WPS5579
Policy Research Working Paper 5579
How Does Public Information
on Central Bank Intervention Strategies
Affect Exchange Rate Volatility?
The Case of Peru
B. Gabriela Mundaca
The World Bank
Development Economics Prospect Group
Emerging Global Trends Team
February 2011
Policy Research Working Paper 5579
Abstract
Intervention operations in the foreign exchange market has moved the sol in the intended direction but only
are used by the Banco Central de Reserva del Peru to during the time the Banco Central de Reserva del Peru
manage both the level and volatility of their exchange has announced it would be active in the foreign exchange
rates. The Banco Central de Reserva del Peru provides market. The authors also find that the expectation of
information to the market about the specific hours of future interventions by the Banco Central de Reserva del
the day interventions would take place and the total Peru decreases the volatility of the sol when it intervenes
amount of intervention. It consistently buys and sells on to avoid an appreciation of the sol; however, the opposite
the foreign exchange market to avoid large appreciations occurs when the intervention takes place to defend
and depreciations of the Peruvian nuevo sol against the the sol from depreciation. Indeed, the sol has been less
U.S. dollar (Sol/USD), respectively. The estimates in this volatile during periods when the Banco Central de
paper indicate that past information on interventions Reserva del Peru has intervened than otherwise.
This paper is a product of the Emerging Global Trends Team, Development Economics Prospect Group. It is part of a
larger effort by the World Bank to provide open access to its research and make a contribution to development policy
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The author may be contacted at gmundaca@worldbank.org.
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Produced by the Research Support Team
How does public information on central bank
intervention strategies affect exchange rate
volatility? The case of Peru
B. Gabriela Mundaca *
*
The views and conclusions expressed in this paper are from the author's alone, and in no way reflect those
of the World Bank, its Executive Directors, or the countries they represent. Any errors are the responsibility of
the author alone.
I am very thankful to the Central Bank of Peru, Banco Central de Reserva del Peru, which kindly provided me
the data. This paper was presented at the XXVIII Encuentro de Economistas organized by the Banco Central
de Reserva del Peru (BCRP) in November 2010 in Lima, Peru.
Introduction
Some central banks in emerging economies target the exchange rate level while others have
other aims: to slow the rate of change of the exchange rate; to dampen exchange rate
volatility (in some cases to satisfy an inflation target); to supply liquidity to the forex market;
or to influence the level of foreign reserves. Some other central banks have a mixture of
objectives. See BIS (2005).
The Banco Central de Reserva del Peru (BCRP) has had an inflation targeting
framework for monetary policy since 2002. However, Peru is a dual-currency economy with
predominant dollarization, and the BCRP, being aware of such conditions, cannot completely
neglect how the exchange rate develops when designing and implementing monetary policy
in Peru. The BRCP cannot increase further the inherent risks of the domestic currency, and
instead promote the role of the currency as store of value and avoid excessive volatility to
avoid harmful consequences. High volatility of the sol/USD could have effects on first,
inflation given the degree of openness of Peru; second, international trade because the market
for derivatives is not yet well developed in Peru (see Mundaca (2010)); and third, the balance
sheets of the Peruvian private sector given the relatively highly dollarized of the economy.
Therefore, the BCRP has as mandate to smooth out the path of the exchange rate and avoid
high exchange rate volatility by intervening in the foreign exchange market.
The BCRP is also taking measures to promote de-dollarization in its inflation
targeting regime, and it is now evident that financial dollarization has steadily decreased over
recent years. For example, in 2004, 70% of credit to the private sector was denominated in
foreign currency; by the end of 2009, this figure decreased to around 55% (deposits are more
or less 50%). The measures that have been taken are using the interest rate (i.e., overnight
2
interest rates) as an operational target to stabilize and make predictable the relevant short-
term interest rates in the domestic currency. This practice should naturally contribute to the
development of the yield curve of interest rates for different maturities for public debt in
domestic currency. This will in turn foster incentives for issuing long-term instruments by the
private sector that can be used to hedge against exchange rate risk and foreign exchange
liquidity risks. In addition, the BCRP also requires that commercial banks have large reserves
on their foreign currency liabilities. The implementation of these policies to de-dollarize the
economy, together with stronger economic fundamentals, should eventually decrease the
need to both intervene in the foreign exchange market over time, and accumulate
international reserves to carry out such interventions. Furthermore, there are risks involved in
making the exchange rate into a nominal anchor for monetary policy and overriding the
already institutionalized inflation targeting. The latter may cause shifts in expectations as the
market becomes uncertain as to what the BCRP's objectives really are.
The goals of this paper are threefold: i) to briefly present a stochastic optimal control
model for central bank interventions in the foreign exchange market similar to that presented
in Mundaca and Oksendal (1998); (ii) to empirically test the predictions of our theoretical
optimal control model by estimating the Central Bank of Peru's (Banco Central de Reserva
del Peru (BCRP)) reaction function for intervening in the foreign exchange market; and (iii)
to test the predictions of our model by empirically analyzing the effect of the BCRP's
intervention policy on the exchange rate of the Peruvian currency, the sol, against the US
dollar and its volatility.
3
This paper's empirical analysis uses intra-daily exchange rate data from 2004 to
2009. Because the BCRP's interventions are always made public at the end of its official
participation in the foreign exchange market, we are able to differentiate between the effect
of past information of interventions and expectations of future interventions on the exchange
rate. This distinction is important because the whole purpose of making the information on
intervention activities public is to reduce uncertainty and to establish that the BCRP is
committed to achieving certain goals. Moreover, we use the intervention decisions that are
observed by the market to test the significance of the signaling channel (Mussa (1981)) of the
intended monetary policies. Expected future and unannounced central bank participation in
the foreign exchange market involves a good deal of asymmetric information; as a
consequence, uncertainty may or may not dissipate completely. We will study the
significance of this uncertainty.
The studies outlined in the relevant literature that examine the effect of central bank
interventions on the volatility of the exchange rate have obtained mixed results. However,
these differences are mainly attributable to the varying quality of the data used in the
empirical exercises, as well as the monetary policy regimes, data frequencies, and the
econometric methods used to measure the effects of interventions on the exchange rate.
We use the methodology of Mundaca and Oksendal (1998) to model an optimal
intervention policy for central banks to stabilize the exchange rate. Two types of controls are
considered: discrete interventions, which cause a jump in the exchange, and continuous small
interventions, with the purpose of smoothing variation in the exchange rate. The first control
represents the infrequent but large interventions to prevent large variability due to random
4
events (i.e., political events), and the continuous control takes place to smooth out changes in
the sol that inevitably result from adverse changes in economic fundamentals. As in Mundaca
and Oksendal (1998), the range of variation of the exchange rate is determined endogenously
from the optimal stochastic intervention control problem.
We test our model of stochastic control empirically using intra-daily data. Even when
the period within which the BCRP would intervene has been made public (between 11:00
and 13:30 everyday), forward-looking market participants still remain uncertain as to if or
when interventions will take place. This uncertainty occurs because on a daily basis, the
market does not know how much appreciation/depreciation on one side and volatility on the
other side the BCRP is ready to tolerate. The market needs to assess the probability of
intervention by the BCRP. Therefore, it should be not only interesting but also useful to
analyze the effect of such uncertainty regarding the probability of intervening, and to
compare it with the effect that past and public information on interventions may have on both
the level and the volatility of the exchange rate itself. To carry out these tasks, our empirical
model considers the unannounced future interventions as dichotomous, endogenous variables
that both depend and affect the exchange rate. Modeling future interventions as endogenous
is realistic because market participants make decisions on the exchange rate, taking into
account their beliefs about possible central bank interventions in the foreign exchange
markets. Finally, this study shows that the disturbances of the exchange rate mean equation
are characterized not only by an autoregressive conditional heteroscedastic (ARCH) process
but also by another source of heteroscedasticity, namely their correlation with the
intervention variables. Accordingly, we allow expectations of central bank's interventions
enter as explanatory variables in the conditional mean and variance of the exchange rate.
5
The paper is organized as follows. Section 2 presents the theoretical model of the
optimal control of the exchange rate. Section 3 includes a quick glance at the key aspects of
foreign exchange intervention policies in Peru and a summary of the statistics of the main
variables used in the empirical analysis. Section 4 contains the empirical model that is used
to test the theoretical model. We present our estimation results of the central bank's
intervention and the conditional mean and variance of the exchange rate in Section 5. Section
6 concludes.
1. A theoretical model for the optimal control of the exchange rate
Using the theory of combined stochastic control, we model the monetary authorities as
minimizing the total costs of large exchange rate deviation from certain means and of
intervening in the foreign exchange market with the purpose of stabilizing the exchange rate.
Yt denotes the level of the exchange rate: sol/USD. The central bank aims to keep Yt stable
and at least close to some average Y . To achieve its objective, it implements two types of
control:
i) The central bank can intervene frequently with small amounts of foreign
exchange to smooth the exchange rate's movements. This type of control, m=
(mt)tR, is called continuous control. The set of all continuous control is
denoted by U.
ii) The central bank may intervene in the foreign exchange market forcefully
selling or buying a large selected amount of foreign exchange, j, at discrete
6
and selected (stochastic) times, j, to avoid drastic changes in the exchange
rate. This type of intervention is represented by the double sequence:
(1 ,2 ,..., N ; 1 , 2 ,..., N ) . (1)
(1) is the impulse control in which N , k k+1 and k as k N (so
that if N is finite, then N = ). The set of all impulse controls is denoted by
V.
The pair w = (m,) U × V is called a combined stochastic control. Large deviations
of the exchange rate from its mean on a daily basis, are costly for the economy, but the
central bank can apply the controls w = (m,) to stabilize the exchange rate and thus reduce
these costs. Note, however, that it is also costly for the central bank to implement such
controls. Mohanty and Turner (2005) have documented the consequences of too frequent
interventions. Consequently, the central bank in this paper will then implement such controls
in an optimal manner.
Thus, if the pair w = (m,) is implemented, the exchange rate will follow the
following stochastic process:
t
Yt y0 b(m )ds B ( ) ( ) ; or
s 0
s
t
j: j t
j (2.1)
t
Yt y0 b(m )ds B ( ) ( )
s 0
s
t
j: j t
j . (2.2)
y0 is the initial value of sol/USD, Yt; > 0 is a constant; b(ms) measures the effect of
continuous interventions by the central bank, selling (m < 0) and buying (m > 0) foreign
7
currency, on the exchange rate; while () denotes the effect on the exchange rate of
occasional interventions, buying (if > 0) or selling (if < 0). Bt() for denotes
Brownian motion.
Assume that the discount rate is > 0 and that the cost of large deviations of the
exchange rate from its mean is K(Yt Y ) for K(x) 0 for all x. Let R(m) be the cost of
applying the continuous control (i.e., not enough economies of scale), and the costs of
discrete interventions are denoted by L(j) > 0 (i.e., large sterilizations create conflicts with
monetary policy).
Taking into consideration the above, the total and discounted expected cost of
applying the combined intervention control w is as follows:
T t
e ( K (Yt Y ) R(m))dt L( j )e .
j
J ( s, y ) E
w s, y
(3)
s j: j T
T is a given (fixed) future time and Es,y denotes expectations with respect to the
probability law of Yt with initial value y and mean value Y . We also assume that the costs of
selling foreign currency are not necessarily the same as those of buying foreign currency.
The optimization of equation (3) determines the characteristics of the stochastic
process of the sol/USD and the variables governing such a process.1
1
Further details can be found in Mundaca and Oksendal (1998).
8
2. Key aspects of the foreign exchange intervention policies in Peru and statistical
summary
3.1 The Banco Central de Reserva del Peru (BCRP) and its intervention policies
Peru attempts to follow a flexible exchange rate while adopting inflation targeting. The
BCRP determines, on a daily basis, the implicit band within which the sol is allowed to move
against the US dollar. This implicit band is not publicly known, but the BCRP has made it
clear that it aims to minimize excessive volatility of the sol. According to Humala and
Rodriguez (2009), the BCRP intervenes to reduce excess volatility in the exchange market,
but in recent years, interventions also have concentrated on US dollar purchases. Such
interventions might indicate that Peru may sometimes prefer a depreciated sol against the US
dollar, at least when depreciation is not substantiated by economic fundamentals. As an
institutional issue, note that the BCRP has also made known that if it finds it necessary to
intervene in the foreign exchange market on any day t, it will do so only between 11.00 am
and 1:00 pm on that day. It is also known that decisions to intervene on day t are principally
based on observing the sol at 11.00 am and how it has developed with respect to previous
days. The public are informed about the total amount of intervention by the BCRP at 1:00
pm. (Armas (2005)).
3.2 Some general stylized facts and a summary of statistics
This paper's data have been obtained from the officials at the BCRP. General statistics of the
relevant variables, including those used for the empirical work, are shown in Table 1.
The last three rows in Table 1 show that the exchange rate is on average the least
variable between 11.00 am and 1:00 pm on any particular day (represented by Xt13-11); it is
9
more variable during the other periods. Recall that the BCRP only intervenes between 11.00
am and 1:00 pm and that this is known by the market.
Table 1. Summary of statistics of variables used in the empirical analysis
Series Obs Mean Std. Deviation Minimum Maximum
Net Interventions 1483 14.5945 60.2236 -443.8000 478.7000
Accumulated Interventions
in the last 4 days: X t4days 1484 58.5201 194.8345 -1277.0000 1626.4000
Bid price at 1100 1483 3.1726 0.1912 2.4950 3.5055
Ask price at 1100 1483 3.1745 0.1902 2.6920 3.5075
(bid+ask)/2 at 1100:Yt11 1483 3.1735 0.1906 2.6915 3.5065
Bid price at 1330 1483 3.1721 0.1913 2.4950 3.5035
Ask price at 1330 1483 3.1748 0.1897 2.6940 3.5075
(bid+ask)/2 at 1330:Yt13 1483 3.1735 0.1904 2.6935 3.5055
SPREAD 1483 0.0774 0.0974 -0.3176 1.5554
log(Yt11/ Yt-1 13
)*100:Xt11-13 1483 -0.0110 0.4026 -7.6205 8.1808
log(Yt13/Yt11)*100:Xt13-11 1483 -0.0011 0.2184 -3.5380 2.7790
log(Yt13/Yt-113)*100:Xt13-13 1483 -0.0122 0.4489 -7.6205 8.1977
Such statistics indicate that the Peruvian sol seems to be less volatile during periods
when the BCRP can officially participate in the foreign exchange market. The BCRP has
informed the public that regardless of how the exchange rate moves, it does not participate at
other times of the day, i.e. between day t at 11.00 am and day t-1 at 1:00 pm (represented by
Xt11-13). However, the time interval in which the central bank can be both present and absent
is between 1:00 pm at day t and 1:00 pm at day t-1 (represented by Xt13-13).
10
The following figures show the average between the bid and ask prices for the
sol/USD observed at 11.00 am (Figure 1) and the percentage change in the exchange rate at
different times of the day represented by the difference in the logs of the exchange rate
(Figures 2 and 3). Figure 2 shows the differences between the logs of the average bid and ask
prices observed at 11.00 am at day t and the logs of the average bid and ask prices observed
at 1:00 pm at day t-1. Xt11-13 is the only period in which it is known that the BCRP can be active in
the forex. Figure 3, however, shows the difference between the logs of the average bid and ask
prices observed at 1:00 pm on day t and the logs of the average bid and ask prices observed
at 11.00 pm on day t, Xt13-11, the period in which the central bank is absent in the forex. The
development of the (100 times) log difference of the bid and ask at 11.00 am is displayed in
Figure 4. Each of the figures also includes the patterns of the net interventions by the BCRP
in millions of USD. Net positive interventions indicate net buying of foreign reserves by the
BCRP, and negative interventions indicate net selling of foreign reserves.
Figure 1. Sol/USD observed at 11.00 am Figure 2. Changes in logs of Sol/USD
and Net Interventions by BCRP and Net Interventions by BCRP: Xt11-13
11:00 am Interbank Rates. 2004 - 2009 Interbank Rates. 2004 - 2009
3.6 500 9 500
8
3.4 7
250 250
6
3.2
% Change
mill USD
mill USD
5
0 0
4
3.0
3
-250 -250
2.8 2
1
2.6 -500 0 -500
3200 3400 3600 3800 4000 4200 4400 3200 3400 3600 3800 4000 4200 4400
SOLUSD1100 Net InterventUSD StandDevSol/USD BCRP NetInterven
11
Figure 3. Changes in logs of Sol/USD Figure 4. Bid-Ask Spread in the
and Net Interventions by BCRP: Xt13-11 Interbank Rate and Net Interventions
by BCRP
Interbank Rates. 2004 - 2009 Interbank Rates. 2004 - 2009
2.5 500 1.75 500
1.50
2.0
250 1.25
250
1.00
1.5
% Change
mill USD
mill USD
0.75
0 0
0.50
1.0
0.25
-250 -250
0.5 0.00
-0.25
0.0 -500 -0.50 -500
3200 3400 3600 3800 4000 4200 4400 3200 3400 3600 3800 4000 4200 4400
StandDevSol/USD BCRP NetInterven bid-ask spread Net InterventUSD
Figures 1, 2, and 3 suggest that the BCRP decisions to intervene target both the levels
and the changes in the sol/USD. Regarding spreads, it is not clear from Figure 4 whether the
BCRP responds to large spreads and makes any attempt to avoid them, but we test for that
possibility.
Notice that Figures 2 and 3 confirm the results of the sample statistics on the
percentage changes in the exchange rate measured during times when the BCRP has
announced that it can intervene and times when the BCRP has indicated it will not intervene
in the forex. Notice that during the period between August 2008 (observation 4200) and
December 2008 (observation 4300), the sol experienced a rapid depreciation and the highest
volatility within the period of study. Nevertheless, the volatility was always smaller between
11.00 am and 1:00 pm on any specific day. We next need to determine whether such
distinction is due to the BCRP's intervention policy. How is the behavior of the participants
in the exchange rate market affected by BCRP announcing that it will participate and by how
much (at the end of its intervention activities)? How do market expectations regarding future
12
intervention affect the exchange rate level and its volatility? We attempt to answer these
questions in the following sections.
3. An empirical model for the sol/USD rate
We test our theoretical model first estimating the central bank's reaction function for
intervening; and second, by estimating the conditional mean and variance of the sol/USD
rate. The variance is assumed to follow the Exponential GARCH (1,1) process identified by
Nelson (1991) (EGARCH(1,1)). Expected central bank intervention decisions entering in
both the conditional mean and variance, are assumed to be endogenously determined. Past
information on intervention is also analyzed. The empirical analysis here is an extension of
Mundaca's (2001) econometric methodology.
4.1 Reaction functions of the Banco Central de Reserva del Peru (BCRP) for intervening
This section presents an empirical adaptation of the combined stochastic control, the pair w =
(m,) presented in Section 2, which embodies the central bank's optimal decisions to
intervene to smooth the movements of the exchange rate: large and infrequent interventions
and continuous interventions in the foreign exchange market. Such optimal decisions should
minimize the central bank's costs.
Consider MB and MS the variables representing the central bank participation buying
and selling foreign exchange, respectively. These decisions to intervene are defined as
follows:
M tB 11apprect 1 12 ( X t11 X t4days ) 13 Spreadt 1 tB .
1 (4.1)
13
M tS 21deprect 1 22 ( X t11 X t4days ) 23Spreadt 1 tS .
1 (4.2)
The exchange rate used here is the (log) of the average between the bid and ask prices
observed at 11.00 am, Xt11. Recall that it is public information that the central bank makes
decisions after analyzing how the exchange rate has developed until 11.00 am on the day it is
evaluating whether to intervene or not. The variables apprec and deprec represent only
appreciation and depreciation of the sol with respect to the US dollar between today at 11:00
am and the day before at 1:00 pm (the last time that the central bank could have intervened).
Thus, the parameters 11 and 21 will indicate whether the central bank only buys foreign
exchange when the sol appreciates, or sells only if the sol depreciates. X t4days is the log of the
1
average change in the sol/USD over the last 4 days observed at 11:00 am. The spread is (100
times) the difference in logs of the bid and ask prices observed at t-1. We consider the
possibility that the central bank may be interested in correcting sufficiently large spreads by
intervening to alleviate lack of liquidity.
The market (and the econometrician) does not know the precise timing for future
central bank interventions, and they consequently needs to form expectations about the
central bank participation in the forex market. In view of this, we model intervention
decisions, MB and MS, as qualitative variables. MB and MS are greater than zero if the central
bank intervenes and zero otherwise. We define the dummy variables IB and IS, which are
going to be related to MB and MS in the following manner:
14
ItB = 1 iff MtB = ZtBB tB> 0
ItB = 0 iff MtB = ZtBB tB = 0 (5)
ItS = 1 iff MtS = ZtSS tS > 0
ItS = 0 iff MtS = ZtSS tS = 0.
Also, B = (11, 12, 13); S = (21, 22, 23); and ZtB and ZtS are matrices of
explanatory variables accompanying the 's of the decisions to intervene as defined in
equations (4.1) and (4.2).
We use the probit ML to estimate the parameters in (4.1) and (4.2), taking into
account (5) and using intra-daily data for the sol/USD between 2004 and 2009. Now, tB and
tS are random disturbances with the following distributions:
tB ~ N(0,1); tS ~ N(0,1); and cov(tBtS) = 0.
4.2 Empirical specification of the model for the exchange rate
Estimation of the model containing equations (2) and (3) requires identification and
estimation of their parameters. Note that the central bank is assumed to minimize the cost of
intervening, which implies minimization of K(Yt Y ), R(m), and L(j) > 0. Once this
minimization is achieved, the exchange rate is expected to evolve as described in (2). We
need to determine an econometric specification to estimated parameters of equation (2). Let
us consider a possible econometric specification for the conditional mean of sol/USD:
Et X t Wt t . (6)
15
Et+1[Xt] is the expected change in the exchange rate. Wt includes lags of X t and central
bank interventions in the foreign exchange market, both past and expected future
interventions.
As mentioned above, the BCRP does not intervene on any day earlier than 11.00 am or
later than 1:00 pm. This is common knowledge to the market, and the BCRP announces the
total amount of its intervention each day after finishing its participation in the foreign
exchange market at 1:00 pm. Nevertheless, on any particular day, participants in the market
(and the econometrician) are unable to know the exact timing of past and future possible
interventions. Note that receipt of a signal is not the same as a materialized intervention. The
actual time and amount of intervention occurring during the day are never made public.
Our specified equation (6) emphasizes the simultaneous determination of the expected
exchange rate and these expected future interventions. We designed our empirical model to
capture this simultaneity as accurately as possible. In this regard, we consider that the BCRP
makes decisions about whether to intervene or not every day at around 11.00 am. We also
consider that at the same time, market participants form expectations about both possible
central bank interventions and the future exchange rate at different time periods in a specific
day. With regard to the expectations of the market participants, the following strategies are
adopted:
Strategy 1: We consider how the market forms expectations about a possible exchange
rate change between 1:00 pm the previous day (which is the time when the BCRP
publishes its intervention activities and the last exchange rate observation the
16
econometrician has available in any particular day) to 11.00 am today. Keep in mind that
during this period, the BCRP has committed to not intervene at all in the foreign
exchange market.
Strategy 2: We consider how the market forms expectations about a possible exchange
rate change between 11.00 am and 13.30 pm on the same day.
Strategy 1 truly and solely represents how potential central bank interventions in the
permitted time frame affect the formation of market expectations on the exchange rate.
Strategy 2 allows us to capture partly the effect of signals on actual interventions and partly
the effect of expectations that interventions might take place between 11.00 am and 1:00 pm.
Note that even though the BCRP does not publicize its intervention activities until 1:00 pm
every day, the market might receive some signals as to whether the BCRP is present in the
forex between 11.00 am and 1:00 pm and yet an actual intervention might not materialize.
Thus, the two strategies comprise a period when the BCRP has announced it will intervene
and a period when the BCRP has committed to not intervene at all.
Now, following the arguments presented above and bearing in mind that independent of
what assumptions we make about the disturbance t, equation (6) alone cannot represent the
correct process for the exchange rate because future expected central bank interventions are
endogenous. Here, we hypothesize that future central bank decisions to intervene affect the
exchange rate, and such decisions depend on the exchange rate itself. To obtain consistent
estimates, one must therefore consider that the disturbance t is correlated with these future
intervention decision variables. More specifically, the error terms of the central bank's
reaction functions for intervening, tB and tS will be correlated with t. Thus, the estimation
17
method needs to take into account (4.1), (4.2) and (5) together with (6). Taken together, these
equations constitute an endogenous switching regression model for the exchange rate where
the switch is defined by the criteria functions (4.1), (4.2) and (5) (see Johnson and Kotz
(1972), Olsen (1980) and Mundaca (2001) for further details). That is
Et [X t | M tB 0; M tS 0; t 1 ] 1X t 1 2 X t 2 Intervt 1 Et [ t | M tB 0; M tS 0; t 1 ]
1X t 1 2 X t 2 Intervt 1 B Et [ tB | tB Z tB B ; t 1 ] S Et [ tS | tS ZtS S ; t 1 ]
( Z tB B ) ( Z tS S )
1X t 1 2 X t 2 Intervt 1 B S .
( Z tB B ) ( Z tS S )
(7)
In (7), t-1 represents all information available up to time t-1. We consider different AR
orders for Xt and found that the best representation is AR(2) for Xt. Note that the hazard
functions (ZtBB)/(ZtBB) and (ZtSS)/(ZtSS) are the truncated means of Et[tB|tB <
ZtBB] and Et[tS|tS < ZtSS], respectively, and they represent the conditional distributions of
MtB and MtS. More intuitively, the hazard functions represent the rates at which the
intervention spells are completed in a specific day, given that they took place that day. We
include information on interventions, Intervt-1, which are common knowledge to the market
on the day and time that the BCRP decides whether to intervene or not. The disturbance of
the mean equation (7), for example, t, is assumed to have zero mean and certain conditional
variance. This variance is assumed to follow an Exponential GARCH(1,1) (EGARCH(1,1))
process which was introduced by Nelson (1991), but it also includes the effect of central
18
banking interventions: both past interventions observed by the market and the squares of the
hazard functions. We then redefine Nelson's natural logarithm of the conditional variance as
follows:
t 1 2
ln(ht ) c a1 t 1 b ln(ht 1 )
ht 1 ht 1 1
. (8)
2 2
( Z tB B ) ( Z tS S )
B B B
S S S
Intervt 1
(Zt ) ( Z t )
The EGARCH models are motivated by evidence that large negative shocks have a
larger effect on volatility than corresponding large positive shocks. Historical volatility
measures, including GARCH models, do not capture this asymmetry. Another advantage of
the EGARCH model is that there is no need to artificially impose non-negativity constraints
on the model parameters. This is made possible because for the conditional variance, one
models log(2). Note that we also assume an EGARCH(1,1) process for the exchange rate,
assuming t-distribution for the error terms to account for the leptokurtosis of the exchange
rate.
The strategy to estimate (4.1), (4.2), (5), (7) and (8) consists of a two-stage method
suggested by Heckman (1978) and Lee (1978). In the first step, we estimated (4.1) and (4.2)
with observations IB and IS as a typical Probit model to obtain the estimates of the 's and
thereafter (ZtBB)/(ZtBB) and (ZtSS)/(ZtSS). In the second step, equations (7) and (8)
are estimated by numerically maximizing the likelihood function for the EGARCH(1,1)
model.
19
Again, by specifying the logarithm of the variance ht as a function of t, Nelson
ensured that the conditional variance stays positive even if some of the coefficients in (8) are
negative. Introducing t 1 / ht 1 permits us to analyze whether positive or negative values
of t will increase or decrease the conditional variance.
4. Estimation results
5.1 The intervention equations
We estimate the parameters of the intervention criteria, equations (4.1) and (4.2), with
observations ItB and ItS as a standard probit model. These estimates are presented in Table 2.
Table 2. Probit estimates of the criteria functions for intervening.
(Standard errors are in parentheses.)
Dependent Variable MtB Dependent Variable MtS
Coefficients Estimates Coefficients Estimates
11 0.3810 21 -1.1235
(0.0633) (0.0821)
12 -0.3855 22 1.0463
(0.0769) (0.0817)
13 -8.0346 23 -4.8294
(0.5882) (0.3789)
Observations 1469 1469
Log Likelihood -879.26 -647.79
The results indicate that the central bank seems to be consequent in its intervention
decisions. That is, the probability of intervening buying (selling) foreign currency increases
when the exchange rate observed at 11.00 am (ask price) at time t appreciates (depreciates)
20
with respect to its value the day before (at t-1), also observed at 11.00 am.2 The behavior of
the exchange rate during the preceding 4 days is also important to the intervention decisions
of the BCRP. For example, if the sol appreciates with respect to the average exchange rate in
the preceding 4 days, the probability of intervening by buying foreign currency increases.
This probability is reduced, however, if the sol depreciates. Similarly, it is more likely that
the BCRP will sell foreign currency if the sol depreciates with respect to the previous 4 last
days.
Regarding the spread, we find that a widening of the bid-ask spread reduces both the
probabilities of selling and buying foreign currency. As we know, the bid-ask spread is an
important part of transactions costs for international trade and investment. A widening of this
spread decreases a firm's profit and thus discourages it from engaging in international trade
or investment. It is therefore surprising that the BCRP does not seem to be addressing its
intervention policy toward reducing the spread.
In conclusion, the BCRP appears to have a consistent intervention policy in the sense
that it avoids large variations of the exchange rate while allowing a smoothing of changes in
the exchange rate on a daily basis. The BCRP seeks to avoid large and quick appreciations
and depreciations of the sol by buying and selling foreign currency, respectively. We have
yet to test whether such a well intended intervention policy actually decreases the volatility
of the sol against the USD and moves the sol in the desirable direction.
2
Other times were also considered but never resulted in significant parameters.
21
5.2 The effect of interventions on the exchange rate
We will now present and explain the estimates of our EGARCH model, in which we make
the conditional mean (equation (7)) and the conditional variance (equation (8)) depend on the
interventions decisions by the BCRP. The estimates are shown in Table 3, and those in bold
are at least significant at the 5% level. Notably, our results do not support the random walk
hypothesis because the autoregressive parameters and the expected interventions and/or past
information on interventions affect future changes in the conditional mean of the exchange
rate. The empirical results can be summarized as follows:
(a) Common knowledge past interventions (previous day) seem to have a desirable effect on
the expected change in the exchange rate, but only between 11.00 am and 1:00 pm on the
same day (Xt13-11), the period when the BCRP has committed to intervene if necessary
and optimal. However, during the time interval when the BCRP is totally absent in the
forex market, there are undesirable effects on the expected exchange rate changes
between 11.00 am today and 1:00 pm the day before (Xt11-13). For example, the previous
day's interventions of selling (buying) foreign currency seem to have further depreciated
(appreciated) the sol during those times. This result could mean that information
regarding past interventions can only successfully affect market expectations in the right
direction and remind market participants that the central bank is committed to avoid large
variations of the sol between 11.00 am and 1:00 pm.3
3
We also considered accumulated intervention over 5 and 6 days; the results remained qualitative unchanged.
22
Table 3. Estimated parameters of the conditional mean and variance for the sol/USD.
(Standard errors are in parentheses)
Explanatory Variables Effect on Xt11-13 Effect on Xt13-11
MEAN EQUATION
1 0.0986 -0.0184
(0.0245) (0.0141)
2 0.1246 0.0414
(0.0225) (0.0172)
-0.15810-3 0.16810-3
(0.34910-4 (0.47210-4)
B 0.0332 0.0030
(0.0038) (0.0058)
S -0.0330 0.0023
(0.0029) (0.0040)
VARIANCE EQUATION
c -0.4390 -0.4055
(0.0495) (0.0661)
a1 0.7391 0.5152
(0.1801) (0.0775)
0.1080 0.0043
(0.0431) (0.0356)
b1 0.9675 0.9686
(0.0077) (0.0100)
B -0.0103 0.0023
(0.0045) (0.0056)
S 0.0193 -0.0036
(0.0072) (0.0091)
0.48210-3 0.20410-3
(0.35210-3) (0.32710-3)
23
(b) Expectations about future central bank interventions in spite of public information
regarding previous interventions do not have desirable effects or have no effect at all on
expected future exchange rates. On one hand, we find that market expectations about
future central bank participation by selling (buying) foreign currency causes additional
depreciation (appreciation) of the sol during the time period when the BCRP does not
participate in the forex. Here, we refer to the effect on Xt11-13. On the other hand,
expected changes in the exchange rate between 11.00 am today and 1:00 pm on the same
day (Xt13-11) appear to be independent of probabilities (as represented by the hazard
functions) that the BCRP might become active in the forex during that time. As explained
above, the market only seems to care what the BCRP has done in the past when it forms
expectations on the exchange rate in a particular day only between 11:00 am and 1:00
pm. It is only during such period that there will be desirable effects on the expected
exchange rate. During other times of the day, there are other factors more than potential
future expectations that drive market expectations. The market may not believe in the
effectiveness of future interventions, even when there is a high probability that they will
take place.
(c) Regarding the effects on the conditional variance, we find that past information on
interventions has no effect on the conditional variance of the expected changes in the
exchange rates at the different time intervals, which are on Xt13-11 and Xt11-13.
Probabilities of future central bank interventions (as represented by the hazard functions)
have no effect on variance of the expected changes of the exchange rate within one day
(Xt13-11), even when this is the period in which the BCRP can intervene. However, for
24
exchange rate changes between today and yesterday (Xt11-13), a higher probability that
the BCRP will intervene in the future by buying foreign currency to avoid drastic
appreciation of the sol against the USD decreases the volatility of the sol. In contrast, an
expectation of higher participation by the central bank to defend the sol against the USD,
or strong sol depreciation, causes higher volatility of the expected changes in the
exchange rate (again on Xt11-13). This effect is almost twice as strong as the effect of
buying foreign currency to avoid appreciation of the sol. These results might explain why
the statistical standard deviation of the expected changes in the exchange rate within one
day seem to be smaller than the expected changes in the exchange rate between today and
the previous day. The latter period coincides with the periods in which the central bank
participation in the forex is not expected.
Figures 5 and 6 show the conditional standard deviation of the change in the log of the
Sol/USD, Xt11-13 and Xt13-11, respectively, together with the net interventions.
Figure 5. EGARCH(1,1) Conditional Figure 6. EGARCH(1,1) Conditional
Standard Deviation of Xt11-13 Standard Deviation of Xt13-11
and net BCRP interventions and net BCRP interventions
Interbank Rates. 2004 - 2009 Interbank Rates. 2004 - 2009
9 500 2.5 500
8
7 2.0
250 250
6
1.5
% Change
% Change
mill USD
mill USD
5
0 0
4
1.0
3
-250 -250
2
0.5
1
0 -500 0.0 -500
3200 3400 3600 3800 4000 4200 4400 3200 3400 3600 3800 4000 4200 4400
StandDevSol/USD BCRP NetInterven StandDevSol/USD BCRP NetInterven
25
Note that between August 2008 and December 2008 (between the 4200 observation and
the 4300 observation), at the worst period of the recent financial crisis, the sol depreciated a
great deal and there were large numbers of interventions by selling USD, as illustrated in
Figure 1. During the same period, the changes in the sol/USD (Figure 2) and its conditional
standard deviation (Figure 5) were very large, especially during the time the BCRP did not
intervene at all: between 11.00 am today and 1:00 pm the day before. This result is in
contrast to the amount of volatility during the time the BCRP can intervene, between 11.00
am and 1:00 pm on any given day (see Figure 3 and Figure 6). We can then conclude that
larger variations of the sol will most likely occur during those times when the sol depreciates
and the BCRP does not intervene.
(d) We also found evidence of asymmetric effects of the shocks on conditional volatility. For
example, if one considers the period during which the BCRP does not intervene, for
given ht-1, a shock causing one-unit decline in t-1 (e.g., an appreciation in the sol) induces
a change in the log of conditional variance by 0.6311 units (= (0.7391)*(-1) +
(0.1080)*(|-1|)), which implies a decrease in the conditional variance. Furthermore, for a
given ht-1, if a shock gives a rise in t-1 by one unit (e.g., a 1% depreciation of the sol),
there will be an increase in the (log) conditional volatility by 0.8471 units (= (0.7391)*(1)
+ (0.1080)*(|1|)). However, during the time frame in which the BCRP does intervene, the
effects on exogeneous shocks on the variance are smaller than they are during the period
the BCRP is not active. That is, for given ht-1, a one-unit decline in t-1 (e.g. a 1%
appreciation of the sol) induces a change in the log of conditional variance by 0.5109
units (= (0.5152)*(-1) + (0.0043)*(|-1|)), which implies a decrease in the conditional
26
variance. Furthermore, for given ht-1, if t-1 rises by one unit (e.g., a 1% depreciation of
the sol), it causes an increase in the (log) conditional volatility by 0.5195 units (=
(0.5152)*(1) + (0.0043)*(|1|)). Thus, if one considers the crisis of 2008 as a
"depreciation" shock to the sol/USD, an increase in t-1, because there was a shortage of
US dollars worldwide and most currencies in both the developed and developing world
depreciated, then one can conclude that any increase in sol volatility must have been due
to the effect of such crisis. It must have been difficult for the BCRP to decrease the sol
volatility caused by the worldwide effect of the 2008 crisis, as our results indicate. Not
even past information on central bank interventions that became common knowledge to
the public dissipated the uncertainty in the market.
In sum, we have shown that the BCRP's intervention policy is consistent in buying USD
when the sol appreciates and selling USD when the sol depreciates. We also find that public
information about past interventions has been effective in moving the sol in the intended
direction. However, this information seems to have had these effects only during times when
the BCRP has informed the market that it will intervene and when interventions were
considered necessary and optimal. Thus, both public information about interventions and the
BCRP's determination to intervene in an optimal manner have been useful in moving the sol
in the desired direction during times of BCRP forex interventions. However, the market does
not seem to be affected by past BCRP intervention policy when forming expectations about
the exchange rate during times when the BCRP is absent from the forex. Overall, the BCRP
does not yet seem to have established a sufficiently strong reputation such that market
participants can predict the BCRP's future participation in the forex. Moreover, expectations
27
formed during times when the BCRP is absent from the forex appear to increase the volatility
of the sol when this currency is on a depreciating trend.
It is quite possible that the BCRP may need additional time, relative to the time period
covered by the data available here, to establish the desired reputation. A crucial question
remains as to whether there is any gain for the BCRP in maintaining a "low volatility" sol
only during a certain (relatively short) period each day. Note that we are not suggesting that
the BCRP should necessarily intervene much more extensively and frequently; this type of
action can be very costly in terms of foreign exchange reserves, which can be used optimally
for other purposes. The Peruvian monetary authorities should carefully evaluate the costs and
benefits of intervening in the forex given their success in maintaining inflation targeting and
a relatively open capital market. In the meantime, it would be advisable for Peruvian
policymakers to concentrate on reforming their financial markets and developing financial
instruments that will permit hedging against exchange rate risks and reduce the degree of
dollarization of the Peruvian economy. As long as the degree of dollarization remains high,
policymakers will argue that it is important for them to intervene in order to reduce the
volatility of the sol relative to the dollar, especially to avoid a significant appreciation of the
sol (because this tends to erode the value of the country's dollar asset holdings). It will be
important to free the Peruvian economy from this straitjacket.
Our results present some support for the "signaling channel" effect of interventions
(Mussa (1981)), which means that by making past intervention activities public, the BCRP
transmits information about its exchange rate objectives. This policy appears to be able to
move the sol in the desired direction, but it can do so only during times when the BCRP
participates in the forex. Such information gives the BCRP some assurance that its intentions
28
are being fulfilled: that it will participate in the forex during the hours it has committed to do
so. However, past information apparently has created some uncertainty about future
movements of the sol, and this has not been helpful for the BCRP in its attempts to establish
policy credibility.
Finally, and importantly, it is also possible that interventions magnify rather than dampen
the effects of shocks to the sol/USD exchange rate, especially for shocks that cause a
depreciation of the sol against the USD. A final recommendation from the above results is
that the BCRP should also address the problem of large bid-ask spreads. Further research
should investigate whether interventions affect the bid-ask spread and whether the volatility
of the exchange rate affects this spread. Naranjo and Nimalendran (2000) hypothesize that
interventions create significant adverse selection problems for dealers. They find that dealers
increase exchange rate spreads around the time of interventions and suggest that in doing so,
dealers protect themselves against the greater information asymmetry of such circumstances.
5. Conclusions
We have considered how interventions affect the process for the exchange rate of sol/USD,
both its conditional mean and variance. Expected future participation of the BCRP in the
foreign exchange market has been modeled as endogenous, a subject that is rarely taken into
account in the relevant literature. We think that our methodology is useful when modeling
central bank interventions in the forex.
Regarding the reaction function for intervening, we found that the BCRP consistently
attempts to move market expectations in the correct direction by buying and selling foreign
exchange currency to prevent drastic appreciation or depreciation of the sol against the USD.
29
We have considered the formation of market expectations about the exchange rate
during different times of the day. We specifically considered expectations regarding
formation of the exchange rate during the time the BCRP is active in the forex and during the
time the BCRP has committed to not participate in the market.
Our empirical analysis indicates that the BCRP's past information on interventions
has been successful in causing the market to expect the sol to move in the desired direction,
but only during the time the BCRP is active in the forex. Thus, market expectations about the
future exchange rate at other times of the day were not favorable, as the market might have
expected that the exchange rate will move in the opposite direction of what the past
intervention policy intends. But making past BCRP participation in the forex publicly known
does not have any effect on the volatility of the sol at any time of the day.
Expectations of future interventions do not move the exchange rate along the intended
path, and may even cause some excess volatility of the sol, especially when the sol
depreciates against the USD. One could, of course, appeal to the work of Morris and Shin
(2006), who demonstrate that even when information (e.g., about past interventions) becomes
common knowledge, asymmetric informational problems may result in coordination failures.
Thus, public information regarding past interventions can easily be interpreted differently by
each market participant and fail to coordinate what public information really means. Such a
theory could explain why the future expected BCRP activities are not always successful in
decreasing volatility and moving the exchange rate in the right direction.
By modeling the conditional volatility of the sol/USD as an EGARCH (1,1) process,
we find evidence that there are asymmetric responses of volatility to positive and negative
shocks.
30
As a final recommendation, the BCRP should try to address the problem of large bid-
ask spreads. Further research should investigate whether interventions affect the bid-ask
spread, and even whether the volatility of the exchange rate affects such spread. This is very
important for participants in foreign trade and investment who are involved in foreign
exchange transactions in general.
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