
rection. Bertoli et al. (2010)  showed that the rela-
tionship between exchange misalignment and forecast
heterogeneity is important for the so-called coordination
channel of intervention. Many papers about intervention
have been published; however, unique among these, this
paper examines day-of-the-week effects in the Tokyo
Foreign Exchange Market. Along with large fluctuations
of exchange rates, some countries intervene in the for-
eign exchange markets to attain stable exchange rates or
to avoid too much currency appreciation. An examina-
tion of the effectiveness and influence on the markets of
this approach is very important.
The article is structured as follows: Section 2 provides
the two models for the foreign exchange market effi-
ciency. Section 3 explains the data employed here. Sec-
tion 4 reveals the empirical method and provides em-
pirical analyses. Finally, Section 5 makes a brief conclu-
2. Empirical Analyses
2.1. A Model for Forward Bias
Forwar d bias is a broa dly accepted empirical rejection of
the UIP condition that suggests that forward exchange
rates are a biased predictor of future spot exchange rates.
Also, forward bias indicates that returns to currency
speculation are predictable, so they generate high eco-
nomic value to risk-averse investors who design dynamic
allocation strategies to avoid the UIP violation. This is
evident in the recent surge in capital flows all over the
world due to the spread of the use of some kinds of
strategies that exploit the forward bias anomaly in the
real world. Financial institutions around the world tackle
this transaction every day.
To check whether or not this UIP condition is accurate
and determine whether forward bias exists, th e following
method is most commonly employed for empirical
is the logarithm of spot exchange rate at
, ft is the logarithm of the forward rate for the
= 0 and
= 1, and tn
is an error
term that can follow up to an n–1 moving average error
term under the null of efficiency.
The Fama regression (1984)  is used to determine
whether the current forward premium ft – st is an unbi-
ased predictor of the future spot exchange rate return
(st+n – st). When agents ar e risk-n eutral an d have ra tional
= 0 and
= 1, and both of them are
significant. The error term should be serially uncorre-
2.2. A Model for Intervention Efficiency
This paper employs the empirical GARCH (generalized
autoregressive conditional heteroskedasticity) model to
examine the effectiveness of interventions on exchange
rates. GARCH is designed to model and forecast condi-
tional variances. The variance of the dependent variable
is modeled as a function of past values of the dependent
variable and independent or exogenous variables.
To control for the other activity of central banks that
may affect exchange rates, interest rate (INTEREST) and
the expectation of exchange rate (EXPECT) are included
in the equation as follows:
3Some studies have focused on sterilized interventions in foreign ex-
change markets. See Klein and Rosengren (1991) , Dominguez
(1992, 1993) [19,20]. Reiz and Taylor (2008)  proposed that coor-
dination channeled through intervention may be effective. Bertoli et al.
(2010)  employed the exchange market pressure (EMP) index and
suggested that the index is sensitive to some assumptions behind the
information available, especially when markets are involved. Kim and
Le (2010)  also suggested that the interventions conducted during
the periods of oral intervention were in general more effective in the
moving exchange rate in the d es ired direction.
where Exchange is percent log difference of Japanese
yen/U.S. dollar exchange rate, D1t, D2t, D3t, D4t, D5t,
Copyright © 2011 SciRes. ME
are day-of-the-week dummy variables for Monday,
Tuesday, Wednesd ay, Thursday, and Friday, respectively
with Saturday as a reference point. Intervention is the
Bank of Japan’s intervention in the foreign exchange
market (a positive value means net purchase of foreign
currency in U.S. dollars). E(Z) is the vector of other
relevant explanatory variables (interest rate and the ex-
pectation of exchange rate).
The data (exchange rates and interest rate) are from
Nikkei Needs (Japanese Nippon KeizaiShinbun, Inc.)
and the Japanese Ministry of Finance in Japan (the day
of intervention and th e volume). Forward exchange rates
are for one month. All of the exchange rates are daily
averages. Prediction data are obtained from AR(1). In-
terest rates are money market overnight rates. The sam-
ple period is 1993 to 2010. Time series properties of the
data are examined. Except for the log of the exchange
rate, all of the data are stationary according to an aug-
mented Dickey-Fuller (ADF) test. The log of the ex-
change rate is integrated at order one and thus becomes
4. Empirical Analysis
4.1. Forward Bias
Table 1 reports the standard regression results for for-
The forward premium (ft – st) has a positive coefficient
of 1.1263 and is significantly different from zero at the
1% level. The coefficient is almost one. In most similar
studies, the value of
takes minus, which is called
forward premium puzzle; however, this result is different
from such cases. The constant term is almost zero and
significant. Forward exchange rates seem to be a predic-
tor of future spot exchange rates. Recently in Japan, ex-
change rate movements frequently seem not to be in ac-
cordance with interest rates (domestic and foreign)
movements. For example, Japanese low or zero interest
rates result in appreciation of the yen; however, forward
exchange rates can be a predictor of future spot exchange
This interpretation of the results is difficult; however,
when deviations from the condition of CIP are large, the
forward premium will become a more accurate forecast
of future changes in the expected spot rate. Consequently,
as deviations from CIP become large and the coefficients
of the forward premium become smaller, the bias of the
forward premium as a predictor of future changes in spot
exchange rates becomes smaller. For the constant term,
there would be some possibility of the existence of
transactions costs as the term is significant. However,
again, the value is almost zero (0.0311). If transaction
costs effects exist, they would be small.
4.2. Intervention Efficiency and Effectiveness
Before estimating the GARCH model for the analysis of
market intervention, it is necessary to understand the
impact of the intervention on exchange rate volatility.
The results of Granger’s causality test show that there is
unidirectional causality between the intervention and
unconditional exchange rate volatility. Volatility was
measured using the squared log difference of exchange
rate. Table 2 shows the result of interventions in the
Japanese Foreign Exchange Market using the GARCH
Model A shows that two days (Monday and Friday) of
the day-of-the-week variables are significant in the equa-
tion. There is evidence of statistically significant day-of-
the-week effects. The market is closed on Saturday and
Sunday, so anomalies may exist. Also, the purchase of
the U.S. dollar brings unexpected appreciation of the
Japanese yen. However, it is not significant.
On the other hand, the Model B equation includes
relevant exogenous explanatory variables and uses
one-day time lag intervention. The results are almost as
expected. One-day time lag interventions have a signifi-
cant effect on the exchange rate as expected. The pur-
chase (sale) of the U.S. dollar brings depreciation (ap-
preciation) of the Japanese yen. The sign of INTEREST
is negative as expected but is not significant. Th e expec-
tation of the exchange rate has a correct significant im-
pact on the exchange rate changes.
Table 1. Regression Results for Forward Bias.
Constant 0.0537 (1.6050) 1.6050*
ft-st 1.1263 (12.2369) 12.2369***
Note. *** denotes significant at 1%, ** a t 5%, and * at 10% r espectively.
Table 2. Results of Interventions in the Japanese Foreign
Model A Model B
Coefficientt value Coefficient t value
Constant 0.0070 0.5620 –0.2426 –2.0160**
Monday –0.3771 –3.5678*** –0.3951 –3.7410***
Tuesday –0.3128 –0.9769 –0.4083 –0.8156
Wednesday–0.2030 –0.8888 –0.2832 –0.6444
Thursday –0.060 –0.6770 –0.0940 –1.0560
Friday –0.1782 –1.7197** –0.2140 –2.0653**
Intervention–0.00001 –0.8116 –0.00003 –2.0451**
(–1) 0.00009 7.6105***
INTEREST –0.0008 –1.1065
EXPECT 0.0022 2.0651**
Adj.R2 0.0848 0.1403
Note. *** denotes significant at 1%, ** a t 5%, and * at 10% r espectively.
Copyright © 2011 SciRes. ME
This paper performed an empirical analysis of the Tokyo
Foreign Exchange Market from two perspectives: for-
ward bias and anomaly. Contrary to most studies that
have analyzed different markets and time periods, for-
ward exchange rates are a predictor of future spot ex-
change rate. Judging only from this result, this market is
This paper also employed the GARCH model to ex-
amine the efficiency and effectiveness of the daily for-
eign exchange market in Japan and found day-of-the-
week anomalies in the market. Also, foreign exchange
market interventio ns influence the exchange rate level as
expected. The intervention is effective in changing the
exchange level, but the contemporaneous effect had a
reverse sign. For the anomalies, day-of-the-week effect
was examined and there are some kinds of anomalies
(Monday and Friday). The results showed that this mar-
ket was not efficient. Closing days in the market may
The selected exchange rate, the sample period exam-
ined, and the empirical method or theoretical model em-
ployed could change the results. Also, coordination
channeled through foreign exchange market interven-
tions may be effective in that they attract the fundamen-
tals. Moreover, some studies have shown that central
bank interven tions tend to in crease exchange rate volatil-
ity.4 There may be some room for further research.
I thank anonymous referees and Akihiro Amano for their
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