Is the Tokyo Foreign Exchange Market Efficient from Two Perspectives of Forward Bias and Anomaly?

doi:10.4236/me.2011.24067

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Modern Economy, 2011, 2, 597-601

doi:10.4236/me.2011.24067 Published Online September 2011 (http://www.SciRP.org/journal/me)

Is the Tokyo Foreign Exchange Market Efficient from Two

Perspectives of Forward Bias and Anomaly?

Yutaka Kurihara

Department of Economics, Aichi University, Aichi, Japan

E-mail: [email protected]

Received April 23, 2011; revised June 13, 2011; accepted Ju ne 23, 2011

Abstract

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

1. Introduction

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) [2] and Fatum and Pederson (2009) [3]

supported this view but Aguilar and Nydalh (2000) [4]

did not. Recent studies have examined th e reason that the

condition does not hold.

Louis et al. (1999) [5] showed that forward markets

that have been tested have become efficient in the sense

that CIP holds well. Cook (2009) [6] 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) [7] indicated that evidence of

declining deviations from equilibrium is consistent with

a more efficient trading environment. Fong et al. (2010)

[8] 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) [9]

empirical results suggested strong conditional het-

eroskedasticity, as well as contemporaneous correlation,

in the mean-corrected volume measure. Kim and Sheen

(2006) [10] and Chari (2007) [11] suggested an asym-

metric volatility in central bank threshold effects. Bertoli

et al. (2011) [12] 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) [13] showed the same results in the case of Pakistan

Breedon and Vitale (2010) [14] suggested that the strong contempora-

neous correlation between order flow and exchange rates is largely due

to portfolio-balance effects. Marsh (2010) [15] also indicated that

strong contemporaneous correlation between order flows and exchange

rate changes essentially disappears on days when the Bank of Japan

intervenes.

1Yamori and Kurihara (2006) [1] examined day-of- the week anoma-

lies in foreign exchange markets in 1980 s and 1990 s.

Y. KURIHARA

598

change rate changes or excess returns, as shown by Fama

(1984) [16]. Recently, Lyons (2001) [17] 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) [23] 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) [15] 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) [22] 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) [12] 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-

sion.

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

analysis:



tn ttttn

ss fs







  (1)

where tn



is the logarithm of spot exchange rate at

time tn



, ft is the logarithm of the forward rate for the

horizon n,



= 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) [16] 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

expectations,



= 0 and



= 1, and both of them are

significant. The error term should be serially uncorre-

lated.

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) [18], Dominguez

(1992, 1993) [19,20]. Reiz and Taylor (2008) [21] proposed that coor-

dination channeled through intervention may be effective. Bertoli et al.

(2010) [12] 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) [22] 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.



Exchanget 016t

DitInterventionE Z

 



 



(2)

where Exchange is percent log difference of Japanese

yen/U.S. dollar exchange rate, D1t, D2t, D3t, D4t, D5t,

Y. KURIHARA599

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).

3. Data

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

stationary.

4. Empirical Analysis

4.1. Forward Bias

Table 1 reports the standard regression results for for-

ward bias.

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

rates.

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.

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***

Adj.R2 0.0311

Note. *** denotes significant at 1%, ** a t 5%, and * at 10% r espectively.

Table 2. Results of Interventions in the Japanese Foreign

Exchange Market.

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**

Intervention

(–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.

Y. KURIHARA

600

5. Conclusions

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

efficient.

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

cause anomalies.

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.

6. Acknowledgements

I thank anonymous referees and Akihiro Amano for their

valuab le comments and suggestio ns.

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