The Information Improving Channel of
Exchange Rate Intervention: How Do Official
Announcements Work?
Kentaro Iwatsubo
Satoshi Kawanishi
August 2011
Discussion Paper No.1116

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANThe Information Improving Channel of Exchange Rate
Intervention: How Do Official Announcements Work?
Kentaro Iwatsuboa,* and Satoshi KawanishibabKobe University, Japan
Sophia University, Japan

August 2011

Abstract
This paper studies the relationship between official announcements and the effectivenessof foreign exchange interventions in a noisy rational expectations equilibrium model. We
show that when heterogeneously informed traders have inaccurate information, an
exchange rate is likely to be misaligned from its fundamental value in the presence ofnoise trades. Then the central bank uses the disclosure of public information to improve
the accuracy of private agents’ information and encourage risk-arbitrage thereby
enhancing the informativeness of the exchange rate. This effect holds, even when thecentral bank does not possess superior information to traders, as long as public
information is not perfectly correlated with the information of traders. We provide
evidence that announced interventions are more effective in periods of high implied
volatility, consistent with the theoretical prediction that the implied volatility of theexchange rate is positively correlated with the information inaccuracy of traders and thedegree of an exchange rate misalignment.

JEL classification: F31, G15
Keywords: Exchange rate; Interventions; Announcements; Implied volatility; Information*

Corresponding author. 2-1 Rokko Nada, Kobe, 657-8501 Japan.
Tel.: +81-78-803-6875 E-mail address: iwatsubo@econ.kobe-u.ac.jp (K. Iwatsubo).

1.

Introduction
There is a rapidly growing literature on the role of communication for monetary

authorities managing market expectations in foreign exchange markets. 1 This new trend reflects
the fact that major central banks such as the Fed and the ECB have become reluctant to interveneand have shifted toward the use of communication policy in the management of their exchange
rates. The Bank of Japan still continues to intervene in the market, albeit with a lower frequency
than before, but also puts serious effort into communication and transparency concerning its
exchange rate policy. 2 Despite this shift towards communication policy, a consensus has not beenreached among researchers on how official announcements as well as actual interventions
influence exchange rate movements.
The portfolio-balance channel and the signaling channel are two traditional channels
through which sterilized interventions can affect exchange rates. In the portfolio-balance channel,
interventions change the composition of portfolios and thus the risk premium due to imperfect
substitutability of the underlying assets (Dominguez and Frankel, 1993). The small scale ofinterventions relative to the large volume of transactions in foreign exchange markets and thehuge value of stocks of international assets has led researchers to emphasize the signaling
hypothesis, by which actual and announced interventions may be perceived by markets as
indicating future monetary policy or developments of other policy measures (Mussa, 1981).
Lewis (1995), Kaminsky and Lewis (1996) and Fatum and Hutchison (1999) find, however, that
U.S. interventions have not conveyed a clear signal about future monetary policy.
The following theoretical models therefore explore the intervention channels under whichcentral banks do not possess superior private information to market participants or influence thefundamental value of the exchange rate. 3 Among these, the coordination channel was first
advocated by Sarno and Taylor (2001) and formulated by Reitz and Taylor (2008). If the strong
and persistent misalignments of exchange rates are caused by non-fundamental influences, suchthat a return to equilibrium is hampered by a coordination failure among fundamental-based
traders, then official intervention may act as a coordinating signal, encouraging speculators to
1

Examples include Beine and Bernal (2007), Beine et al. (2009a, 2009b), Dominguez and Panthaki(2007), Fratzscher (2006, 2008, 2009), Gnabo and Teiletche (2009), Gnabo et al. (2009), and Jansen
and De Haan (2005, 2007).
2
The criticism over currency manipulation is one reason that Japan hesitates to make frequentinterventions. After a six-year moratorium, the Bank of Japan has recently intervened in currency
markets three times: on Sep 15, 2010, March 18, 2011 and August 4, 2011.
3
Bhattacharya and Weller (1997), Vitale (1999), and Ferre and Manzano (2009) consider the secrecy
puzzle with models in which the central bank knows perfectly the fundamental value of the exchange
rate or infers it from the market rate.
2

re-enter the market and at the same time returning the exchange rate to a level consistent witheconomic fundamentals.
Closely related to the coordination channel is the information sharing channel proposedby Popper and Montgomery (2001). Under this channel, even if the central bank has no
information about fundamentals, it can affect the exchange rate by aggregating and disseminatingsome traders’ information about transitory exchange rate disturbances because the sharing of
information makes the exchange rate less noisy and allows all market participants to extract a
better signal of fundamentals from the exchange rate.
A drawback of the coordination channel is that it does not model how the central bankacquires information about the fundamental value of the exchange rate, which is relevant indeciding the time and magnitude of interventions. On the other hand, the information sharing
channel assumes that the central bank frequently gathers information about market conditions
from bank dealers, which enables it to infer the fundamental value. However, the assumption thatthe central bank can distinguish between price-informed dealers and uninformed dealers is toostrong as it is extremely difficult to discern dealer type in reality.
In this paper, we provide an alternative channel to the above two theories, whichhighlights that the (even inaccurate) information endowed to and signaled by the central bankenables traders to improve their information accuracy. This information improving channel isintroduced by incorporating intervention operations into the noisy rational expectations
equilibrium models of Hellwig (1980) and Diamond and Verrecchia (1981). When informed
traders have inaccurate information about fundamental values, an exchange rate is likely to be
misaligned from its fundamental value and exhibit high implied volatility in the presence of noise
trades. In this circumstance, we assume that the central bank intervenes in the market bydisclosing its own signal about the fundamental value or, equivalently, announcing the target
level of the future exchange rate. The announcement of the central bank improves the accuracy of
traders’ information and therefore helps them to engage in risk-arbitrage effectively. As a result,the exchange rate moves towards the fundamental value and becomes less noisy.
It should be stressed that this channel functions even when the central bank does notpossess superior information to private agents. In the model, the equilibrium exchange rate does
not fully reveal all the information available in the market due to the existence of noise trades. In
other words, the market is informationally inefficient. Although informed traders’ risk-arbitrage
is profitable at the expense of noise traders, the arbitrage is limited because the informed traders
are risk averse. We show that the more accurate information the informed traders have, the more3effectively they engage in risk-arbitrage and the more informational efficient the market becomes.
Accordingly, the public signal from the central bank has informational value that affects theexchange rate, as long as traders’ private signals are not perfectly correlated with the public
signal.
Our model has several noteworthy features. First, unlike the coordination channel or the
information sharing channel, our channel is not driven by the homogenization of traders’forecasts of the future exchange rate, but by an increase in the accuracy of their information about
the fundamental value. 4 , 5 Even in our model, both the accuracy improvement of traders’information and the homogenization of their forecasts can be achieved simultaneously by central
bank announcements. However, the latter is not a necessary condition for diminishing exchange
rate misalignments. To address the difference between the mechanism in our model and themechanisms in the coordination channel and the information sharing channel, we show that therelationship between the accuracy improvement of traders’ private information and thehomogenization of their forecasts is nonlinear and that there is a case where worsening informed
traders’ private information could homogenize their forecasts. This is due to the fact that if theprivate information worsens, the informed traders are likely to rely more on their public signal(i.e., the exchange rate) and less on their private signal which includes an independent error term
about the fundamental value across the traders. This will lead to the homogeneity of traders’forecasts.
Second, this model shows that the degree of information inaccuracy of informed traders
about the fundamental value of the exchange rate, which is the key variable in the model, ispositively linked to the implied volatility of the exchange rate. This implies that the information
improving channel is more effective in an environment of high implied volatility or, in otherwords, large market uncertainty because this is when information inaccuracy causes the exchange
rate to be significantly misaligned. Fratzscher (2008) provides consistent evidence that announced
interventions are more likely to be successful if exchange rate volatility is high, i.e. above its
median value, in the previous two weeks. Our theoretical prediction that implied volatility can beSpecifically, Reitz and Taylor (2008) propose a mechanism under which announced and actualinterventions influence informed traders’ confidence in fundamental analysis and coordinate theirrisk-arbitrage behavior. On the other hand, Popper and Montgomery (2001) assume that the central
bank can transmit information to the market about average customer orders originating from a groupof traders who have no information about the future exchange rate. In both channels, official
interventions make traders’ forecasts about the future exchange rate less heterogeneous.
5
Reitz et al. (2010) and Beine et al. (2007) provide empirical evidence on the impact of interventions
on exchange rate forecast heterogeneity.
44

used as a proxy for traders’ information inaccuracy allows us to easily detect an exchange rate
misalignment and provides us with a tractable measure for deciding the timing of FX
interventions. We present evidence that official announcements are more effective whenaccompanied interventions take place in high implied volatility periods.
We exploit changes in Japanese intervention policy to empirically test the theoreticalpredictions of our model. Japanese intervention policy changes frequently with regard toannouncements in accordance with who is in charge of foreign exchange interventions at the
Ministry of Finance. In addition, Japanese intervention strategy in terms of volume and frequency
has not been consistent across the interveners. These uncommon features of Japaneseinterventions allow us to investigate the effect of official announcements, controlling for volume
effects.
Our paper highlights the importance of market conditions for effective interventions.
Although many studies investigate the effects of intervention strategies such as announced andsecret interventions (Dominguez, 1998, 2003a; Beine et al., 2007, 2009a), few studies examine
whether their effectiveness depends on market conditions (Fratzscher, 2006; Dominguez, 2003b).
This paper provides empirical results that announcements have a more significant influence on
the level and reduce the implied volatility of the exchange rate when the implied volatility on theprevious trading day is high. This is consistent with the information improving channel we
propose in this study.
The remainder of the paper is organized as follows. Section 2 demonstrates thetheoretical model of actual and announced interventions in foreign exchange markets. Section 3
describes the intervention data and the sampling scheme. Section 4 explains the empiricalmethodology and Section 5 presents the estimation results. Section 6 contains our conclusions.

2. Theory
In this section, we present a noisy rational expectations equilibrium model with central
bank’s intervention operations. First, we study how the information accuracy of traders relates tothe distribution of exchange rate misalignments, the implied volatility, and heterogeneity ininvestors' forecasts. We then specify the central bank's intervention decision rules to examine theeffect of official announcements on the effectiveness of interventions through improvements in
the information accuracy of traders.
2.1. Assumptions
5Consider a pure exchange economy with three trading periods and two assets, one
riskless domestic currency (with a constant price equal to one) and one risky foreign currency.
The future value of the foreign currency is denoted y in terms of domestic currency, where y isnormally distributed with mean y and variance σy2, and it is revealed in period 3. In period 1 alltraders choose net demand for the foreign currency and its price, denoted p, is determined in themarket. The traders who trade in period 1 receive their payoff of y per unit in period 3 when ybecomes public. We call p and y as the exchange rate of the foreign currency in periods 1 and 3,
respectively. In period 2 the central bank decides whether to intervene in the foreign exchange
market.
We assume that there are n identical informed traders indexed by i =1,..., n. Trader i
receives a signal,(1)

si = y + εiin period 1 about the future value of the foreign currency. The error terms, ε1, ε2,..., εn are drawn
independently from an identical normal distribution with mean 0 and variance σε2. All traders
receive their signals before trade begins. These informed traders have CARA utility with acommon coefficient of risk aversion a > 0 and maximize expected utility, which is a function of
wealth denoted in home currency.
Apart from trades by informed traders, there are noise trades reflecting the demand andsupply for the foreign currency from foreign traders, travelers, and naive arbitragers with biased
belief. We denote the per-capita net demand of noise trades as x, which is assumed to be
independently normally distributed with mean 0 and variance σx2. The random variables, y, x, ε1,

ε2,..., εn, are independent and the informed traders know their distributions.
Under the assumption of CARA utility, it is known that the optimal demand does notdepend on traders' initial wealth. Hence we focus on capital gains, (y − p) zi, where zi is thequantity of the foreign currency that trader i purchases in period 1. Trader i's maximization
problem is simplified as follows:(2)

max E ⎡⎣ − exp[−a( y − p) zi ] si , p ⎤⎦ .
zi

Informed traders know that the demands of other informed traders affect the equilibrium
price of the foreign currency and make rational inferences about underlying information from theprice. To learn from the price, these traders must conjecture a form for the price function, and in
equilibrium this conjecture must be correct. Suppose that the traders conjecture the following
affine price function:6p = β0 + β s

(3)

1 n
si + β x xn∑i =1where β0, βs, and βx are coefficients to be determined. Under this conjecture, we can apply the
projection theorem 6 which assures that the distribution of y conditional on (si, p) is normal. Under
this CARA-Gaussian setting, we can easily derive investor i's demand function for the foreign
currency:
(4)

zi =

E[ y | si , p] − p≡ D( si , p).
a var[ y | si , p ]2.2. Equilibrium exchange rate function
In equilibrium, the total net demand for the foreign currency must equal zero.
n(5)∑ D( s , p) + n ⋅ x = 0i =1iWe find the equilibrium by solving equation (5) for p and then verifying that p is of theform conjectured in (3). Our assumption of homogeneous traders allows us to obtain a closed
form solution. Though we have a closed form solution of the model, its complicated form does
not provide for a study of equilibrium properties. In addition, the model with finite traders
contains a theoretical contradiction. Hellwig (1980) describes it as "schizophrenic," which meansthat traders behave as price takers although each trader can affect the equilibrium price when
traders are finite. To solve this contradiction, we follow Hellwig and study the limit case with
infinite traders. In our setting, his result becomes as follows.
PROPOSITION 1: As n goes infinity, the equilibrium price converges almost surely to(6)
p = y + β s* ( y − y ) + β x* x

σ y2 (a 2σ ε2σ x2 + 1)
aσ ε2σ y2 (a 2σ ε2σ x2 + 1)*
, βx = 2 2 2 2.
where β = 2 2 2 2
σ y (a σ ε σ x + 1) + a 2σ ε4σ x2
σ y (a σ ε σ x + 1) + a 2σ ε4σ x2*sProof: See the Appendix.
This proposition means that, by the strong law of large numbers, the error terms ofprivate signals are canceled out and do not affect the equilibrium price. From now on, we study
the property of this limit case equilibrium as a description of the foreign exchange market. We
use the mean and variance conditional on (si, p) in the equilibrium in order to derive results froma comparative statics analysis in the next section:
6

For a general version of the projection theorem, see Brunnermeier (2001, p.12).
7(7)E[ y | si , p ] = y + α s ⋅ ( si − y ) + α p ⋅ ( p − y ) ,a 2σ x2σ y2σ ε21,where α s = 2
and α p = 2 2 2
2 2
2
2
2
a σ xσ ε + 1
σ y + a σ x (σ y + σ ε )σ ε
(8)var[ y | si , p] =a 2σ x2σ y2σ ε4.
σ y2 + a 2σ x2 (σ y2 + σ ε2 )σ ε2

An important property of this model is informational inefficiency; the equilibrium
exchange rate does not reflect all the available information in the market because of noise trades x.
Following this convention, let us define the fundamental value of the foreign currency as its value
estimated from all information available in the market. Noise trades make it impossible for
informed traders to infer the fundamental value from the exchange rate. Note that thefundamental value is equivalent to the future value y in the limit case with infinite traders because
the infinite private signals and the strong law of large numbers enable us to obtain a perfectestimate of the future value. In contrast, if there is no noise trade as in the model of Grossman(1976), informed traders can infer the fundamental value from the current exchange rate. We canverify from proposition 1 that, when σx2=0, the equilibrium exchange rate is equal to thefundamental value y. Based on this understanding, in the rest of the paper, we define a bubble in
the exchange rate as p − y, the misalignment of the current exchange rate from its fundamental
value. We can measure the informativeness of the exchange rate by the variance of the bubble;
the degree of informativeness increases as var[p - y] decreases.
We show in a later section that, due to informational inefficiency, additional information
provided by the central bank can affect the equilibrium exchange rate. Although additional
information does not change the fundamental value of the foreign currency in the limit case, it
enables informed traders to make more precise estimates of y (the smaller conditional variance ofy) and therefore to have a larger position as indicated by equation (4). As a result of informed
traders’ active trades, the exchange rate shifts toward the fundamental value y.
2.3. Comparative statics with respect to signal accuracy
In this section, we analyze how traders’ information accuracy has an influence on the
distribution of the bubble, implied volatility and the heterogeneity of forecasts in the foreignexchange market before the central bank intervenes in the market. We show that less accurate
information reduces the informativeness of the exchange rate and increases implied volatility,
while the effect on the heterogeneity of traders’ forecasts is ambiguous.
8

A. Distribution of the bubble
We first study the effect of σε2 on the distribution of the bubble. Since p is a linear
function of normal random variables and y is also normal, p − y is normally distributed. The pricefunction (6) implies that the mean is zero, and the variance is(9)var[ p − y ] = (1 − β s* ) 2 σ y2 + β x*2σ x2 .
Then we can show that

(10)

d
dσ ε2

var[ p − y ] > 0 .

Proof: See the Appendix.
The positive sign implies that when traders have more accurate signal (smaller σε2), theexchange rate p in period 1 distributes closer to the fundamental value y. The reason is that when
the private signal is accurate, informed traders' risk-arbitrage becomes more effective. Suchrisk-arbitrage leads the exchange rate to distribute closer to its fundamental value and enhance theinformativeness of the exchange rate. Conversely, when private information is less accurate, theexchange rate is likely to be disturbed more by noise trades and thus is noisier in period 1.
Although the parameter σε2 is unobservable, the following market variables are supposed
to be used as proxies for it: implied volatility and the heterogeneity of traders' forecasts. We
investigate the relationship between σε2 and these two variables analytically.
B. Implied volatility
Implied volatility is a concept developed in the study of option pricing. Under someassumptions, the equilibrium price for a call option is a monotone function of the volatility ofunderlying asset returns. This volatility is, by definition, subjectively expected by investors in themarket, and thus unobservable. If the market works as the theory assumes, however, we can infer
volatility from the observed call price in the market by using the inverse function of the call
option price function.
In our model, volatility corresponds to the conditional variance of y on each trader'sinformation, var[ y | si , p ] . The effect of σε2 on implied volatility is given by
(11)

∂
∂σ ε2

var[ y | si , p ] =a 2σ ε2σ x2σ y4[σ + a σ σ (σ + σ )]
2
y

2

2

ε

2
x

2
y

9

2

ε

2

(2 + a 2σ ε2σ x2 ) > 0 for all i.

This expression is consistent with intuition. When private signals are less accurate, thepublic signal (in this case, p) is also less accurate, and the conditional variance of y is therefore
larger. The strictly positive sign for (11) allows us to regard implied volatility as a proxy for σε2.
C. Heterogeneity of forecasts
As traders have dispersed private information, their conditional expectations for y on
their information are also dispersed. One may presume that less accurate information leads toheterogeneity of forecasts among traders. This is correct if we define trader i's forecasts as equal
to their private information si. However, the trader’s forecasts should be defined as the
expectation based on both their private information and all available information including public
information. If the heterogeneity of traders' forecasts is defined this way, it is not always a goodproxy for σε2.
Suppose we take a sample of M traders. The heterogeneity of forecasts, denoted H, isgiven by the following statistics:
(12)

⎞
1 M ⎛
1 M
⎜ E[ y | si , p] − ∑ E[ y | s j , p ] ⎟H ( s1 ,L, sM , p) =∑⎜⎟M i =1 ⎝M j =1⎠

2.

Putting (7) into (12), we have(13)2

α s2 M ⎛⎜1 M ⎞⎟H ( s1 ,L, sM , p) =−ε
⎜ i M ∑ε j ⎟ .
M∑
i =1 ⎝
j =1⎠
When M is sufficiently large, this statistics distributes near the mean

(14)

E[ H ( s1 ,L, sM , p)] =( M − 1) 2 2αsσε .
MPROPOSITION 2
(15)

d
dσ ε2

E[ H ( s1 ,L , sM , p )] > 0

if and only if
(16)

σε <
2

a 2σ x2σ y2 + a 4σ x4σ y4 + 12a 2σ x2σ y2
2a 2σ x2

∈ (σ y2 , ∞) .

Proof: See the Appendix.
This proposition assures that, as long as the error term is less volatile than thefundamental value of the exchange rate, the heterogeneity of forecasts is increasing with σε2.
However, this proposition does not hold when traders' private signals are too inaccurate to rely on.
10In this case, private signals do not influence their posterior beliefs significantly. Since all traders
have common prior beliefs in our model, traders' forecasts {E[y|si, p]}i stay closer to the common
unconditional expectation E[y]= μ and thus the difference in forecasts is decreasing with σε2. Thisnonlinear relationship between the heterogeneity of forecasts and the measure of information
inaccuracy is important for differentiating the mechanism of official interventions in our modelfrom those of the coordination channel and the information sharing channel.
2.4. Intervention by the central bank
To complete our theoretical argument, we allow the central bank to intervene in theforeign exchange market if necessary in period 2. For simplicity, we deal with official
interventions as if they are unexpected events for informed traders. If we relax this assumption
and allow for dynamic interaction between the central bank and traders, the model becomes toocomplicated to analyze. However, we do not regard this assumption as critical for our results.
Note that interventions support the risk-arbitrage of informed traders, instead of ruining it.
Basically, informed traders buy under-priced foreign currency and sell over-priced foreign
currency because they know the exchange rate turns out to be the true value of the currency inperiod 3. If traders follow such an investment style, they can get an advanced cash flow in period
2 thanks to the intervention by the central bank, which attempts to push the exchange rate toward
the true value based on its information in period 2. Thus, we believe that traders' behavior is notaffected significantly by interventions, even if they are expected.
We assume that the central bank also receives imperfect information through thefollowing signal:(17)

sB = y +εB.
The error term εB has an independent normal distribution with mean 0 and variance θσε2,

where θ is a strictly positive constant and represents the accuracy level of the central bank's
information relative to informed traders. For example, θ smaller than 1 implies the central bankhas more accurate information than traders. Note that when σε2 is large, both informed traders andthe central bank have less accurate information. In other words, we assume that when it isdifficult for informed traders to predict the true future value of the foreign currency, it is alsodifficult for the central bank. We also assume that the distributions of random variables (y, x, ε)and the constant term θ are common knowledge among traders and the central bank and that therational central bank knows the objective function of informed traders.

11Using this private information and the exchange rate p observed in period 1, the central
bank follows the following simple statistical decision rule.
INTERVENTION RULE 7 : For a given probability π in (0, 1), if P[y > p|sB, p] > π, or if
P[y < p|sB, p] > π, then the central bank intervenes in the foreign exchange market to move thecurrent exchange rate toward E[y|sB, p]. π is set to a high value close to 1 in order to avoid agovernment failure.
This rule implies that the central bank intervenes in the foreign exchange market to movethe exchange rate toward the fundamental value when it judges statistically that there is a bubble.
Statistically speaking, interventions take place when a null hypothesis of no bubble is rejectedwith significance level 1 − π. Parameter π represents how prudent the central bank is. Because thecentral bank has imperfect information, and thus the intervention can make the bubble bigger
based on information with a serious error. This is why the prudent parameter π should be set
sufficiently high.
The conditional distribution of y − p based on the central bank's information (sB, p) is
normal with mean E[y|sB, p] − p, and variance var[y|sB, p]. Therefore, the intervention condition is
replaced byE[ y | sB , p ] − p > Zπ var[ y | sB , p ] .
Zπ is the solution for Φ(Z) =π, where Φ is the cumulative distribution function of the standard(18)

normal distribution. The left hand side of inequality (18) represents the bubble subjectively
recognized by the central bank. The right hand side is constant. That is, the central bankintervenes when the expected bubble is larger than a critical value. The expected bubble can be
decomposed in the following manner:(19)

E[ y | s B , p] − p = ( E[ y | s B , p] − y ) + ( y − p)
This decomposition indicates that the expected bubble is comprised of the true bubble y− p, and the central bank's estimation error mainly due to εB. Needless to say, the aim of theintervention is to clear the true bubble. Although it is impossible for the central bank todiscriminate between the true bubble and the estimation error, the central bank can clear the
subjectively recognized bubble.
7

The spirit of this decision rule is analogous to the statistical decision-making of manufacturers when
testing whether their products satisfy quality requirements. See Shewhart (1931)’s quality control
chart.
12

Under this model setting, the central bank has two intervention measures: actualintervention and official announcement. To examine the effect of interventions, we need to
specify traders' information and their reaction to interventions. We assume that interventions are
unexpected events and therefore traders only realize that an intervention has occurred and update
their posterior beliefs when the central bank makes an announcement. Actual interventions
without any announcement are assumed to be unobservable like noise trades, and thus traderscannot update their posterior beliefs. We also assume that, when the central bank announces,
informed traders know the distribution of the central bank's signal. That is, they know that thecentral bank also has imperfect information and that the error term is independent of their own
private signals. Using this information they make rational inferences about y based on theannouncement, and modify their demand function for the foreign currency in Period 2.
A. Actual interventions
The central bank can move the exchange rate toward the subjective fundamental value,E[y|sB, p], by trading the foreign currency in a manner that cancels the noise trade x. Note that thedemand curve for the foreign currency is downward sloping when the market is informationallyinefficient. Therefore, any trade can affect the exchange rate along the demand curve. 8 The
required trade for this purpose is (E[y|sB,p] −p)/ βx*. If the interventions are too costly due to low
foreign reserves or a high borrowing cost, the exchange rate will not reach the target.
B. Official announcements
Under informational inefficiency, the central bank can affect the exchange rate byproviding additional information to informed traders, which stimulates their risk-arbitrage. To see
the pure effect of official announcements, suppose that the central bank announce sB publicly but
does not engage in any market operations. Note that, as long as the informed traders know thatthe central bank is also rational, announcing a signal sB and the central bank's target E[y|sB, p] areequivalent because the conditional expectation of y is a one-to-one function of sB given the public
signal p.
Let p' be the equilibrium exchange rate after the official announcement of sB, which canbe represented as
8

We assume that traders would not recognize interventions without official announcements. Thismeans that traders suppose the change in the exchange rate is caused by a change in the noise trade,not by an intervention, and modify their demand for the foreign currency along the demand function
(4).
13

(20)

p′ = y + γ y ( y − y ) + γ B ε B + γ x x .
The modified exchange rate is affected by the central bank's information error, εB. As thisfunction is too complicated to derive a closed form solution for coefficients γ’s we analyze it
numerically and obtain the following results.
First, the post-announcement implied volatility decreases to var[y| si, sB, p], which isalways strictly lower than pre-announcement implied volatility var[y| si, p] for any finite θ. 9 The
additional information through announced interventions makes traders' information more accurate
as the error term εB is independent of private investors’ information error εi.
Second, on average, the announcement successfully diminishes the “true bubble” with thehelp of active risk-arbitrage. As the demand function (4) demonstrates, lower implied volatility
allows traders to bet larger positions based on their information. In other words, official
announcements make risk-arbitrage by informed traders more active and effective than before.
Figure 1 shows the effect of an announcement on the variance of the bubble (the reciprocal of theinformativeness of the exchange rate). The graph is drawn for a set of parameters. The
announcement has a larger effect for smaller θ when the central bank has more accurate
information than informed traders. When θ is quite large, the announcement has little effect.
Since informed traders are rational and know θ, an unreliable announcement is simply ignoredand does not harm the market. In the middle range, the effect depends on parameters. For
reasonable parameters, a central bank with the same accuracy level as traders (i.e. θ = 1) candiminish the variance of the bubble to roughly half of its initial size. Note that the above results
represent an average effect. We cannot exclude the case where the announcement may
unintentionally increase the bubble when the central bank receives an unusually bad signal εB.
This happens with a low probability, however, as the central bank is too cautious to intervene in
the market when the variance of the signal is large.
Third, the post-announcement forecasts of traders (E[y|si,sB,p]) distribute closer to eachother than pre-announcement forecasts (E[y|si,p]). Figure 2 presents the effect of anannouncement on the heterogeneity of forecasts. As explained in Section 2.3 C, pre-announced
heterogeneity has an inverse-U shaped relationship with information inaccuracy. Heterogeneity
increases until σε2 reaches a threshold level (in this case, σε2 = 7.1) and decreases thereafter.
When the central bank announces its public signal, traders’ forecasts homogenize regardless of
9

In equilibrium, p' is a linear combination of sB and p (See Appendix D). This implies that var[y| si, sB,
p, p'] equals var[y| si, sB, p]. In addition, since sB has an independent error term, we have var[y| si, sB,p] < var[y| si, p].
14

the value of θ because the public signal is common for all traders and they utilized theinformation to form their expectations. Obviously, the degree of homogenization caused by anannouncement depends on θ. When it is quite small, the announcement has a large effect on thehomogenization of forecasts.
C. Actual interventions and official announcements
What if the central bank implements actual interventions and official announcements
simultaneously? The answer depends critically on the credibility of the central bank's market
operation. If traders believe that the central bank can achieve the target of its market operation
after the announcement, then it is rational for traders to buy (sell) the foreign currency as much as
possible when the price is lower (higher) than the target price because such arbitrage is risklessgiven the belief. This riskless arbitrage causes the exchange rate to reach the target before thecentral bank conducts the actual interventions. A situation that will occur even if the required
interventions are too costly for the central bank to achieve by itself, as long as traders believe it
has enough reserves. In contrast, if traders believe that the central bank does not have enoughreserves, then the exchange rate moves to p', but will not reach the target E[y|sB, p] without thecentral bank's actual interventions. In fact, this situation is like a coordination game in which
traders' beliefs are self-fulfilling. Credible monetary authorities can achieve the target without
actual interventions by winning the traders over to their side.
2.5. Hypotheses derived from the model
Our model provides several theoretical predictions on the foreign exchange market andthe effectiveness of interventions. First, in the presence of noise trades, an exchange rate is likely
to be more misaligned from its fundamental value and exhibit a higher implied volatility when
informed traders have less accurate information. Second, under plausible assumptions, the degreeof information inaccuracy about the fundamental value and the implied volatility of an exchange
rate are positively correlated. Hence, implied volatility can be used as a policy tool to determine
the timing and magnitude of interventions, as the impact of interventions is greater when implied
volatility is higher. Third, official announcements can make the exchange rate less noisy (i.e.
increase the informativeness) and reduce both implied volatility and the heterogeneity of forecasts
because they contribute to the improvement of traders’ information accuracy. This holds evenwhen the central bank does not possess superior information to that of traders.

15

Thesepredictions

providethefollowing

testable

hypotheses:

First,

official

announcements and actual interventions have a more significant impact on the level of theexchange rate when the implied volatility of the exchange rate is high. Second, if they are
conducted in a timely manner, the implied volatility of the exchange rate and the heterogeneity offorecasts are reduced.
Reitz et al. (2010) provide empirical evidence that central bank interventions reduce
forecast dispersion, which is consistent with the coordination channel and the information sharing
channel as well as our theory. To highlight the aspects of our theory that differ from the previous
two channels, we leave heterogeneity in forecasts and empirically test whether high implied
volatility of the exchange rate is a pre-condition for effective interventions and announcements
using Japanese and US intervention data.

3.

Data and Japanese intervention policy changes
To address the announcement effect, we classify interventions into three categories using

news reports provided by Bloomberg: announced interventions, unannounced but reported
interventions, and secret interventions. 10 ‘Announced interventions’ are those accompanied by
official statements from government officials on the intervention day. The government officials
may include the Minister of Finance, the Vice Minister of Finance for International Affairs, theDirector General of the International Bureau and the Governor of the BOJ. They often confirm
interventions by publicly stating that the BOJ intervened in the market. Then the statements arebroadcast along with the name of the official making the announcement within a few minutes by
newswires. ‘Unannounced but reported interventions’ are reported by newswires but without any
corresponding official statements. Newswire reports sometimes quote traders as saying, “[s]ome
traders said that the BOJ intervened in the market at around 115 yen during the morning session”
or “[t]he BOJ apparently bought dollars against yen.” On the other hand, ‘secret interventions’ are
not reported by the newswires, but do actually take place.
It is well known that the Japanese intervention policy changed in June 1995 when Eisuke
Sakakibara took over as Director General of the International Finance Bureau. He made adeliberate decision to reduce the frequency and increase the volume of interventions (Sakakibara,
2002). 11 Accordingly, some studies on Japanese interventions divide their sample periods into preand post June 1995 (Ito, 2003; Beine et al., 2009b). Intervention policy also changed after his
10

We double-checked the classification of interventions using Reuters.
Dr. Sakakibara became famous in the market after being nicknamed “Mr. Yen” by the NY Times(Sep 16, 1995).
1611

resignation, especially in terms of making official announcements about interventions. Hence, we
divide our sample period into four sub-periods according to who is the Vice Minister of Financefor International Affairs of the MOF at the time, as he has the most influence on Japaneseintervention decisions. 12 The sub-sample periods are period 1 (6/15/1992 - 6/20/1995), period 2(6/21/1995 - 7/7/1999), period 3 (7/8/1999 - 1/13/2003) and period 4 (1/14/2003 - 5/27/2004).
Intervention techniques are quite different depending on the person who actually decides. Figure
3 illustrates the movement of the yen/dollar rates and intervention volume during the full sample
period.
Table 1 displays the average volume and intervention types for the whole sample period
and the four sub-periods from May 13, 1991 to July 2, 2004. During the sample period, there are
343 intervention days for the yen/dollar rate (10.1% of the sample). Among the intervention days,
208 (60.6%) are correctly reported by newswires, while 135 (39.6%) are not reported but haveactually taken place (secret interventions). 12.8% of the intervention days are announced bygovernment officials (announced interventions) and 47.8% are not announced but are reported by
newswires (unannounced interventions).
Period 1 is characterized by frequent, small interventions. In this period, frequency is thehighest among the four sub-periods (averaging an intervention every 4.77 days) and the averagevolume of an intervention was 47 billion yen, which is the smallest among the four sub-periods.
There are 18 days of coordinated interventions with the Federal Reserve Bank of NY in period 1.
During period 1, only 6.1% of interventions are announced, while more than 70% areunannounced but reported interventions.
In period 2, when Dr. Sakakibara was in charge of interventions, he reduced theintervention frequency (averaging 39.83 days between interventions), while increasing the
average size of interventions (510 billion yen per day). The ratio of both ‘officially announced’and ‘unannounced but reported’ interventions was high (91.6%). In addition, half of theannounced interventions in period 2 were accompanied by Federal Reserve Bank of NY
interventions.
In period 3 the trend of infrequent but large interventions continued. There were only 25
intervention days (averaging 36.72 days per intervention) and the average volume of an

12

The MOF determines the volume and timing of interventions and the BOJ, which receives the orderfrom the MOF, executes the intervention in the foreign exchange market. The decision makers forintervention are limited to the Minister of Finance, the Vice Minister and Deputy Vice Minister ofFinance for International Affairs, the Director General of the International Bureau and the Director of
the foreign Exchange Market Division. (Sakakibara, 2002)17

intervention was approximately 530 billion yen, which is the largest among the four sub-periods.
It is remarkable that all of the interventions in period 3 were announced.
In period 4 the intervention policy changed dramatically from infrequent and large tofrequent and medium-sized. The frequency of interventions in period 4 increased to an average of
one intervention every 2.78 business days. Another big change was the very high ratio of secretinterventions, which made up 74.4% of all interventions in this period. After Mr. Mizoguchi was
appointed as Vice Minister of Finance for International Affairs, government officials declined tomake comments or give any interviews. Instead of announcing interventions as they occurred, the
MOF started to reveal the monthly volume of interventions at the end of each month and thevolume of the interventions every three months. In response to the change in the intervention
strategy, newswire reports turned to vague statements such as “market participants are keeping
watch for a possible intervention” and “[t]he BOJ seemed to be active in the market.”

4.

Empirical methodology
In the empirical sections, we test our hypothesis that official announcements and actualinterventions are more effective when the implied volatility of an exchange rate is higher. We
would expect that the level of the exchange rate will move in the desired direction and theimplied volatility of the exchange rate will be reduced if they are conducted in a timely manner.
This hypothesis can be tested using the GARCH model and the OLS model using implied
volatilities extracted from option prices. The former examines the impact of interventions on thelevel and the ex-post volatility of an exchange rate, while the latter on the ex-ante volatility
representing investors’ expected future volatility. Following Beine et al. (2009a) and Dominguez(1998), the GARCH (1, 1) model of the yen-dollar exchange rate has the following specification:(21)

rt = a0 + a ' X t + ε t ,ht = α 0 + α ε2
1 t −1

ε t | Ω t −1 ~ N (0, ht ),+ α 2 ht −1 + b ' | X t |, α 0 > 0, 0 ≤ α1 , α 2 ≤ 1, α1 + α 2 < 1

where rt = 100 ln(S t / S t −1 ) is the logarithmic return of the spot exchange rate (expressed as apercentage) with S t as the yen/dollar rate (NY close). X t denotes a vector of independent
variables related to the Japanese and U.S. interventions as well as macro variables that may affectexchange rates.
Three dummies are considered in the estimation equations for announced interventions,
unannounced but reported interventions and secret interventions for Japan and the U.S. These18

dummies are independent of intervention volume by both countries, 13 and take a value of +1 if
such an intervention strategy is carried out for dollar purchases (yen sales), -1 for yen purchases(dollar sales) and zero otherwise. The intervention volume variable is also signed with + (dollar
purchases) and – (yen purchases). If dollar purchase interventions by the U.S. and Japanesemonetary authorities tend to cause the dollar to appreciate and the yen to depreciate, thecoefficients are expected to be positive. As suggested by Dominguez (1998), we also include theinterest rate differential between the Japanese and U.S. overnight money market rates in the level
equation in order to account for relative contemporaneous monetary policies in both countries. 14
We include a holiday dummy in the volatility equation which takes a value of 1 if the previous
day is a holiday and 0 otherwise. All variables in the volatility equation are taken to be theabsolute values of those in the mean equation.
Following Bonser-Neal and Tanner (1996) and Dominguez (1998), the effects of official
announcements and actual interventions on the implied volatility of the exchange rate are tested
using the following specification:(22)

iv t = a ' Yt + b' Z t −1 + ε twhere ivt = 100 ln( IVt / IVt −1 ) is the logarithmic return of implied volatility (expressed as apercentage) with IVt the implied volatility estimate derived from at-the-money option prices(one- and three-month) on the spot yen/dollar rates from the NY market (10 AM EST). The
variables concerning the Japanese interventions and macro variables are included in Yt . On theother hand, following Dominguez (1998), the variables related to the Fed’s intervention are
lagged by one day, which are included in Z t −1 , because market participants do not know (withcertainty) the Fed’s Tuesday interventions on Tuesday morning. Since variables related tointerventions are all taken as absolute values, we expect negative signs for the coefficients if
interventions are effective in reducing implied volatility.
13

Existing empirical research testing the signaling hypothesis using news reports typically splitsinterventions into reported and secret interventions and analyzes the significance of the coefficientsfor the volume of each type of intervention (Dominguez, 1998; Beine et al., 2002). This paper
analyzes the efficency of interventions using intercept dummies that represent reported and secretinterventions, while controlling for intervention volume. Although market traders do not know theexact intervention volumes on intervention days, they can guess the approximate sizes based onmarket rumors and trading activity, especially when large-scale interventions are carried out. This
contradicts the view of shifting slopes because the difference between announced and unannounced
interventions lessens as intervention volume increases. We pre-test the model incorporating both slope
and intercept dummies and find that using intercept dummies is preferable to shifting slopes.
14
The overnight market rates are the Federal Funds rate for the U.S. and the call rate for Japan.
19

A potential caveat of our regressions is that interventions may be endogenous. Kearns
and Rigobon (2004) suggest an empirical methodology for taking this endogeneity into accountby directly modeling the potential behavior and reaction of central banks. It is well known,
however, that specifying the determinants of interventions is not an easy task. Most studies on thereaction functions of central bank interventions use either a binary choice approach or a nested
logit model and do not fully specify intervention volume (Ito and Yabu, 2007; Beine et al.,2009b). There is a risk, therefore, of misspecification when specifying a parametric model ofintervention behavior that corrects for the endogeneity bias. Moreover, as suggested by Fratzscher(2006), the literature, including Sarno and Taylor (2001), has shown that actual interventions tend
to be of the leaning-against-the-wind type, i.e. they usually go against the previous exchange rate
trend. Therefore, if endogeneity generates a bias, it will be a downward bias, and the true effect ofinterventions may be even larger.

5.

Estimation results

5.1. Linear estimation of announcement effects
We first examine whether officially announced interventions have a larger effect on
exchange rates than secret interventions and unannounced but reported interventions. Table 2
presents the results of the GARCH estimations for the full sample period as well as the four
subsample periods distinguished by Vice Ministers of Finance for International Affairs of MOF.
In the results of the mean equation for the full sample period, the coefficient of the Japanese
announced interventions dummy is significantly positive, while those of the Japaneseunannounced but reported interventions dummy and the secret interventions dummy are
significantly negative, suggesting that announced interventions are not just effective but
significantly more effective than non-announcement interventions. The negative signs of the
non-announcement interventions do not necessarily imply that interventions without official
announcements inversely affect the return of exchange rate. Taking into account the volume
effect, such strategies can be effective although their efficiency is significantly less than that ofannounced interventions.
During the full sample period, whenever the U.S. authorities intervened, the Japanese
authorities intervened on the same day. As there were no unilateral U.S. interventions, but weremany unilateral Japanese interventions, the U.S. intervention dummies with and without official
announcements capture the impacts of coordinated interventions between the U.S. and Japan. On

20the other hand, the Japanese intervention dummies represent the Japanese unilateral intervention
effect because we take into account the effect of coordinated interventions.
Both announced and unannounced but reported U.S. interventions are significantly
effective, conditional on the volume of the intervention. On the other hand, the intervention
volume does not affect exchange rates if we control for the intervention dummies. With regard tocoordinated interventions, it is whether the intervention is announced and/or reported that has asignificant influence on exchange rates, not the volume of the intervention.
Table 2 also presents the regression results for the four sub-sample periods. Interestingly,
the coefficient of the dummy for secret interventions is significantly negative in period 1, whilethat of the dummy for announcement is significantly positive in period 2. This sharp contrast
suggests that Dr. Sakakibara’s policy change in favor of official announcements might lead tomore successful interventions. However, the evidence that the intervention announcement iseffective only in period 2 and not in other sub-sample periods may question previous studies
which show that official announcements have unambiguous effects (Fratzscher, 2006; Beine et al.,2009a).
The results from the volatility equation are also striking. In the full sample, neither theJapanese intervention volume nor its announced intervention dummy is significant. Moreover, theunannounced but reported intervention dummy is significantly negative. Together with the resultsfrom the mean equation, this evidence suggests that Japanese interventions are quite effective instabilizing the market as well as affecting the level of exchange rate in the desired direction.
However, the four sub-sample regressions show that announced interventions are volatility
enhancing in periods 2 and 3, while unannounced interventions contribute to lower volatility inperiods 1 and 4. One may conclude that the difference in intervention policies may lead to thedifference in outcome. Specifically, if the central bank aims to alter the previous exchange rate
trend, i.e., the leaning-against-the-wind policy, announced interventions are appropriate although
they are accompanied by an increase in volatility. On the other hand, if stabilizing exchange rate
movements is the primary objective, the central bank should choose secret interventions even if
they may have little effect on the exchange rate level.
A careful comparison between periods 2 and 3, however, allows us to find that this is notalways true. Although Mr. Kuroda followed Dr. Sakakibara’s announcement strategy, hisinterventions are not effective in period 3. This implies that official announcements alone do notnecessarily guarantee the success of interventions.

21

5.2. Non-linear estimation of announcement effects
We then investigate whether the effectiveness of announcements hinges on market
conditions just before the intervention takes place. Specifically, we test whether theannouncements on interventions have a stronger impact when traders have inaccurate informationand the exchange rate misalignment is therefore large. We use the implied volatility derived fromat-the-money option prices (one- and three-month) on the spot yen/dollar rates as a proxy for theabove two variables as they are positively related as shown in our model.
Tables 3 reports the results of the GARCH model in which we introduce the interaction
repressor: the product of the intervention dummy and the implied volatility (one- andthree-month) of the exchange rate. To prevent a simultaneity problem, the interaction terms
consist of the one period lagged values of implied volatility. Since implied volatility is highly
persistent, the one period lag is a proxy for the implied volatility just before an intervention. The
results of volatility equation are omitted for the sake of space because the interaction terms are
not significant.
In the first column of Table 3 (results for the whole sample period), the result of theestimation with one-month and three-month implied volatility is displayed. The coefficient of theinteraction term between the Japanese announcement dummy and the lagged implied volatility issignificantly positive, while that of the Japanese announced dummy is significantly negative. Thissuggests that announcement effects have a non-linear relationship with exchange rate changes,
which depend on the implied volatility of the previous business day. Based on these coefficients,
we infer that official announcements influence exchange rates in the desired direction if thelagged implied volatility is greater than 11.38% for 1 month maturity and 11.32% for 3 monthmaturity, respectively. Furthermore, the significantly positive coefficient of the interaction term
between the Japanese intervention volume and lagged implied volatility shows that large-scaleinterventions are effective when lagged implied volatility is sufficiently high (more than 3.78%
for 1 month and 3.60% for 3 month, respectively). In contrast, keeping interventions secret (boththe unannounced but reported interventions and the secret interventions) has no significant impact
on the exchange rates themselves. The results for period 2 show that lagged implied volatility ofmore than 10.43% for 1 month and 11.30% for 3 month, respectively, are required for announced
interventions to be effective. When implied volatility on the last trading day is sufficiently high,the effect of official announcements on exchange rate is significant.
Table 4 also shows a similar non-linearity effect for announcements on current implied
volatility depending on lagged implied volatility. The result for the whole sample period suggests
22that when lagged implied volatility is more than 13.99% for 1 month, official announcements can
reduce current implied volatility because the interaction term has a negative coefficient and theannounced intervention dummy is positively signed. However, the coefficient of the interaction
term between intervention volume and lagged implied volatility is significantly positive,
mitigating the effect on volatility. We then need to consider both volume effect andannouncement effect simultaneously. For example, suppose the intervention volume is 200 billion
yen (the average for the whole sample period). We find that a lagged implied volatility of morethan 15.24% is needed for an announced intervention to reduce the volatility of exchange rates.
This indicates that lagged implied volatility, serving as a proxy for information inaccuracy andthe degree of an exchange rate misalignment, is an important determinant of the efficiency ofannouncements and interventions on both the level and expected volatility of exchange rates.
Figure 4 displays the movements of 1 month and 3 month implied volatilities and suggests that
Mr. Yen conducted announced interventions when the implied volatility was high, especially inthe summer of 1995 and in April and June of 1998.

6. Conclusion
This paper contributes to the existing literature on foreign exchange interventions. First,
we present an alternative channel for exchange rate interventions under which announcements by
the central bank can make the exchange rate more efficient through an improvement in traders’information about the exchange rate’s fundamental value, even when the information disclosedby the central bank is inferior to that of traders. Second, this model provides the testable
implication that announced interventions are more effective in periods of high implied volatility
because the degree of information inaccuracy and the exchange rate misalignment is positively
correlated with implied volatility. This prediction is borne out empirically in our findings basedon Japanese and U.S. intervention data.

Acknowledgement
Part of this work was completed when Iwatsubo was visiting Cass Business School, City
University London. We are grateful to Yin-Wong Chen, Robert Chirinko, Shinichi Fukuda,
Takatoshi Ito, Ian Marsh, Lukas Menkhoff, Richard Payne, Ghon Rhee, Lucio Sarno, Mark Taylor,
Cedric Tille, Toshiro Tsutsui, Takashi Ui and seminar participants for their useful comments on
previous drafts and Junko Shimizu for excellent research assistance. Iwatsubo is thankful for
financial support from Grant-in-Aid for Young Scientists (B21730253).

23

Appendix
A. Proof of PROPOSITION 1
We first derive a rational expectations equilibrium with finite traders and show that theequilibrium price function converges to (6). By applying the projection theorem, we derive the
distribution of y conditional on (si, p) which is normal with mean
E y si , p = y + α s (n)(si − Esi ) + α p (n)( p − Ep)
(A1)

[

]

cov( s i , p ) ⎞⎛ var s i⎟⎟
= y + (cov( y, s i ) cov( y , p ) )⎜⎜
cov(
,
)
var
s
p
p
i
⎠
⎝

−1

⎛ si − Es i ⎞
⎟⎟
⎜⎜
p
Ep
−
⎠,
⎝

and variance(A2)

cov( si , p ) ⎞⎛ var si⎟var[y si , p ] = σ − (cov( y, si ) cov( y, p ) )⎜⎜var p ⎟⎠
⎝ cov(si , p )2
y−1⎛ cov( y, si ) ⎞⎜⎜⎟⎟⎝ cov( y, p ) ⎠ ,where the variance and covariance with regards to p are derived from the conjectural exchange
rate function. Since the conditional variance is constant and common for all traders, we omit
indicator i for the conditional variance hereafter.
By definition, Esi = y . Putting the demand function into the market clearing condition andtaking the unconditional expectation, we have Ep = y . The market clearing condition can besolved for p as follows:
(A3)

p= y+

a var[ y | s, p ]α s (n) 1 n( si − y ) +x.
∑
1 − α p (n) n i =1
1 − α p ( n)Thus, the rational expectations equilibrium is derived from the following simultaneous
equations:

α s ( n)),1 − α p ( n)(A4)β 0 = y (1 −

(A5)

βs =

α s ( n),1 − α p ( n)

(A6)

βx =

a var[ y | s, p ].
1 − α p ( n)We can solve the closed form solution for the simultaneous equations by taking the ratio of βs
and βx. A careful calculation obtains the following equation:(A7)βs
α s ( n)==β x a var[ y | s, p]β x2σ x2

n 2σ x2
.
=
2
2
2
2 2
1 2
a
σ
[(
β
/
β
)
(
n
−
1
)
σ
+
n
σ
]
2
2 1
2 2
ε
ε
s
x
x
aσ ε [ β s (1 − )σ ε + β x σ x ]nnConsider this as a cubic equation of k ≡ βs/βx. By applying the Cardano formula for a cubic
equation, we can find the unique solution as an explicit function of exogenous parameters.

24

4ω2
4ω2
2
3 − ω1 − ω1 +27 +27 ∈ (0,1 / aσ 2 ) ,
(A8)
k=
ε
2
2
n 2σ x2
n 2σ x2
where ω1 ≡ −.
,ω ≡a(n − 1)σ ε4 2 (n − 1)σ ε2
3 − ω1 + ω1 +2

3

3

Using k, the equilibrium coefficients are solved explicitly.

1
β 0 = y (1 − kβ x ) , β s = kβ x , and β x =
k

1
n
.
1
1 4
2 2
2
2 2
2 1
2 2
σ yσ x + k (1 − )σ ε σ y + k (1 − )σ ε + σ ε σ xnnnσ y2σ x2 + k 2 (1 − )σ ε2σ y2

Now we show the convergence of this equilibrium exchange rate function to (6). Since {εi} arei.i.d. random variable with mean zero, we can apply the strong law of large number and obtain

1 nsi = y
∑
n→∞ n
i =1

(A9)

lim

almost surely.

Thus, the equilibrium function converges to(A10)
p = y + β s* ( y − y ) + β x* x ,where the coefficients are the limit of βs and βx. Taking the limits of both sides of (A7), we have
lim k = 1 / aσ ε2 , which leads to
n→∞

(A11)

σ y2 (a 2σ ε2σ x2 + 1)
aσ ε2σ y2 (a 2σ ε2σ x2 + 1)*
β ≡ lim β s = 2 2 2 2, β x ≡ lim β x = 2 2 2 2
.
n→∞
n→∞
σ y (a σ ε σ x + 1) + a 2σ ε4σ x2
σ y (a σ ε σ x + 1) + a 2σ ε4σ x2*
s

QED
B. Proof of inequality (10)From the equilibrium function, the variance is given as a function of underlying parameters:[a 2σ ε4σ x2 ]2 σ y2 + [aσ ε2σ y2 (a 2σ ε2σ x2 + 1)]2 σ x2
var[ p − y ] = (1 − β ) σ + β σ =(A12).
[σ y2 (a 2σ ε2σ x2 + 1) + a 2σ ε4σ x2 ]2Thus, the derivative of the variance w.r.t. σε2 isa 2σ x2σ y2 ⎡⎛ d
⎞
d
(A13)
var[ p − y ] ={a 2σ ε8σ x2 + σ ε4σ y2 (a 2σ ε2σ x2 + 1) 2 }⎟⎟ D1
⎢⎜⎜
2
3
2
dσ ε
D1 ⎣⎝ dσ ε
⎠
* 2
s

2
y

*2
x

2
x

⎛ d
⎞⎤
− 2{a 2σ ε8σ x2 + σ ε4σ y2 ( a 2σ ε2σ x2 + 1) 2 }⎜⎜D1 ⎟⎟⎥
2⎝ dσ ε
⎠⎦
2
2 2 2
2 4 2
where D1 ≡ σ y (a σ ε σ x + 1) + a σ ε σ x . The derivatives in the square bracket are

(A14)

d
dσ ε2

{a 2σ ε8σ x2 + σ ε4σ y2 (a 2σ ε2σ x2 + 1) 2 } = 4a 2σ x2 (a 2σ x2σ y2 + 1)σ ε6 + 6a 2σ x2σ y2σ ε4 + 2σ y2σ ε2 ,25

(A15)d

D1 = 2a 2σ x2σ ε2 + a 2σ x2σ y2 .

dσ ε2Thus, we have dvar[p−y]/dσε2=

a 2σ x2σ y2
4a 4σ x4σ y2 (a 2σ x2σ y2 + 2)σ ε8 + 4a 2σ x2σ y2 ( 2a 2σ x2σ y2 + 1)σ ε6 + 6a 2σ x2σ y4σ ε4 + 2σ y4σ ε2 > 0
D13

[

]

QED
C. Proof of PROPOSITION 2
Equation (13) implies
(A16)

⎛ d
⎞
⎞
⎛ d
α sσ ε ⎟ .
sgn⎜⎜ 2 E[ H ( s1 ,L, sM , p)] ⎟⎟ = sgn⎜
d
σ
⎠
⎝ ε
⎝ dσ ε⎠The coefficient αs is given in (7). We have
(A17)

d

dσ ε

α sσ ε =a 2σ x2σ y2σ ε2(3σ y2 + a 2σ x2σ y2σ ε2 − a 2σ x2σ ε4 ) .
[σ y2 + a 2σ x2 (σ y2 + σ ε2 )σ ε2 ]2The sign of the derivative is determined by the sign of the term in parenthesis in (A17), which
is a concave quadratic function with one positive and one negative intersections. Note σε2 > 0.
Then we can conclude that derivative (A17) is positive as long as σε2 is less than the positive
intersection. The condition is(A19)

σ ε2 <

a 2σ x2σ y2 + a 4σ x4σ y4 + 12a 2σ x2σ y2
2a 2σ x2.

The boundary is strictly larger than σy2. This completes the proof for PROPOSITION 2.

QED

D. Procedure for numerical exercises on Figure 1 and Figure 2
As we derived for the pre-announcement equilibrium price function in section 2.2, the post
announcement price function is derived as a fixed point of the correspondence from an affine
price function in the form of equation (20) to another price function satisfying the market clearing
condition,p′ = y + γ y ( y − y ) + γ B ε B + γ x x .
(20)
The rational traders use this price function and other information to derive the net demand
function for the foreign currency. Investor i has four information signals si, sB, p, p', so thedemand function iszi ( si , s B , p, p′) =E[ y | si , s B , p, p′] − p′.
a var[ y | si , s B , p, p′]

Before deriving conditional expectations, we should note the following fact.
Fact: Price function p' in (20) is a linear combination of sB and price function p in (6), and26

therefore either p or p' is redundant for rational investors.
Otherwise rational investors can solve three linear equations (6), (17), and (20) and pin down
three unknown variables (y, εB, x), and therefore the price after the announcement p' must become
y. Of course, the announcement of the imperfect signal, sB, cannot clear the informational
inefficiency perfectly. We have checked the redundancy for the numerically derived pricefunctions although we use the fact without proof.
This fact allows us to ignore the pre-announcement price, p, to calculate the conditional
expectations as given byE[ y | si , s B , p, p′] = E[ y | si , s B , p′] ,var[ y | si , s B , p, p′] = var[ y | si , sB , p′] .
Still the conditional expectations have three signals as conditions. To simplify the calculations,
we introduce the sufficient statistic of the first two signals, si and sB. Let wi be the sufficient
statistic, then it is given aswi =τ s si + τ B sB
τ ε +τ ε= y+ s i B B ,τ s +τ B
τ s +τ B

where

1
1
= σ ε− 2 and τ B == θ −1σ ε− 2 .
var(ε i )var(ε B )τs and τB are the precision of the signals, showing how reliable the signals are. Being theτs =sufficient statistic implies the following equivalences:
E[ y | si , s B , p′] = E[ y | wi , p′] ,var[ y | wi , p′] = var[ y | wi , p′] .
That is, in order to derive the conditional expectations it is sufficient to know wi, and theweighted averages of si and sB. You do not need each value of si and sB. It is worth noting that theweights of si and sB are their precisions. A more precise signal has a greater impact on theconditional expectations.
Now conditional expectations have just two signals as conditions, and we can apply the
projection theorem that we used in the proof of proposition 1. Thus, we haveE[ y | si , s B , p, p′] = E[ y | wi , p′]−1

cov(wi , p′) ⎞ ⎛ wi − Ewi ⎞⎛ var wi⎟ ⎜⎟= y + (cov( y, wi ) cov( y, p′) )⎜⎜var p′ ⎟⎠ ⎜⎝ p′ − Ep′ ⎟⎠⎝ cov(wi , p′)= y + λw ( wi − Ewi ) + λ p′ ( p′ − Ep′)

var[ y | si , s B , p, p′] = var[ y | wi , p′]cov(wi , p′) ⎞⎛ var wi⎟= σ − (cov( y, wi ) cov( y, p′) )⎜⎜var p′ ⎟⎠⎝ cov(wi , p′)2yThe expected values, variances, and co-variances are
Ewi = Ep′ = y ,var wi = σ y2 +1,
τ s +τ B
27−1⎛ cov( y, wi ) ⎞⎟⎟⎜⎜⎝ cov( y, p′) ⎠ .

var p′ = γ y2σ y2 + γ B2σ B2 + γ x2σ x2 ,cov(wi , p′) = γ yσ y2 +γB,τi +τ Bcov( y, wi ) = σ y2 , andcov( y, p′) = γ yσ y2 .
Putting these into the demand function, we get the demand function as a linear function of wi
and p'. Substituting the linear demand function into the market clearing condition and take thelimit of n going to infinity, we have another price function in the form of equation (20).
The rational expectations equilibrium requires that the derived price function be equivalent to
the original price function (20). Since the price function is specified by the confidents (γy, γB, γx),
we need to find the fixed point of the correspondence from the coefficients of equation (20) to thecoefficients of the derived price function.
Since it is too difficult to derive the fixed point coefficients analytically, we use a simple
numerical procedure. In the numerical procedure to find the fixed point, we have to give values ofparameters. For given parameter values, we start from an arbitrary set of positive coefficients (γy0,
γB0, γx0), and then derive the coefficients (γy1, γB1, γx1) of the market clearing price function. If (γy1,
γB1, γx1) are incidentally equal to (γy0, γB0, γx0), this is the set of parameters we are looking for. If
not, we feed back the derived coefficients (γy1, γB1, γx1) as an input of the correspondence, andderive new coefficients (γy2, γB2, γx2). If (γy2, γB2, γx2) are incidentally equal to (γy1, γB1, γx1), this is
the set of parameters we are looking for. If not, we repeat the process until we reach to the fixed
correspondence.
In Fig. 1, we fix four parameters as σy2 = 5, σε2 = 3, σx2 = 5, a=1 and take different values for θ.
For each value of θ, we first derive the equilibrium price function. Then, using that function we
calculatevar[ p′ − y ] = (1 − γ *y ) 2 σ y2 + γ B*2θσ ε2 + γ x*2σ x2for each value of θ.
In Fig. 2, we fix three parameters as σy2 = 5, σx2 = 5, a=1, and give different values for θ and2σε . For each pair of θ and σε2, we first derive the equilibrium price function. Then, using thatfunction we calculate22( M − 1) ⎛ λw ⋅ τ s ⎞ 2 ⎛ λw ⋅τ s ⎞⎜⎟ σ ε ≈ ⎜⎜⎟⎟ σ ε 2
E[ H ( s1 ,L, sM , s B , q)] =+M ⎜⎝ τ s + τ B ⎟⎠
τ
τ
B ⎠
⎝ s
when M is large.

28

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32

Table 1. Intervention policy in Japan and the U.S.
Period＜Full sample period ： 3430 days＞
5/13/1991-7/2/2004
Average volume of interventions per day(unit: 100 million yen for JP int. and 1million
dollars for US int.)＜Period 1 ： 1072 days＞
5/13/1991-6/20/1995
Average volume of interventions per day(unit: 100 million yen for JP int. and 1million
dollars for US int.)＜Period 2 ： 1056 days＞
6/21/1995-7/7/1999
Average volume of interventions per day(unit: 100 million yen for JP int. and 1million
dollars for US int.)＜Period 3 ： 918 days＞
7/8/1999-1/13/2003
Average volume of interventions per day(unit: 100 million yen for JP int. and 1million
dollars for US int.)＜Period 4 ： 384 days＞
1/14/2003-7/2/2004
Average volume of interventions per day(unit: 100 million yen for JP int. and 1million
dollars for US int.)

Total
intervention
days
343

JP Interventions
Unannounced
Announced
but reported
interventions
interventions

Secretinterventions

Totalintervention
days

44
12.8%

164
47.8%

135
39.4%

22

1991

4225

1735

1573

165

10
6.1%

118
71.5%

470

642

24

US Interventions
Unannounced but
Announced
Secretreportedinterventions
interventions
interventions
11
50.0%

11
50.0%

0.0%

358

398

318

0

37
22.4%

18

7
38.9%

11
61.1%

0.0%

514

281

328

344

318

0

8
33.3%

14
58.3%

2
8.3%

4

4
100.0%

0
0.0%

0.0%

5105

4598

6025

683

492

492

0

0

25

25
100.0%

0
0.0%

0
0.0%

0

0

0

0

5282

5282

0

0

0

0

0

0

129

1
0.8%

32
24.8%

96
74.4%

0

0

0

0

2719

10667

4359

2090

0

0

0

0

Source: The Ministry of Finance of Japan, Quarterly Review of Federal Reserve Bank of NY, Bloomberg and Reuters.
Note. The US interventions during the sample period were all coordinated with the Japan.

33

0

0

0

Table 2. GARCH estimation with intervention dummies
Full sample
periodPeriod 1 (PreSakakibara)

Period 2(Sakakibara)

Period 3(Kuroda)-0.036 **(0.016)-0.011 ***(0.004)0.059 ***
(0.011)0.404(0.566)0.185 *
(0.099)-0.201 ***(0.051)-0.149 **(0.062)0.717 **
(0.340)0.751 ***
(0.197)-0.036 *(0.021)-0.012(0.010)-0.363 ***(0.080)-1.081 **(0.491)0.914(0.584)-0.103 **(0.042)-0.037(0.115)-0.249(0.703)
1.214 ***
(0.166)-0.201(0.299)-0.051(0.061)0.084 *
(0.045)4.221(5.784)0.803 **
(0.351)-0.246(0.302)0.382(0.511)0.038(2.102)--0.039(0.049)-0.009(0.011)
0.057(0.035)0.023(0.237)--0.332(0.254)-0.266(0.231)0.030 ***
(0.011)
0.174(3.894)-0.015(0.114)-0.094(0.063)-JP announced
intervention dummy
JP unannounced but
reported int. dummy
JP secret intervention
dummy
US announced
intervention dummy
US unannounced but
reported int. dummy

0.006 **
(0.003)0.032 ***
(0.003)0.953 ***
(0.005)0.007(0.009)0.001(0.002)
0.346 *
(0.198)-0.017(0.016)-0.034 ***(0.006)0.004(0.005)0.044(0.084)0.286 ***
(0.079)0.258 ***
(0.040)0.007 **
(0.003)0.983 ***
(0.003)0.003 ***
(0.001)0.021(0.014)0.373 ***
(0.090)-0.130(0.112)-0.031 ***(0.007)0.014(0.012)0.137(0.156)-0.015(0.038)0.339 ***
(0.034)0.059 ***
(0.007)0.939 ***
(0.007)0.014 ***
(0.004)-0.031 **(0.013)-0.354(1.230)0.471 *
(0.260)0.056(0.048)-0.110 ***(0.023)0.078(0.558)-0.435 **
(0.195)0.008 ***
(0.003)0.912 ***
(0.003)0.001(0.001)-0.021 ***(0.006)0.104 ***
(0.031)-0.088 ***
(0.031)0.181 ***
(0.051)0.574 ***
(0.100)0.039(0.035)-0.011 ***(0.004)-0.045(0.947)0.088(0.062)-0.049 **(0.021)-Obs.
Log Likelihood

3430-3453.09

1072-1027.8

1056-1146.3

918-896.061

384-305.017

Mean Equation
Constant
Interest rate differential
JP intervention volume
US intervention volume
JP announced
intervention dummy
JP unannounced but
reported int. dummy
JP secret intervention
dummy
US announced
intervention dummy
US unannounced but
reported int. dummy
Variance Equation
ConstantArch(-1)
Garch (-1)
Holiday
JP intervention volume
US intervention volume

Period 4(Mizoguchi)Standard errors are in parenthesis. *, ** and *** denote statistical significance at the 10%,
5% and 1% levels, respectively. There were no US interventions in Periods 3 and 4. The
scales are 100 million yen for JP interventions and 1 million dollars for US interventions.

34

Table 3. GARCH estimation with intervention dummies and implied volatility
Full sample
periodMean Equation
Constant

Period 1 (PreSakakibara)

Period 2(Sakakibara)

Period 3(Kuroda)Period 4(Mizoguchi)

JP int. volume ×IV(-1, 1m)
JP announced int. ×
IV(-1, 1m)
JP unannounced int. ×
IV(-1, 1m)
JP secret int. ×
IV(-1, 1m)-0.025(0.050)-0.010 **(0.005)-0.034(0.052)-0.112(0.428)-1.570 ***(0.510)-0.089(0.219)-0.006(0.369)0.968 ***
(0.263)0.946 ***
(0.138)0.000(0.005)0.009 **
(0.005)0.138 ***
(0.040)-0.014(0.019)-0.015(0.039)-0.253 **(0.122)0.001(0.012)0.048(0.576)-0.755(0.523)-1.595(2.911)-0.145(0.359)0.134(0.684)0.067(1.281)1.294 ***
(0.161)0.024 *
(0.013)-0.032(0.043)0.168(0.208)-0.003(0.029)-0.021(0.064)-0.190(0.308)-0.060(0.061)-0.116(0.345)-1.036(5.025)-5.185 **(2.298)-1.263(2.285)-8.884(148.348)
2.212(1.782)-0.004(0.006)0.016(0.027)0.497 ***
(0.170)0.081(0.170)0.708(11.136)-0.014(0.110)-0.008(0.012)-0.146(0.346)0.621(2.196)-0.002(0.011)0.016(0.028)-0.042(0.176)--0.321(0.358)-0.330(0.234)-0.083(0.233)-0.185(5220)
0.649(1.023)0.372(0.707)-0.009(0.024)0.014(0.025)-0.078(0.113)-0.054(0.076)Obs.
Log likelihood

3429-3467.9

1071-1058.1

1056-1149.57

918-897.937

384-312.375

Full sample
periodPeriod 1 (PreSakakibara)

Period 2(Sakakibara)

Period 3(Kuroda)Period 4(Mizoguchi)Interest rate differential
JP intervention volume
US intervention volume
JP announced
intervention dummy
JP unannounced but
reported int. dummy
JP secret intervention
dummy
US announced
intervention dummy
US unannounced but
reported int. dummyIV(-1, 1m)

Mean Equation
Constant

JP int. volume ×IV(-1, 3m)
JP announced int. ×
IV(-1, 3m)
JP unannounced int. ×
IV(-1, 3m)
JP secret int. ×
IV(-1, 3m)-0.038(0.061)-0.010 *(0.005)-0.036(0.061)-0.178(0.419)-2.355 ***(0.593)-0.010(0.296)-0.015(0.423)0.893 ***
(0.268)0.968 ***
(0.137)0.001(0.006)0.010 *
(0.006)0.208 ***
(0.048)-0.021(0.027)-0.014(0.044)-0.487 **(0.190)0.011(0.013)-0.224(0.751)-0.707(0.497)-2.187(3.716)0.126(0.499)0.468(0.979)0.076(1.299)1.302 ***
(0.159)0.047 **
(0.019)-0.012(0.059)0.217(0.279)-0.027(0.042)-0.053(0.091)-0.097(0.318)-0.045(0.062)0.226(0.526)-0.070(15.587)-7.808 **(3.480)-4.814(3.938)-7.550(95.031)
1.521(4.974)-0.005(0.007)-0.011(0.041)
0.691 ***
(0.260)0.596(7.046)0.000(0.000)-0.036(0.141)-0.006(0.013)-0.196(0.350)0.502(2.318)0.001(0.015)0.020(0.029)-0.032(0.193)--0.325(0.443)-0.336(0.235)-0.114(0.313)-0.069(15925.990)
1.141(1.482)0.631(1.006)-0.009(0.036)0.017(0.034)-0.130(0.167)-0.082(0.109)Obs.
Log likelihood

3429-3464.43

1071-1056.79

1056-1151.71

918-897.325

384-312.332

Interest rate differential
JP intervention volume
US intervention volume
JP announced
intervention dummy
JP unannounced but
reported int. dummy
JP secret intervention
dummy
US announced
intervention dummy
US unannounced but
reported int. dummyIV(-1, 3m)

35

Standard errors are in parenthesis. *, ** and *** denote statistical significance at the 10%,
5% and 1% levels, respectively. There were no US interventions in Periods 3 and 4. The
scales are 100 million yen for JP interventions and 1 million dollars for US interventions.
The implied volatility is calculated from the yen/dollar option price (at the money).

36

Table 4. Implied volatility estimation with intervention dummies% change in IV(1m)Constant
IV(-1, 1m)
Holiday
JP intervention volume
US intervention volume(-1)
JP announced
intervention dummy
JP unannounced but
reported int. dummy
JP secret intervention
dummy
US announced
intervention dummy
US unannounced but
reported int. dummy
JP int. volume ×IV(-1, 1m)
JP announced int. ×
IV(-1, 1m)
JP unannounced int. ×
IV(-1, 1m)
JP secret int. ×
IV(-1, 1m)
Obs.
2

Adj. R% change in IV(3m)Constant
IV(-1, 3m)
Holiday
JP intervention volume
US intervention volume(-1)
JP announced
intervention dummy
JP unannounced but
reported int. dummy
JP secret intervention
dummy
US announced
int. dummy (-1)
US unannounced but
reported int. dum. (-1)
JP int. volume ×IV(-1, 3m)
JP announced int. ×
IV(-1, 3m)
JP unannounced int. ×
IV(-1, 3m)
JP secret int. ×
IV(-1, 3m)
Obs.
2

Adj. R

Full sample
period
1.597 ***
(0.587)-0.196 ***(0.054)1.704 ***
(0.220)-1.224 **(0.530)-5.274(7.599)18.282 ***(6.020)6.207 **
(2.497)1.792(2.134)7.572(4.951)
7.782 *
(4.104)0.134 ***
(0.047)-1.307 ***(0.479)-0.437 **(0.214)-0.209(0.210)Period 1 (PreSakakibara)2.726 ***
(0.891)-0.349 ***(0.089)2.109 ***
(0.434)19.277 **(7.870)-8.062(7.069)10.284(9.785)-2.421(4.575)-1.519(3.958)4.119(3.224)6.950 *
(3.963)-1.207 **(0.581)-0.745(0.824)0.203(0.367)0.094(0.333)

Period 2(Sakakibara)
1.506(1.029)1.120 ***
(0.406)1.120 ***
(0.406)-1.075(2.356)-23.428(20.235)
15.700(13.302)12.690(14.053)
19.770 ***(2.578)24.375 *(13.173)
0.111(0.180)-1.172(0.922)-0.825(1.117)-1.196 ***(0.200)

3429

1071

1056

0.058
Full sample
period0.087
Period 1 (PreSakakibara)

0.046
Period 2(Sakakibara)

0.961 **
(0.388)-0.106 ***(0.035)0.609 ***
(0.136)-0.792 **(0.372)-3.515(3.913)8.993 **
(4.378)3.305 *
(1.749)1.135(1.730)4.298(2.947)
3.838 *
(2.028)0.082 **
(0.033)-0.629 *(0.367)-0.228(0.156)-0.124(0.176)

1.827 ***
(0.708)-0.213 ***(0.070)0.979 ***
(0.238)12.435 *(6.532)-4.764(3.188)7.519(7.794)-2.316(3.431)-1.476(3.302)
1.975(1.580)3.321 *
(1.739)-0.849(0.522)-0.572(0.677)0.206(0.289)0.088(0.302)0.952(0.687)-0.089(0.055)0.381(0.262)-1.962(1.653)-15.780(14.462)
20.546 *(11.450)
15.040(9.861)
6.065 ***
(1.782)15.169(9.866)0.158(0.125)-1.548 *(0.811)-1.043(0.775)-0.276 **(0.136)

Period 3(Kuroda)3.415 ***
(1.020)-0.361 ***(0.096)
1.598 ***
(0.348)1.836(2.019)-1.284(12.546)-0.057(0.161)0.035(1.009)918
0.087
Period 3(Kuroda)2.366 ***
(0.777)-0.229 ***(0.072)0.431 *
(0.245)0.201(0.878)-3.272(8.173)0.027(0.065)0.313(0.645)-Period 4(Mizoguchi)
5.399(3.304)-0.616 *(0.344)2.436 ***
(0.668)-0.637(1.465)7.667 **
(3.474)0.381(7.621)
4.333(5.600)0.075(0.153)-0.024(0.764)-0.571(0.601)384
0.085
Period 4(Mizoguchi)
5.030 *
(2.588)-0.547 **(0.275)0.647(0.405)-0.459(1.450)5.576 **
(2.382)-0.602(7.314)2.671(4.478)0.050(0.157)0.077(0.783)-0.330(0.484)

3429

1071

1056

918

384

0.030

0.065

0.025

0.048

0.028

37

Standard errors are in parenthesis. *, ** and *** denote statistical significance at the 10%、
5% and 1% levels, respectively. There were no US interventions in Periods 3 and 4. The
scales are 100 million yen for JP interventions and million dollars for US interventions. The
implied volatility is calculated from the yen/dollar option price (at the money).

38

Figure 1. The effect of an announcement on the variance of a bubble.
20.00

Pre-announcement

15.00

var[ p − y ]10.00

Post-announcement
var[ p’ − y ]
5.00

0.00

10−2

10−1

1

θ

102

10

The graph is drawn for the following parameters. σy2 = 5, σε2 = 3, σx2 = 5, a = 1.
Figure 2. The effect of an announcement on the heterogeneity of forecasts.
1.2

Pre-announcement heterogeneity1θ = 10θ=3

0.8

Post-announcement
0.6

heterogeneity

θ=1
0.4

0.2

0
0

5

10

15

The graph is drawn for the following parameters. σy2 = 5, σx2 = 5, a = 1.

39

20

σε2

Figure 3. Japanese interventions and yen/dollar rate
8000

75

Intervention volume (dollar purchases, montly
total)
Yen/dollar rate (monthly average)(billion yen)

(yen/dollar)
85

6000

95
4000
105

2000
115

125

0

135
‐2000

‐4000

145

Period 1

Period 2

Period 3

Period 4

Mr.Chino/Mr.Nakahira

Mr.Kato/Mr.Sakakibara

Mr.Kuroda

Mr.Mizoguchi

40

(%)

20

May‐91
Sep‐91
Jan‐92
May‐92
Sep‐92Jan‐93
May‐93
Sep‐93Jan‐94
May‐94
Sep‐94
Jan‐95
May‐95
Sep‐95
Jan‐96
May‐96
Sep‐96
Jan‐97
May‐97
Sep‐97
Jan‐98
May‐98
Sep‐98Jan‐99May‐99Sep‐99Jan‐00
May‐00
Sep‐00Jan‐01
May‐01
Sep‐01
Jan‐02
May‐02
Sep‐02Jan‐03May‐03
Sep‐03Jan‐04May‐04

Figure 4. Implied volatility
25

Implied volatility(1M)

Implied volatility
(3M)

15

10

5

Period 1
Period 2
Period 3
Period 40Mr.Chino/Mr.Nakahira
Mr.Kato/Mr.Sakakibara
Mr.Kuroda
Mr.Mizoguchi

41