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WORKING PAPER SERIES

NO. 447 / FEBRUARY 2005

FOREIGN EXCHANGE

OPTION AND RETURNS

BASED CORRELATION

FORECASTS

EVALUATION AND

TWO APPLICATIONS

by Olli Castrén

and Stefano Mazzotta

In 2005 all ECB

publications

will feature

a motif taken

from the

€50 banknote.

W ORKING PAPER SERIES

NO. 447 / FEBRUARY 2005

This paper can be downloaded without charge from

http://www.ecb.int or from the Social Science Research Network

electronic library at http://ssrn.com/abstract_id=668247.

FOREIGN EXCHANGE

OPTION AND RETURNS

BASED CORRELATION

FORECASTS

EVALUATION AND

TWO APPLICATIONS

1

by Olli Castrén

2

and Stefano Mazzotta

3

1 The OTC volatilities used in this paper were provided by Citibank N.A.We are grateful to Peter Christoffersen and Lorenzo Cappiello

who provided many ideas and suggestions to this work, and Stelios Makrydakis and participants in an internal ECB seminar

for useful comments.The usual disclaimer applies.

2 Corresponding author: DG-Economics, European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany;

e-mail: Olli.Castren@ecb.int

3 McGill University - Faculty of Management, 1001 Sherbrooke St.West, Montreal, Quebec H3A1G5, Canada;

e-mail: stefano.mazzotta@mail.mcgill.ca

© European Central Bank, 2005

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The views expressed in this paper do not

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Central Bank.

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Working Paper Series is available from

the ECB website, http://www.ecb.int.

ISSN 1561-0810 (print)

ISSN 1725-2806 (online)

3

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Working Paper Series No. 447

February 2005

CONTENTS

Abstract 4

Non-technical summary 5

1. Introduction 7

2. Correlation forecast evaluation 10

2.1. Data issues 10

2.2. The forecasting object of interest 11

2.3. The measures of correlation 13

3. Correlation forecast evaluation

methodology and results

3.1. Efficiency and bias 18

4. Two applications of correlation forecasts 19

4.1. Scenario analysis for the euro nominal

effective exchange rate index 19

and correlation among cross-rates 23

5. Concluding remarks 26

References 27

Appendices 1-2 30

33

41

European Central Bank working paper series 46

4.2. Exchange rate intervention

16

Appendix 3 Charts

Appendix 4 Tables

Abstract: We compare option-implied correlation forecasts from a dataset consisting

of over 10 years of daily data on over-the-counter (OTC) currency option prices to a

set of return-based correlation measures and assess the relative quality of the

correlation forecasts. We find that while the predictive power of implied correlation is

not always superior to that of returns based correlations measures, it tends to provide

the most consistent results across currencies. Predictions that use both implied and

returns-based correlations generate the highest adjusted R

2

s, explaining up to 42 per

cent of the realised correlations. We then apply the correlation forecasts to two policy-

relevant topics, to produce scenario analyses for the euro effective exchange rate

index, and to analyse the impact on cross-currency co-movement of interventions on

the JPY/USD exchange rate.

Keywords: Correlation forecasts, currency options data, effective exchange rate.

JEL classification: F31, F37, G15.

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Working Paper Series No. 447

February 2005

Non-technical summary

The purpose of this study is to investigate the extent to which it is possible to use

returns based measures and foreign exchange options based measures to predict the

correlation between bilateral exchange rates. In particular, we study whether the

forward-looking information contained in the OTC currency options data can provide

good forecasts of the future realised correlation between exchange rates by

themselves or in addition to various correlation forecasts derived from returns based

measures. Armed with the results from the correlation forecast analysis, we then

illustrate two different applications of the methodology for policy related purposes.

There is ample anecdotal evidence that over time, certain currency pairs tend to move

in tandem. In other words, when one of the two exchange rates appreciates

(depreciates), the other tends to follow a similar pattern. In economic terms, these

patterns are interesting from several points of view. First, the reason why two

currency pairs show a positive correlation over time could be that their dynamics is

driven by the same economic fundamentals. Second, a sudden fall in an otherwise

relatively steady degree of correlation could be indicative of attempts by

policymakers to try to influence the dynamics of some particular exchange rate. Third,

a set of correlations among several exchange rates could provide an idea about which

currencies are facing excess demand in the foreign exchange market. And fourth, if

we have a reliable forecast of the correlation relationship between, say, the euro and

the currencies of two or more euro area major trading partner economies, then the

impact of an assumed future movement in one of the bilateral exchange rates on the

future movements in the other bilateral exchange rates can be assessed using these

correlation forecasts. For a central bank that uses exchange rates mainly as an

indicator for future inflationary risks, it is important to have a forecast of as many of

the bilateral exchange rates entering into the effective exchange rate basket as

possible. Forecasts of correlation provide one way of expanding the information on

future developments received from individual bilateral exchange rates.

We find that the implied correlation calculated from currency options prices shows

predictive power for the future realised correlation among most major currency pairs.

However, for the exchange rate pairs that show correlation predictability, implied

5

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Working Paper Series No. 447

February 2005

correlation is not the only one that produces good forecasts. Both GARCH and

RiskMetrics correlation forecasts show substantial predictive power. In substance, the

two types of correlations forecasts seem to nicely complement each other in that the

best forecasts are often produced when implied and return-based correlations are used

jointly. The highest adjusted R

2

is almost invariably obtained from the encompassing

(multivariate) regressions. The total predictability obtained using a combination of

forecasts ranges from 18 to 38 per cent for the entire sample and from 20 to 42 per

cent for the post-January 1999 sample.

After assessing the relative forecasting properties of the various methodologies, we

apply the correlations measures on two policy relevant cases. In the first study, the

correlation forecasts are employed to generate scenario analysis for the euro effective

exchange rate conditional on assumptions on the future evolution of the JPY/USD

exchange rate. In the second case, we study whether the interventions by the Japanese

authorities on the JPY/USD exchange rate in the 1990s and 2000s have affected the

patterns of co-movement among the JPY/EUR and USD/EUR exchange rates. We

find that when included as an additional explanatory variable in the correlation

forecast regressions, interventions improve upon the explanatory power of the model.

Therefore, it cannot be excluded that interventions on the JPY/USD rate tend to

increase the co-movement among the euro cross rates (JPY/EUR and USD/EUR).

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Working Paper Series No. 447

February 2005

1. Introduction

The purpose of this study is to investigate the extent to which it is possible to use

returns based measures and foreign exchange options based measures to predict the

correlation between bilateral exchange rates. In particular, we study whether the

forward-looking information contained in the OTC currency options data can provide

good forecasts of the future realised correlation between exchange rates by

themselves or in addition to various correlation forecasts derived from returns based

measures. Armed with the results from the correlation forecast analysis, we then

illustrate two different applications of the methodology for policy related purposes.

There is ample anecdotal evidence that over time, certain currency pairs tend to move

in tandem. In other words, when one of the two exchange rates appreciates

(depreciates), the other tends to follow a similar pattern. In economic terms, these

patterns are interesting from several points of view. First, the reason why two

currency pairs show a positive correlation over time could be that their dynamics is

driven by the same economic fundamentals. Second, a sudden fall in a historically

stable correlation relationship could be indicative of attempts by policymakers to try

to influence the dynamics of some particular exchange rate. Third, a set of

correlations among several exchange rates could provide an idea about which

currencies are facing excess demand in the foreign exchange market. And fourth, if

we have a reliable forecast of the correlation relationship between, say, the euro and

the currencies of two or more euro area major trading partner economies, then the

impact of an assumed future movement in one of the bilateral exchange rates on the

future movements in the other bilateral exchange rates can be assessed using these

correlation forecasts. For a central bank that uses exchange rates mainly as an

indicator for future inflationary risks, it is important to have a forecast of as many of

the bilateral exchange rates entering into the effective exchange rate basket as

possible. Forecasts of correlation provide one way of expanding the information on

future developments received from individual bilateral exchange rates.

There is a substantial literature investigating the informational content of options in

relation to asset price returns. Several early contributions use market-based options

data with mixed results to investigate conditional second moments, but they almost

7

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Working Paper Series No. 447

February 2005

invariably concentrate on volatility rather than correlation. Beckers (1981) finds that

not all available information is reflected in the current option price and questions the

efficiency of the option markets. Canina and Figlewski (1993) find

that implied

volatility is a poor forecast of subsequent realized

volatility. Lamoureux and Lastrapes

(1993) provide evidence against restrictions of option pricing models which assume

that variance risk is not priced. However,

Jorion (1995) finds that statistical models of

volatility based on returns are dominated by implied volatility forecasts even when the

former are given the advantage of ex post in sample parameter estimation. He also

finds evidence of bias. More recently,

Christensen and Prabhala (1998) use longer

time series and non-overlapping data and find that implied volatility outperforms past

volatility in forecasting future volatility. Fleming (1998) finds that implied volatility

dominates historical volatility in terms of ex ante forecasting power and suggests that

a linear model which corrects for the bias present in implied volatility forecasts can

provide a useful market-based estimator of conditional volatility. Blair, Poon, and

Taylor (2001), find that nearly all relevant information is provided by the VIX index

and there is not much incremental information in high-frequency index returns. Neely

(2003) finds that econometric projections supplement implied volatility in out-of-

sample forecasting and delta hedging. He also provides some explanations for the bias

and inefficiency pointing to autocorrelation and measurement errors in implied

volatility. Pong, Shackleton, Taylor and Xu (2004) find that high-frequency historical

forecasts are superior to implied volatilities using OTC data for horizons up to one

week. Covrig and Low (2003) use OTC data to find that quoted implied volatility

subsumes the information content of historically based forecasts at shorter horizons,

while the former is as good as the latter at longer horizons. Finally, Christoffersen and

Mazzotta (2004) systematically assess the quality of option based volatility, interval

and density forecasts for the major currencies 1992-2003. They find that implied

volatilities explain a large share of the variation in realized volatility and that wide-

range interval and density forecasts are often misspecified whereas narrow-range

interval forecasts are well specified.

It is of course striking that all of the above studies investigate options informational

content with regard to volatility forecasts. Studies investigating exchange rate

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Working Paper Series No. 447

February 2005

correlations implied by market data are, on the contrary, rather sparse.

1

The

contributions perhaps closest related to our work are Siegel (1997), Campa and Chang

(1998) and Lopez and Walter (2000), who specifically focus on exchange rate

correlations. Campa and Chang find that implied correlation among the DEM/USD,

USD/JPY and DEM/JPY currency pairs from January 1989 to May 1995 outperform

alternative forecasts at one- and three month horizons. In addition, they find that when

included in joint forecast regressions, implied correlation always incrementally

improves the performance of other forecasts.

In this study, we extend upon the results by Campa and Chang by looking at several

other currencies in a larger sample that also covers the first five years of the single

European currency. In particular, we focus our attention on the correlations between

the following exchange rate pairs: USD/EUR-JPY/EUR; USD/EUR-GBP/EUR;

GBP/EUR-JPY/EUR; USD/GBP-JPY/GBP; USD/JPY-GBP/JPY; USD/EUR-

PLN/EUR; and USD/EUR-CZK/EUR.

2

Our sample starts in January 1992 and ends in

March 2004, except for the Polish zloty and the Czech koruna currency pairs for

which the sample period commences at January 2001. Prior to the launch of the euro

in January 1999, we use data on D-mark currency pairs. This is reflected in our

estimations in that all regressions are run in two samples, the full sample and the post-

January 1999 sample. In the case of the full sample the notation, for simplicity, refers

only to the euro.

We find that the implied correlation calculated from currency options prices shows

predictive power for the future realised correlation among all currency pairs except

the GBP/EUR-JPY/EUR. However, for the exchange rate pairs that show correlation

predictability, implied correlation is not the only one that produces good forecasts.

Both GARCH and RiskMetrics correlation forecasts show substantial predictive

power. In substance, the two types of correlations forecasts seem to nicely

complement each other in that the best forecasts are often produced when implied and

return-based correlations are used jointly. The highest adjusted R

2

is almost invariably

1

However, there exists a more generous literature in correlations among stock and bond markets. Good

reviews of such studies are provided Kroner and Ng (1998) and Cappiello, Engle and Sheppard (2003).

2

The choice of the particular correlation pairs is partially dictated by data availability on the currency

options, as will be discussed in more detail below.

9

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Working Paper Series No. 447

February 2005

obtained from the encompassing (multivariate) regressions. The total predictability

obtained using a combination of forecasts ranges from 18 to 38 per cent for the entire

sample and from 20 to 42 per cent for the post-January 1999 sample.

After assessing the relative forecasting properties of the various methodologies, we

apply the correlations measures on two policy relevant cases. In the first study, the

correlation forecasts are employed to generate scenario analysis for the euro effective

exchange rate conditional on assumptions on the future evolution of the JPY/USD

exchange rate. In the second case, we study whether the interventions by the Japanese

authorities on the JPY/USD exchange rate in the 1990s and 2000s have affected the

patterns of co-movement among the JPY/EUR and USD/EUR exchange rates.

The rest of this study is organised as follows. Section 2 introduces the framework in

which the various correlation measures will be analysed. Section 3 specifies the

estimated equations and the reports the results. Section 4 presents the two applications

and Section 5 concludes.

2. Correlation Forecast Evaluation

2.1. Data issues

The currency options data used in this study consists of 1-month implied volatilities

on a large number of exchange rates, obtained from Citigroup. Traditionally, the bulk

of trading in options is on OTC basis and not at centralised futures/options exchanges.

Christensen, Hansen and Prabhala (2001) argue that in terms of forecasting properties,

OTC options data could be of superior quality relative to exchange traded options.

This is because OTC prices are quoted daily with fixed “moneyness“ (the distance

between the forward rate and the option’s strike price) in contrast with market-traded

options, which have fixed strike prices and thus time-varying moneyness as the

forward exchange rate changes. Moreover, the trading volume in OTC options is often

much larger than in the corresponding market traded contracts. The underlying

liquidity on OTC quotes is therefore deeper, which makes the OTC quotes a more

reliable source for information extraction. The fact that the currency options market is

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Working Paper Series No. 447

February 2005

heavily concentrated on a few global players does that the liquidity problems can be

reduced further if data from these institutions is available. Citigroup has a significant

market share both in options on major exchange rates as well as on the emerging

currencies.

2.2. The Forecasting Object of Interest

The methodologies we adopt for this study are in several ways similar to those used to

investigate volatility predictability from OTC currency options in Christoffersen and

Mazzotta (2004), with some major differences. The particular object of interest of our

study is forecasting the realised future sample correlation of an exchange rate pair

over the horizon of the following h = 21 trading days.

There exists substantial literature regarding the use of realized volatility as a measure

of equity and foreign exchange variability (see e.g. Andersen and Bollerslev (1998)

and Andersen et al. (2001a, 2001b, 2003)). The common thread of this literature is the

idea that one can sum squared log returns at a frequency higher than that of interest to

obtain a measure of the realized quadratic variation over the frequency of interest. For

instance, one can compute the monthly variance as the sum of squared daily log

returns or the daily variance as the sum of intraday squared log returns. In this

theoretical framework, by increasing the sampling frequency it is possible to construct

ex post realized volatility measures for the integrated latent volatilities that are

asymptotically free of measurement error. In practice, the benefit of increasing the

frequency is offset by the microstructure noise which is invariably included in the

observed market quotes.

One approach commonly taken is to strike a balance between the horizon of interest

and the number of sub-periods in which such horizon is divided for the purpose of

computing the squared returns. In the case of daily variance estimates, whereas early

work suggests using 5-minute returns more recent contributions indicate that 30-

minute returns (i.e. about 16-18 data points per trading day) provide a measure of

daily volatility relatively robust to microstructure noise. In our case, since we want a

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February 2005

measure of monthly correlation, the sum of own and cross products of demeaned

3

daily log return over the 21 trading days can be considered a sufficiently robust

measure of monthly realized co-variation. The measure of correlation we obtain is

nothing but the ex-post sample correlation over the next 21 trading days. Following

the conventions established in the above mentioned literature, we call this measure

“realised correlation”, henceforth RC. We define RC for the next h days as follows

1, 1, 1, 2, 2, 1,

1

12,

12

1

()(

(, )

h

ti t th ti t th

i

RC

th

RR

RR RR

h

RR

ρ

σσ

++++ ++

=

−−

=

∑

)

, (2.1)

where

2

,

1

1 h

Rj jt i

i

R

h

σ

,

+

=

=

∑

(2.2)

and

1, 1, 1, 1

ln( / )

ti ti ti

RSS

+++−

=

(2.3)

are the FX spot return of exchange rate S

1

on day t+i.

The plots of all correlation measures are illustrated in Appendix 3 (note that we have

labelled the realised correlation as “historical correlation” as the latter is simply a

lagged realised correlation as will be explained in more detail below). The charts

show that on daily basis, the measures are very volatile. In particular, it seems that the

correlations between the USD/EUR and JPY/EUR currency pairs, between the

USD/EUR and GBP/EUR currency pairs, between the USD/GBP and JPY/GBP

currency pairs, and between the USD/JPY and GBP/JPY currency pairs have

fluctuated in the positive territory most of the time. Moreover, the positive correlation

seems to be higher in the post-euro subsample.

3

Although asymptotically the mean should be irrelevant and in practice is very close to zero almost

always in the case of correlation it is a good empirical practice to subtract the sample mean from each

21-day sample to constrain the realised correlation to be between minus one and one.

12

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Working Paper Series No. 447

February 2005

2.3. The Measures of Correlation

To forecast future realised correlation, four alternative correlation measures are

applied. First, we calculate the implied correlation from options implied volatility. To

do so it is necessary to assume that in addition to the Black and Scholes model also

the triangular parity condition between exchange rate cross rates holds.

Being based on options data, implied correlation provides a forward-looking

perspective to the analysis of co-movements between currency pairs. Because

exchange rate options provide information on the currency options market’s

uncertainty about the price of one currency in terms of another, with three currencies

and options on each of the possible exchange rate pairings we can derive an estimate

of the market’s expected future, or implied, correlation between any two of the

exchange rates. To put it in another way, implied correlation represents the degree of

co-movement between two currencies using a third currency as a numeraire.

The implied correlations are derived using the well-known Black-Scholes pricing

formula as well as exploiting the arbitrage condition on currencies. The Black-Scholes

formula allows one to derive implied volatilities for the underlying asset. The no-

arbitrage condition provides, given the proportional changes in returns of two

exchange rates, R

1

and R

2

, the proportional change in the return of a third exchange

rate R

3

simply as R

3

= R

1

– R

2

. It then follows that

()

(

)

(

)

(

)

312 1

2,VarR VarR VarR CovRR=+−

2

, (2.4)

whereby it is straightforward to derive the implied correlation (IC) between R

1

and R

2

knowing Var(R

1

), Var (R

2

), and Var (R

3

).

4

The implied correlation is then defined as

22 2

1, 2, 3,

12,

1, 2,

(, )

2

tt

IC

th

tt

RR

t

σ

σσ

ρ

σσ

+−

=

. (2.5)

4

See Malz (1997), Butler and Cooper (1997) and Brandt and Diebold (2003) for further details.

13

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Working Paper Series No. 447

February 2005

In (2.5), σ

2

1,t

=Var

t

(R

1

) and σ

2

2,t

= Var

t

(R

2

), can be measured by the square of the

implied volatility on each of the currency pairs. The implied correlation for a

particular date can then be calculated simply by inserting values for the implied

volatilities in the equation.

Bollerslev and Zhou (2003)

5

point out that if the volatility risk is priced in the options

markets then implied volatility is a biased predictor of realized volatility. In fact,

implied volatilities are often empirically found to be upward biased estimates of the

objective volatility. In a standard stochastic volatility set up, it can be shown that if

the price of volatility risk is zero, the process followed by the volatility is identical

under the objective and the risk neutral measures. In such a case there would be no

bias. However, the volatility risk premium is generally estimated to be negative which

in turn implies that the volatility process under the risk neutral measure will have

higher drift. These theoretical arguments do apply to the computation of implied

correlation as well. However, because such a potential bias could affect all variances

used in the computation of the implied correlation in (2.5), it is not clear a priori that

the bias for implied correlations is a problem as severe as it is for volatilities. We will

show below that bias is indeed present in correlations computed from options.

The other three volatility forecasts are derived from historical FX returns only. The

simplest possible forecast is the historical h-day volatility, defined as

,

tt

. (2.6)

(1,2) (1,2)

,

HC RC

th t hh

ρρ

−

=

The historical correlation is simply the lagged realized correlation. Alternatively, we

can consider second moments that apply an exponential weighting scheme putting

progressively less weight on distant observations. The simplest measure using such a

scheme is the Exponential Smoother or RiskMetrics correlation. Daily variance and

covariance then evolve as

() ()

() ()

21222

(1), 1 1, 1 (1), 1,

1

212

(1,2), 1 1, 1 2, 1 (1,2), 1, 2,

1

11

11

i

ttitt

i

i

ttitit

i

RR

R

RR

σλλλσλ

σλλ λσλ

∞

−

+−+

=

∞

−

+−+−+

=

=− = +−

=− = +−

∑

∑

%%

%%

R

. (2.7)

5

See also Bandi and Perron (2003), Chernov (2003), and Bates (2002).

14

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Working Paper Series No. 447

February 2005

Following JP Morgan we simply fix λ=0.94 for all the daily FX returns. The forecast

for h-day correlation is therefore

2

(,), 1

(,)

1

,1 ,1

jk t

RM j k

t

jt kt

σ

ρ

σσ

+

+

+

+

=

%

%%

. (2.8)

The third estimate for correlation based on past exchange rate returns that is

considered here is the GARCH correlation. The GARCH methodology permits the

calculation of time-varying second moments for the universe of assets that are

considered by the researcher. According to this approach, variances and correlations

are conditional on a time-varying information set that allows one to update the

estimated second moments at each point in time when new information becomes

available. We have adopted a bivariate GARCH model where R

t

is defined as the

vector of returns

(

)

1, 2,

,

ttt

R

RR=

. (2.9)

We assume that R

t

follows a GARCH process

12

tt

RH

t

ε

=

. (2.10)

In (2.10) ε

t

is an identical and independently distributed vector sequence with mean

zero and unit variance. The conditional covariance H

t

evolves according to a diagonal

BEKK GARCH process

6

(2.11)

11,12,1

'' '

where

H = 2 x 2, A, = 2 x 2 diagonal, = 2 x 2 lower triangular

H(1,1) = variance of exchange rate 1

H(2,2) = variance of exchange rate 2

H(1,2) = covariance

tttt

HHRR

−−−

=ΩΩ+Β Β+Α Α

ΒΩ

of currency 1 and currency 2

6

See Engle and Kroner (1995) for further details.

15

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Working Paper Series No. 447

February 2005

The next day GARCH correlation is thus defined as

1

121

11

H(1,2)

(, )

H(1,1) H(2,2)

GARCH

t

t

tt

RR

ρ

+

+

+

+

=

. (2.12)

In contrast to the RiskMetrics model, which implies a random walk volatility process,

to forecast the 21 days ahead correlation with GARCH it is necessary to consider the

mean reversion of the model and iteratively forecast variances and covariances. The

computations to obtain the GARCH correlation forecasts are detailed in Appendix 1.

The plots of the GARCH correlations (GC) for the various exchange rate pairs are

found in Appendix 3. The plots are substantially smoother than those obtained from

historical correlations.

3. Correlation Forecast Evaluation Methodology and Results

To compare the forecasting capability of the different correlation measures, we run

simple linear predictability regressions. These are carried out in-sample, by using

different windows for the realised correlation (the left-hand side variable) and for the

right-hand side variables. In other words, we assess how various estimates of monthly

exchange rate correlations have in the past predicted realised correlation one month

ahead in time. More specifically, the following univariate regressions are first run for

each correlation

,,

RC j j

th th th

ab

,

ρ

ρε

=+ +

(3.1)

for j = IC, HC, GC.

These univariate regressions

7

serve to assess the fit through the adjusted R

2

and to

check how close the estimates of a are to 0 and how close the estimates of b are to 1.

In addition, bivariate regressions are performed, including the implied correlation and

the two return-based forecasts in turn, as follows

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Working Paper Series No. 447

February 2005

(3.2)

jIC

ht

j

ht

IC

ht

RC

ht

cba

,

,,,,

ερρρ

+++=

for j = HC, GC.

These bivariate regressions shed some light into whether the return-based correlation

forecasts add anything to the market-based forecast implied from currency options.

Finally, a regression will be run including all three correlation forecasts in the same

equation, in order to asses the relative merits of the different correlation forecasts.

The results are reported in Tables 1 and 2 of Appendix 4 where both regression point

estimates as well as standard errors corrected for heteroskedasticity and

autocorrelation, using GMM, are included. The robust Newey-West weighting matrix

with a pre-specified bandwidth equal to 21 days is applied. The regression fit is

reported using adjusted R

2

. Table 2 of Appendix 4 includes the same regressions than

Table 1, but now using the sample period beginning from January 1999.

We find that correlation between foreign exchange pairs is predictable to a substantial

extent. The adjusted R

2

of the GMM regressions

8

ranges from 18 to 38 per cent for

the entire sample and from 20 to 42 per cent for the post-January 1999 sample.

However, for the exchange rate pairs that show correlation predictability, implied

correlation is only in a few cases the best univariate forecast. Both GARCH and

RiskMetrics correlation forecasts show considerable predictive power, too.

When comparing these results with predictability regressions for volatility forecasts,

one difference we find is, therefore, that information from currency options prices

does not always seem to be as helpful in predicting correlation as it is in predicting

volatility. Returns based measures sometimes perform better than correlation

measures based on options data. We note however that the return based measures also

sometimes perform very poorly. This is in contrast with the implied correlation, which

seems to be more consistent as it shows less variability in the predictive power from

one pair of exchange rates to the other. In substance, the two types of correlations

forecasts seem to nicely complement each other. The best forecasts obtain when

7

See e.g. Fleming et al (1995)

8

For the technicalities regarding the GMM implementation refer to Christoffersen Mazzotta (2004).

17

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Working Paper Series No. 447

February 2005

return based measures are used jointly with market based measures, as the highest

adjusted R

2

is almost invariably obtained from the encompassing (multivariate)

regressions.

For the entire sample implied correlation and GARCH correlation generally show

good predictive power and typically outperform historical correlations. Implied and

GARCH correlations between the most important currency pairs from the euro area

perspective, i.e. the correlations between the USD/EUR; GBP/EUR and the

USD/EUR; JPY/EUR exchange rates, provide reliable forecasts of future correlation.

They can thus be useful in assessing near-term future inflationary risks that originate

from exchange rate movements. Perhaps surprisingly, in the post-1999 sample the

best forecasts are RiskMetrics and implied correlation, both winning the race in 3 out

of 7 cases. It is possible that RiskMetrics displays a better ability to model the

extremely high persistence of typical forex correlations. However, we conjecture that

the fact that RiskMetrics outperform GARCH may be due to the choice of the

adjusted R

2

as the metric to determine the best forecast.

9

We leave an in-depth

analysis of this and related issues for future research.

3.1. Efficiency and Bias

To study the merit of each correlation forecasts with regard to the relative efficiency

and bias we perform a Mincer-Zarnowitz (1969) decomposition of the MSE into bias

squared, ineﬃciency and random variation.

10

The decomposition is as follows: MSE

= [E[y] − E[ŷ]]

2

+ (1 − β)

2

Var(ŷ) + (1 − R

2

) Var(y), where y is the variable of

interest, in our case the realised correlation, and ŷ is each correlation forecast in turn.

From the regression of y on ŷ and a constant, we obtain the slope coeﬃcient β and the

regression fit, R

2

. The Mincer-Zarnowitz regressions are run for each of the currency

pairs and for each of the currency forecasts. Table 3 in Appendix 4 reports the MSEs

in absolute value and their decomposition into bias squared, inefficiency, and residual

variation, in percentage of the total MSE. It appears that bias is generally higher for

the implied correlation than is for all the other correlation forecasts, with the only

exception of the RiskMetrics correlation for the USD/EUR-JPY/EUR pair for the

entire sample. In the same sample, historical correlation is shown to be the least

9

For the importance of the loss function see e.g. Christoffersen and Jacobs (2004)

10

We thank an anonymous referee for pointing us in this direction.

18

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Working Paper Series No. 447

February 2005

efficient of the correlation forecasts. In the post 1999 sample however, implied

correlation bias becomes less of an issue, almost disappearing for the USD/EUR-

GBP/EUR and GBP/EUR-JPY/EUR pairs. A notable exception to this pattern is the

USD/JPY-GBP/JPY implied correlation bias which almost doubles to 47.29 per cent.

In the post 1999 sample the historical correlation is shown to be rather inefficient but

substantially unbiased. RiskMetrics correlation appears to be somewhat inefficient

for some currency pair and biased for others. GARCH often perform better than the

other forecasts under one measure but not the other.

In summary, although in general implied correlation from options is more efficient

but biased and return based measures are less biased but also less efficient, the

ranking does not hold for all the currency pairs in both sample periods. In other

words, the decomposition reinforces the idea that different measures of correlation

may have different informational content and therefore they may contribute to provide

the best forecasts when used jointly.

4. Two applications of correlation forecasts

Measures of correlation were above shown to provide effective forecasts of future

realised correlation. A question that arises from the practical perspective is then

whether such measures can contribute to enhance our understanding on exchange rate

developments beyond the simple co-movement among various bilateral exchange

rates. In this section we propose and illustrate two applications where correlation

forecasts can be useful when monitoring and assessing exchange rate developments.

4.1. Scenario analysis for the euro nominal effective exchange rate index

The nominal effective exchange rate (NEER) index of a currency is commonly

calculated as a weighed average whereby the various bilateral exchange rates of the

most important trading partner currencies are aggregated using the respective trade

shares as weights. The resulting index would then better reflect the possible future

inflationary risks originating from exchange rate movements in so far as diverging

movements of bilateral exchange rates would partially cancel each other out. Many

central banks therefore use the NEER among indicators of medium-term risks to price

19

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Working Paper Series No. 447

February 2005

stability. In addition, the price-deflated real effective exchange rates (REERs) provide

an insight to the economy’s overall price competitiveness in the medium to long term.

In the context of forward-looking monetary policy, various scenarios for the likely

future developments of the NEER index could prove useful in assessing the risks to a

given baseline model. Due to the known near-impossibility of forecasting bilateral

exchange rates it should be clear that assessing the future level of an index that

consists of a large number of bilateral rates should, if anything, multiply the difficulty

of the task. However, by using measures of correlation it is, in principle, possible to

construct consistent scenarios for future movements in a NEER index conditional on

an assumption of a future change in one bilateral exchange rate only.

As an example, we take the euro nominal effective exchange rate index with the

narrow group of trading partner currencies, calculated by the ECB.

11

Since the

weights in the euro NEER are rather concentrated on the currencies of the three

largest trading partner countries of the euro area (the United States, the UK and

Japan), we analyse how the changes in these currencies, conditional on an assumed

movement in another major world exchange rate, the Japanese yen-US dollar rate, are

reflected in the NEER index. We consider here the sample period starting from

January 1999 only. To this end, we exploit the property of conditional expectation

under bivariate normal distribution that can be written as follows.

))(()()(

1

,

,

,,1,11, ++++

−+==

tt

tY

tXi

tYXititttit

YEXEYXE

ϑ

σ

σ

ρϑ

(4.1)

i= USD/EUR, JPY/EUR, GBP/EUR

In (4.1), the left-hand side captures the level expected to be realised at time t+1 of the

bilateral exchange rate of the euro against the dollar, the pound or the yen (X

i

), given

an assumption

ϑ

made at time t about the level of the JPY/USD exchange rate (Y) to

be realised at t+1. The right-hand side of (4.1) shows how this conditional expectation

on X

i

differs from the unconditional expectation of that exchange rate that is provided

at time t by the t+1 horizon forward exchange rate E

t

(X

i,t+1

). In particular, under the

11

A detailed overview of the methodology used to calculate the euro effective exchange rate indices is

provided by Buldorini, Makrydakis and Thimann (2002).

20

ECB

Working Paper Series No. 447

February 2005

horizon of 1 month, the spread between the assumed future level

ϑ

of the JPY/USD

exchange rate and the 1-month forward JPY/USD rate E

t

(Y

t+1

) is multiplied by the

forecast correlation between the JPY/USD and the relevant bilateral euro exchange

rate, scaled by the ratio of forecast volatilities. After having calculated the conditional

expectations for the three main euro bilateral exchange rates, the conditional

expectation of the NEER index can be calculated by multiplying the former with the

relevant trade weights, and aggregating across currencies.

12

In Appendix 2, we run regressions à la Fama and find that the conditional

expectations on the bilateral USD/EUR, JPY/EUR or GBP/EUR exchange rates as

calculated using equation 4.1 produce estimates that outperform the forecasts

provided by the forward exchange rates. We can now construct a framework for

scenario analysis on the euro NEER index. To this end, the particular question we

want to ask is the following. What is the impact on the expectation of the euro NEER

one-month ahead, given that today the Japanese yen is expected to appreciate by 10%

against the US dollar over one month’s horizon? Clearly, since the measures of

correlation are time-varying the impact on the euro NEER of an expected yen

appreciation against the US dollar vary across different dates. For instance, a scenario

where the euro NEER would be expected to move significantly following an expected

10% move in the JPY/USD rate would presuppose that the euro would be expected to

move in the same direction against all three major currencies. In that case, the

USD/JPY rate would need to be positively correlated against all three major bilateral

euro exchange rates.

13

Table A illustrates the scenarios on the bilateral euro exchange

rates and on the euro NEER for four selected dates using GARCH correlation

forecasts.

12

Note that since the calculation of the expectation of the euro NEER requires as input the correlation

between the GBP/EUR and the JPY/USD exchange rates, which do not enter the same exchange rate

“triangle”, the correlation forecasts using the implied correlation approach cannot be used for this

exercise.

13

The results have to be qualified in so far as the three main currencies “only” represent some 70% of

the weight in euro NEER basket. In the calculations it is assumed that the other bilateral rates do not

change, although some of them could be rather sensitive to movements in the JPY/USD rate.

21

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Working Paper Series No. 447

February 2005

Table A: Scenarios for the euro exchange rates one month ahead (GARCH correlation)

Assumption: 10% JPY appreciation against US dollar in 1 month’s

time

USD/EUR GBP/EUR JPY/EUR Euro NEER

27 Sep 2000 -7.21% -2.95% -22.6% -6.24%

21 Jan 2002 0.47% -1.01% -11.88% -2.01%

22 Jul 2002 6.89% 0.67% -0.85% 1.71%

12 Dec 2003 2.48% 1.58% -1.37% 0.76%

Positive (negative) reading denotes euro appreciation (depreciation).

The forecast co-movements of the various bilateral euro exchange rates conditional on

the assumed 10% appreciation of the yen vis-à-vis the US dollar vary substantially

across episodes. This is also reflected by the fact that the euro NEER depreciates in

some occasions, while it appreciates in others. Therefore, expectations on a stronger

yen against the US dollar could contribute to higher or lower expected import prices

and inflationary pressures in the euro area, depending on the particular correlation

configuration in the FX market at the time when the scenario is conducted.

Looking at the conditional expectations of the bilateral rates, a general observation is

that the conditional expectations on the movements in the euro bilateral exchange

rates have changed over time. In particular, there is a tendency from expected euro

weakness against the US dollar and the pound towards expected euro strength as a

response to the assumed 10% appreciation of the yen against the US dollar. Moreover,

there is a tendency from a sharp towards more moderate projected future euro

depreciation against the yen. What could be the factors contributing to the

constellation during the early years of the single currency whereby an appreciation of

the yen against the dollar would have contributed to a stronger dollar against the euro,

rather than to a general weakness of the US currency? Soon after its launch in January

1999, the euro entered a protracted period of broad-based depreciation that by fall of

2000 was considered to have brought the single currency out of line of the underlying

fundamentals. The euro exchange rates subsequently stabilised but remained weak

throughout 2001. From 2002 Q2 onwards the US dollar started depreciating against

all major currencies amid growing concerns regarding the large US current account

deficit. This seems to have changed also the correlations that measure the interplay

22

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Working Paper Series No. 447

February 2005

among the various bilateral exchange rates and, consequently, the conditional

expectations regarding future movements in the euro NEER as a response to a

hypothetical yen appreciation vis-à-vis the US currency. Finally, throughout 2003 the

Japanese authorities markedly increased the intervention activity to retard the pace of

yen appreciation against the US dollar. In that context, a sudden switch in policy to

“tolerate” a 10% appreciation of the yen could have been seen as reducing the

pressure on the euro to appreciate against the US currency. This would explain the

conditional expectation indicating a more moderate appreciation of the euro relative

to the US dollar than was the case in mid-2002.

In the 1990s and in the early 2000s, the attempts by Japanese authorities to counter

the pressures of yen appreciation against the US dollar were often seen as a potential

factor affecting G3 exchange rate dynamics.

14

How is foreign exchange market intervention supposed to affect exchange rates and

their cross-rates? According to the standard monetary or portfolio balance approach to

interventions, an increased supply of a currency (or bonds denominated in that

currency) in the context of an open market operation should imply a depreciation of

that currency against all other currencies in the market until the equilibrium is

restored. For example, an intervention operation by the Japanese authorities where the

yen is sold against the US dollar should imply a depreciation of the yen not only

against the US dollar but also against the euro, the pound and so on. Conversely, the

purchase of US dollars should exert a general upward pressure on the US currency in

the market. Therefore, a yen-selling intervention against the US dollar should, ceteris

paribus, contribute to a weaker yen and a stronger US dollar also against the euro.

However, as argued by Sarno and Taylor (20001), the daily trading volumes in the

foreign exchange markets are so large that even relatively sizeable interventions are

unlikely to affect the levels of major currencies through the monetary or the portfolio

channels. On the other hand, if the interventions are repeated and follow a systematic

14

See Castrén (2004) and Ito (2002) for analyses of the Japanese interventions using official Japanese

intervention data.

23

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Working Paper Series No. 447

February 2005

4.2. Exchange rate intervention and correlation among cross-rates

strategy, possibly combined with oral communication, they are likely to affect the

market’s expectations regarding the “desired” level of the USD/JPY rate. In such a

constellation, the adjustment pressures in the FX market are likely to be channelled

increasingly through currency pairs that are not actively managed.

15

Following the

previous example, with the USD/JPY rate “managed” by systematic intervention any

pressure on the US dollar to depreciate – for instance due to the large US current

account deficit – would imply that the euro would be expected to appreciate over time

both against the dollar and, due to the interventions on the JPY/USD rate, against the

yen. If this hypothesis were correct, the implications of interventions should

demonstrate themselves in increased correlation between the euro cross rates.

We will augment our earlier correlation forecast regressions by incorporating a

variable that measures the daily purchases of Japanese yen carried out by the Bank of

Japan in the FX market between April 1992 and March 2004. Our goal is to analyse

whether data on the interventions on the JPY/USD exchange rate can improve the

forecasts of correlation between the USD/EUR and JPY/EUR exchange rates. In other

words, we want to find out whether interventions can work as an additional

explanatory factor for realised correlation between the two cross rates of the particular

exchange rate that is the focus of the market operation. The particular equation we

estimate is

,

,,

RC j j

th th t th

ab cINT

ρ

ρ

=+ + +

ε

(4.2)

for j = HC, RMC, GC, IC

The regressions serve to assess whether the coefficients of the intervention variable

are positive and significant and whether the adjusted R

2

improves relative to standard

correlation forecast equations.

The results are summarized in Table B. The regressions show that the variable

measuring the BoJ yen-purchasing interventions receives the negative and statistically

15

BIS (2004) reports evidence from Reuters and EBS trading systems suggests that in 2002-2004, there

was a marked reduction in absolute trading volumes in the JPY/USD exchange rate while the absolute

volumes on the USD/EUR and the USD/GBP exchange rates sharply increased. The period

incorporates some of the most pronounced episodes of interventions by the BoJ that could have

reduced the traders’ appetite to take large yen positions.

24

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Working Paper Series No. 447

February 2005

significant coefficient in all regressions. The interpretation of the negative coefficient

is that yen-selling interventions (almost all observations in the data set were yen sales)

have a positive impact on the forecasts of future realised correlation. In all cases, the

adjusted R

2

s improve; the increase is particularly marked in the case of implied

correlation forecast (15% in the full sample). Hence, an intervention strategy that aims

at systematically stabilising a particular exchange rate over time could increase the

expected future co-movement among its cross exchange rates as reflected in particular

by the currency options prices.

Table B: Japanese interventions on JPY/USD and forecasts of correlation

between USD/EUR and JPY/EUR (standard errors in parenthesis)

Full sample Post euro sample

Correlation

(b)

Intervention

(c)

R

2

Correlation

(b)

Intervention

(c)

R

2

Implied 0.747*

(0.105)

0.745*

(0.067)

-0.28*

(0.053)

0.205

0.220

0.924*

(0.113)

0.920*

(0.069)

-0.013*

(0.044)

0.359

0.365

Historical

0.564*

(0.053)

0.561*

(0.037)

-0.197*

(0.045)

0.314

0.326

0.583*

(0.076)

0.581*

(0.050)

-0.013*

(0.044)

0.343

0.349

RiskMetri

cs

0.874*

(0.112)

0.871*

(0.079)

-0.022*

(0.046)

0.235

0.242

1.168*

(0.143)

1.163*

(0.093)

-0.011*

(0.044)

0.382

0.387

GARCH

0.858*

(0.066)

0.854*

(0.049)

-0.020*

(0.045)

0.329

0.341

0.834*

(0.094)

0.832*

(0.094)

-0.014*

(0.045)

0.362

0.370

*Denotes a significant estimate at 5% level

25

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Working Paper Series No. 447

February 2005

5. Concluding remarks

The various estimations of correlation between the major bilateral exchange rates

show distinctive fluctuations over time. The correlations generally increased soon

after the introduction of the euro, but have more recently returned closer to their

longer-term average levels. This development reflects the episode of broad-based euro

depreciation 1999-2000, followed in 2002-early 2003 by euro appreciation that was

somewhat more prominent against the US dollar than against the pound sterling and

the Japanese yen.

Regarding the ability to forecast future correlation, implied correlation can predict up

to 36% of future realized correlation. Nevertheless, it is not univocally the best

predictor of future correlation as GARCH and RiskMetrics correlations yield

occasionally very good predictive power, too. When used together, implied

correlation, GARCH correlation and RiskMetrics correlation are particularly useful in

predicting future correlation between the major euro currency pairs at the one-month

horizon. The predictive power seems to have strengthened after the introduction of the

euro.

When applying the estimated correlation measures, we found that using correlation

forecasts to analyse scenarios for effective exchange rates is useful as an expected

movement in one currency pair seems to indicate a very different impact on the

effective exchange rate in various points in time. The time-varying correlation

forecasts take into account the market’s current perception of the relative adjustment

of various exchange rates as a response to a sudden movement in one major exchange

rate. Mapping these bilateral movements into the NEER index provides conditional

forecasts that could be a useful input in analysing scenarios for future inflationary

risks. Furthermore, we show that data on interventions on the JPY/USD exchange rate

improve the ability of implied correlation in particular to forecast future realised

correlation. This effect, that is not consistent with the monetary or portfolio channels

of interventions, suggests that systematic intervention might be capable of affecting

the options market’s perception about future co-movement among the cross-rates of

the currency pair that is on the focus of the market operation.

26

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Working Paper Series No. 447

February 2005

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Appendix 1

In contrast with the RiskMetrics model, the GARCH model implies a non-constant

term structure of variance and covariance. To compute the GRACH forecast it is

necessary to take into account the mean reverting nature of the process.

In particular, the persistence of currency 1 is A(1,1)

2

+ B(1,1)

2

; similarly, the

persistence of currency 2 = A(2,2)

2

+ B(2,2)

2

; the persistence of the covariance is =

A(1,1)*A(2,2) + B(1,1)*B(2,2).

The unconditional second moment for forex rates can be computes as:

Ucvar(1) = Ω(1,1)

2

/(1 – persistence(1))

Ucvar(2) = (Ω (2,2)

2

+ Ω (2,1)

2

)/(1 –persistence(2))

Ucovar(1,2) = Ω (1,1)* Ω (2,1)/(1 – persistence(1,2))

The term structures are:

21

(i-1)

i=1

21

(i-1)

i=1

21

(i-1)

i=1

Term(1) = Persistence(j)

Term (2) = Persistence(k)

Term (1,2) = Persistence(j,k)

∑

∑

∑

The variance 21 days ahead forecasts are:

GARCHterm(1) = (21*Ucvar(1) – Ucvar(1)*Term(1) + H(1,1)*Term(1));

GARCHterm(2) = (21*Ucvar(2) – Ucvar(2)*Term(2) + H(2,2)*Term(2));

GARCHterm(1,1) = (21*Ucvar(1,2) – Ucvar(1,2)*Term(1,2) + H(1,2)*Term(1,2).

Finally, the 21 days ahead GARCH correlation forecast is

121,21

GARCHterm(1,2)

(, ) =

GARCHterm(1) GARCHterm(2)

GARCH

t

RR

ρ

+

.

30

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Working Paper Series No. 447

February 2005

Appendix 2

In this appendix, we assess the relative forecasting performance of the conditional

expectations, as calculated using equation 4.1, against the forward exchange rates. To

this end, we run regressions à la Fama for all three currency pairs, where the realised

change in the exchange rate over 1-month horizon is regressed on a constant and a

forecast error. The forecast future rate is either the forward exchange rate E

t

(X

i,t+1

) or

the conditional expectation

)(

11,

ϑ

=

++ ttit

YXE

, where

ϑ

is chosen to be the realised

value of the JPY/EUR exchange rate 1 month ahead in time:

16

eXYXEXX

eXXEXX

tittittiti

titittiti

+−=+=−

+

−

+=−

+++

++

))((

))((

,11,,1,

,1,,1,

ϑβα

β

α

(A2.1)

The null hypothesis is that

α

is equal to a possibly non-zero constant (including

Jensen’s inequality term) and

β

equals positive unity. The sample period covers the

period of euro exchange rates only, i.e. it stretches from 4 January 1999 to 31 March

2004.

Table C summarises the results of the Fama regressions for the forward exchange

rates and for the conditional expectations where three different correlation forecasts

are applied (historical, RiskMetrics and GARCH correlation).

Table C: Results from the regressions of equation

Conditional expectation based on correlation

Forward rate

Historical RiskMetrics GARCH

USD/EUR -0.553*

(0.058)

0.085*

(0.037)

0.121*

(0.013)

0.125*

(0.041)

GBP/EUR 0.204*

(0.095)

0.264*

(0.054)

0.193*

(0.023)

0.397*

(0.070)

JPY/EUR 0.593*

(0.003)

0.616*

(0.029)

0.035*

(0.008)

0.779*

(0.037)

*Denotes a significant estimate at 5% level

16

We make this choice purely arbitrarily; alternatively, we also used today’s spot exchange rates as a

proxy for υ and found that the results were little changed.

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The results show that, in line with several earlier studies, for the USD/EUR the

β

coefficient is significant and negative in the forward rate regression, amounting to the

familiar forward bias puzzle. However, the coefficients from the regressions including

conditional expectations are all correctly signed (positive) indicating that the

estimators do not suffer from the bias. Regarding the GBP/EUR and the JPY/EUR

exchange rates, the coefficients are also all correctly signed (positive) and significant.

Moreover, apart from the RiskMetrics correlation, the coefficients from the

regressions using conditional expectations are higher than from the regressions that

use forward exchange rates. The constant terms were small and significant for most of

the regressions involving the USD/EUR and JPY/EUR rates, and significant in some

cases for the GBP/EUR rate. The R

2

s were generally higher for the regressions that

use conditional expectations.

All in all, it cannot be excluded that expectations conditional on future developments

in the JPY/USD exchange rate, that use the information on correlation forecasts, can

improve upon the forecasting power of forward exchange rates in the case of the

bilateral euro exchange rates.

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Appendix 3 Charts

1: Correlations pre-January 1999

17

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_czkeur

Chart 1. Historical Correlation. Pre 1999.

17

For all the pre-1999 period or the full sample period the DEM proxies for the EUR.

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-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_czkeur

Chart 2. Implied Correlation. Pre 1999.

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-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_czkeur

Chart 3. RiskMetrics Correlation. Pre 1999.

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-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1992 1993 1994 1995 1996 1997 1998

usdeur_czkeur

Chart 4. GARCH correlation. Pre 1999.

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2: Correlations post-January 1999

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_czkeur

Chart 5. Historical Correlation. Post 1999.

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-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_czkeur

Chart 6: Implied Correlation. Post 1999.

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-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_czkeur

Chart 7. RiskMetrics Correlation. Post 1999.

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-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_gbpeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

gbpeur_jpyeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdgbp_jpyg bp

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdjpy_gbpjpy

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_plzeur

-0.8

-0.4

0.0

0.4

0.8

1999 2000 2001 2002 2003

usdeur_czkeur

Chart 8. GARCH Correlation. Post 1999.

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Appendix 4 Tables (coefficient estimates above; standard errors below)

Table 1. Correlation Predicatability Regressions. All sample: January 1992 - March 2003

USD/EUR-JPY/EUR USD/EUR-GBP/EUR

Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2

0.045 0.747 0.205 0.009 0.79 0.207

0.052 0.105 0.073 0.124

0.178 0.564 0.314 0.209 0.548 0.295

0.027 0.053 0.034 0.058

0.174 0.874 0.229 0.257 0.563 0.125

0.03 0.112 0.048 0.12

0.095 0.858 0.329 0.093 0.875 0.324

0.029 0.066 0.04 0.079

0.053 0.356 0.446 0.346 0.045 0.384 0.426 0.33

0.04 0.095 0.059 0.065 0.12 0.059

0.028 0.452 0.602 0.282 0.009 0.653 0.216 0.219

0.044 0.103 0.115 0.07 0.126 0.113

0.022 0.263 0.706 0.343 -0.022 0.323 0.708 0.347

0.038 0.096 0.085 0.062 0.12 0.086

0.048 0.29 0.367 -0.55 0.59 0.366 -0.008 0.425 0.182 -0.493 0.765 0.383

0.037 0.094 0.105 0.167 0.165 0.062 0.123 0.11 0.137 0.164

GBP/EUR-JPY/EUR USD/GBP-JPY/GBP

Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2

0.021 0.661 0.136 -0.02 0.751 0.203

0.039 0.117 0.049 0.101

0.14 0.351 0.123 0.211 0.315 0.099

0.021 0.063 0.031 0.068

0.133 0.43 0.101 0.166 0.46 0.156

0.022 0.091 0.033 0.075

0.109 0.584 0.171 0.078 0.745 0.174

0.021 0.077 0.042 0.107

0.027 0.47 0.232 0.179 -0.011 0.662 0.097 0.209

0.035 0.112 0.063 0.048 0.113 0.067

0.017 0.506 0.259 0.166 0.001 0.56 0.204 0.221

0.036 0.115 0.089 0.046 0.12 0.084

0.024 0.385 0.43 0.206 -0.033 0.517 0.372 0.227

0.033 0.108 0.084 0.047 0.125 0.132

0.034 0.376 -0.044 -0.476 0.945 0.227 -0.059 0.491 -0.19 0.012 0.669 0.234

0.032 0.103 0.096 0.127 0.173 0.05 0.126 0.102 0.141 0.279

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USD/JPY-GBP/JPY USD/EUR-PLZ/EUR

Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2

0.075 0.698 0.337 -0.101 1.316 0.285

0.068 0.093 0.139 0.261

0.316 0.406 0.161 0.237 0.496 0.234

0.048 0.075 0.085 0.12

0.221 0.565 0.222 0.143 0.69 0.296

0.057 0.091 0.091 0.143

-0.008 0.982 0.228 -0.409 1.786 0.187

0.095 0.16 0.278 0.519

0.075 0.674 0.031 0.338 -0.047 0.955 0.215 0.306

0.067 0.111 0.075 0.113 0.252 0.149

0.07 0.629 0.092 0.34 -0.016 0.675 0.405 0.318

0.068 0.117 0.097 0.109 0.328 0.236

0.016 0.604 0.219 0.342 -0.324 1.065 0.672 0.3

0.083 0.108 0.158 0.299 0.283 0.67

-0.057 0.603 -0.145 -0.013 0.507 0.346 -0.125 0.647 -0.032 0.388 0.293 0.319

0.107 0.114 0.135 0.154 0.275 0.245 0.342 0.125 0.232 0.595

USD/EUR-CZK/EUR

Intercept Implied Historical RiskMetrics GARCH Adj-rbar2

-0.132 0.906 0.186

0.082 0.217

0.175 0.109 0.012

0.047 0.116

0.177 0.114 0.007

0.051 0.154

0.16 0.238 0.002

0.081 0.423

-0.134 0.888 0.039 0.186

0.084 0.202 0.086

-0.134 0.897 0.025 0.185

0.087 0.204 0.121

-0.144 0.897 0.089 0.184

0.108 0.209 0.305

-0.131 0.889 0.074 -0.054 -0.008 0.183

0.104 0.205 0.113 0.233 0.568

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Table 2. Correlation Predicatability Regressions. Sample: March 1999 - March 2004

USD/EUR-JPY/EUR USD/EUR-GBP/EUR

0.1 0.924 0.359 -0.085 1.139 0.217

0.075 0.113 0.188 0.274

0.254 0.583 0.343 0.34 0.473 0.206

0.052 0.076 0.071 0.096

0.189 1.168 0.382 0.253 0.979 0.218

0.056 0.143 0.088 0.198

0.19 0.834 0.362 0.272 0.692 0.206

0.056 0.094 0.1 0.164

0.097 0.577 0.32 0.411 -0.012 0.728 0.294 0.27

0.062 0.139 0.107 0.145 0.205 0.082

0.091 0.473 0.717 0.417 -0.023 0.661 0.608 0.265

0.062 0.17 0.254 0.14 0.191 0.196

0.088 0.512 0.477 0.406 -0.035 0.713 0.412 0.261

0.062 0.14 0.151 0.151 0.211 0.149

0.093 0.485 0.106 0.55 -0.025 0.418 -0.013 0.67 0.185 0.169 0.075 0.27

0.062 0.154 0.123 0.557 0.307 0.144 0.186 0.173 0.386 0.317

GBP/EUR-JPY/EUR USD/GBP-JPY/GBP

0.222 0.467 0.067 0.077 0.682 0.198

0.069 0.141 0.054 0.119

0.251 0.387 0.146 0.274 0.252 0.063

0.038 0.081 0.043 0.094

0.217 0.581 0.152 0.224 0.382 0.1

0.044 0.127 0.047 0.108

0.218 0.586 0.193 0.153 0.612 0.09

0.041 0.095 0.068 0.18

0.179 0.229 0.334 0.158 0.077 0.67 0.014 0.197

0.057 0.13 0.087 0.054 0.129 0.094

0.167 0.178 0.513 0.16 0.076 0.646 0.041 0.198

0.057 0.138 0.147 0.054 0.139 0.12

0.177 0.131 0.543 0.199 0.08 0.696 -0.026 0.197

0.053 0.117 0.107 0.065 0.144 0.207

0.191 0.147 -0.049 -0.309 0.855 0.204 0.149 0.697 0.026 0.335 -0.61 0.204

0.05 0.12 0.14 0.471 0.423 0.064 0.139 0.109 0.157 0.314

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USD/JPY-GBP/JPY USD/EUR-PLZ/EUR

-0.075 0.856 0.242 -0.128 1.368 0.314

0.106 0.144 0.131 0.248

0.412 0.213 0.043 0.225 0.514 0.267

0.061 0.097 0.075 0.105

0.305 0.404 0.103 0.14 0.694 0.329

0.071 0.115 0.078 0.123

0.105 0.771 0.112 -0.456 1.872 0.219

0.118 0.203 0.244 0.458

-0.087 0.943 -0.092 0.247 -0.06 0.965 0.228 0.338

0.108 0.179 0.107 0.107 0.254 0.134

-0.077 0.876 -0.022 0.242 -0.024 0.677 0.416 0.351

0.107 0.201 0.152 0.104 0.316 0.203

-0.068 0.878 -0.042 0.242 -0.358 1.083 0.719 0.332

0.118 0.213 0.289 0.262 0.28 0.611

-0.167 0.79 -0.337 0.192 0.39 0.258 -0.135 0.649 -0.03 0.392 0.302 0.351

0.138 0.216 0.147 0.187 0.425 0.229 0.328 0.125 0.21 0.571

USD/EUR-CZK/EUR

Intercept Implied Historical RiskMetrics GARCH Adj-rbar2

-0.156 0.956 0.206

0.077 0.21

0.166 0.114 0.012

0.046 0.115

0.166 0.126 0.008

0.05 0.151

0.152 0.233 0.002

0.08 0.423

-0.158 0.94 0.037 0.205

0.079 0.196 0.085

-0.158 0.947 0.027 0.205

0.081 0.197 0.118

-0.165 0.948 0.074 0.204

0.103 0.203 0.304

-0.145 0.937 0.068 -0.02 -0.095 0.203

0.1 0.2 0.114 0.227 0.558

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Table 3. Mincer Zarnowitz Decomposition of MSE in Percentage

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.077 16.379 1.513 82.108 0.030 0.061 0.411 99.528

Historical 0.073 0.008 22.189 77.803 0.042 0.040 24.315 75.645

RiskMetrics 0.085 10.684 7.093 82.223 0.091 65.952 0.005 34.043

GARCH 0.056 2.789 0.936 96.275 0.044 24.434 3.717 71.848

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.078 7.778 2.656 89.566 0.044 8.144 0.347 91.509

Historical 0.077 0.005 21.491 78.504 0.052 0.089 21.072 78.839

RiskMetrics 0.088 22.581 0.476 76.943 0.101 61.291 0.489 38.220

GARCH 0.062 3.089 1.294 95.618 0.052 22.414 1.704 75.882

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.071 2.171 2.200 95.629 0.070 1.565 3.166 95.269

Historical 0.095 0.136 23.985 75.878 0.094 0.041 24.650 75.310

RiskMetrics 0.072 0.133 7.875 91.991 0.071 0.049 8.714 91.237

GARCH 0.080 0.358 4.284 95.358 0.081 0.738 5.730 93.532

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.082 33.949 0.165 65.885 0.083 35.371 0.035 64.593

Historical 0.124 0.132 46.572 53.295 0.123 0.324 45.211 54.465

RiskMetrics 0.099 0.029 33.026 66.945 0.099 0.001 31.743 68.256

GARCH 0.070 1.932 3.623 94.445 0.071 1.124 3.553 95.323

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.088 7.151 3.708 89.141 0.065 0.084 8.620 91.296

Historical 0.118 0.001 32.415 67.584 0.077 0.013 29.989 69.998

RiskMetrics 0.099 0.537 16.411 83.052 0.065 9.191 7.749 83.060

GARCH 0.085 1.299 9.349 89.352 0.064 10.222 9.597 80.182

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.091 18.372 2.238 79.390 0.051 6.521 4.774 88.705

Historical 0.124 0.007 34.097 65.896 0.085 0.000 37.359 62.641

RiskMetrics 0.096 0.001 20.289 79.711 0.066 0.040 22.535 77.425

GARCH 0.077 0.000 2.405 97.595 0.054 0.612 3.863 95.525

MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual

Implied 0.061 24.794 6.556 68.650 0.065 47.291 0.475 52.235

Historical 0.074 0.009 29.115 70.875 0.070 0.047 38.557 61.396

RiskMetrics 0.057 0.691 14.431 84.877 0.051 0.885 19.967 79.148

GARCH 0.049 0.677 0.010 99.313 0.041 0.901 1.095 98.004

USD/GBP-JPY/GBP USD/GBP-JPY/GBP

USD/JPY-GBP/JPY USD/JPY-GBP/JPY

USD/EUR-CZK/EUR USD/EUR-CZK/EUR

GBP/EUR-JPY/EUR GBP/EUR-JPY/EUR

USD/EUR-PLZ/EUR USD/EUR-PLZ/EUR

USD/EUR-JPY/EUR USD/EUR-JPY/EUR

All sample Post 1999

USD/EUR-GBP/EUR USD/EUR-GBP/EUR

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European Central Bank working paper series

For a complete list of Working Papers published by the ECB, please visit the ECB’s website

(http://www.ecb.int)

402 “Forecasting euro area inflation using dynamic factor measures of underlying inflation”

by G. Camba-Méndez and G. Kapetanios, November 2004.

403 “Financial market integration and loan competition: when is entry deregulation socially beneficial?”

by L. Kaas, November 2004.

404 “An analysis of systemic risk in alternative securities settlement architectures” by G. Iori,

November 2004.

405 “A joint econometric model of macroeconomic and term structure dynamics” by P. Hördahl,

O. Tristani and D. Vestin, November 2004.

406 “Labour market reform and the sustainability of exchange rate pegs” by O. Castrén, T. Takalo and

G. Wood, November 2004.

407 “Banking consolidation and small business lending” by E. Takáts, November 2004.

408 “The great inflation, limited asset markets participation and aggregate demand: FED policy was better

than you think” by F. O. Bilbiie, November 2004.

409 “Currency mismatch, uncertainty and debt maturity structure” by M. Bussière, M. Fratzscher

and W. Koeniger, November 2004.

410 “Do options-implied RND functions on G3 currencies move around the times of interventions

on the JPY/USD exchange rate? by O. Castrén, November 2004.

411 “Fiscal discipline and the cost of public debt service: some estimates for OECD countries”

by S. Ardagna, F. Caselli and T. Lane, November 2004.

412 “The real effects of money growth in dynamic general equilibrium” by L. Graham and

D. J. Snower, November 2004.

413 “An empirical analysis of price setting behaviour in the Netherlands in the period

1998-2003 using micro data” by N. Jonker, C. Folkertsma and H. Blijenberg, November 2004.

414 “Inflation persistence in the European Union, the euro area, and the United States”

by G. Gadzinski and F. Orlandi, November 2004.

415 “How persistent is disaggregate inflation? An analysis across EU15 countries and

HICP sub-indices” by P. Lünnemann and T. Y. Mathä, November 2004.

416 “Price setting behaviour in Spain: stylised facts using consumer price micro data”

by L. J. Álvarez and I. Hernando, November 2004.

417 “Staggered price contracts and inflation persistence: some general results”

by K. Whelan, November 2004.

418 “Identifying the influences of nominal and real rigidities in aggregate price-setting behavior”

by G. Coenen and A. T. Levin, November 2004.

419 “The design of fiscal rules and forms of governance in European Union countries”

by M. Hallerberg, R. Strauch and J. von Hagen, December 2004.

420 “On prosperity and posterity: the need for fiscal discipline in a monetary union” by C. Detken, V. Gaspar

and B. Winkler, December 2004.

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421 “EU fiscal rules: issues and lessons from political economy” by L. Schuknecht, December 2004.

422 “What determines fiscal balances? An empirical investigation in determinants of changes in OECD

budget balances” by M. Tujula and G. Wolswijk, December 2004.

423 “Price setting in France: new evidence from survey data” by C. Loupias and R. Ricart,

December 2004.

424 “An empirical study of liquidity and information effects of order flow on exchange rates”

by F. Breedon and P. Vitale, December 2004.

425 “Geographic versus industry diversification: constraints matter” by P. Ehling and S. B. Ramos,

January 2005.

426 “Security fungibility and the cost of capital: evidence from global bonds” by D. P. Miller

and J. J. Puthenpurackal, January 2005.

427 “Interlinking securities settlement systems: a strategic commitment?” by K. Kauko, January 2005.

428 “Who benefits from IPO underpricing? Evidence form hybrid bookbuilding offerings”

by V. Pons-Sanz, January 2005.

429 “Cross-border diversification in bank asset portfolios” by C. M. Buch, J. C. Driscoll

and C. Ostergaard, January 2005.

430 “Public policy and the creation of active venture capital markets” by M. Da Rin,

G. Nicodano and A. Sembenelli, January 2005.

431 “Regulation of multinational banks: a theoretical inquiry” by G. Calzolari and G. Loranth, January 2005.

432 “Trading european sovereign bonds: the microstructure of the MTS trading platforms”

by Y. C. Cheung, F. de Jong and B. Rindi, January 2005.

433 “Implementing the stability and growth pact: enforcement and procedural flexibility”

by R. M. W. J. Beetsma and X. Debrun, January 2005.

434 “Interest rates and output in the long-run” by Y. Aksoy and M. A. León-Ledesma, January 2005.

435 “Reforming public expenditure in industrialised countries: are there trade-offs?”

by L. Schuknecht and V. Tanzi, February 2005.

436 “Measuring market and inflation risk premia in France and in Germany”

by L. Cappiello and S. Guéné, February 2005.

437 “What drives international bank flows? Politics, institutions and other determinants”

by E. Papaioannou, February 2005.

438 “Quality of public finances and growth” by A. Afonso, W. Ebert, L. Schuknecht and M. Thöne,

February 2005.

439 “A look at intraday frictions in the euro area overnight deposit market”

by V. Brousseau and A. Manzanares, February 2005.

440 “Estimating and analysing currency options implied risk-neutral density functions for the largest

new EU member states” by O. Castrén, February 2005.

441

442

443

by S. Rosati and S. Secola, February 2005.

“Explaining cross-border large-value payment flows: evidence from TARGET and EURO1 data”

“The Phillips curve and long-term unemployment” by R. Llaudes, February 2005.

“Why do financial systems differ? History matters” by C. Monnet and E. Quintin, February 2005.

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445

February 2005.

446

February 2005.

447

by O. Castrén and S. Mazzotta, February 2005.

and A. al-Nowaihi, February 2005.

“Welfare implications of joining a common currency” by M. Ca’ Zorzi, R. A. De Santis and F. Zampolli,

“Trade effects of the euro: evidence from sectoral data” by R. Baldwin, F. Skudelny and D. Taglioni,

“Foreign exchange option and returns based correlation forecasts: evaluation and two applications”

“Keeping up with the Joneses, reference dependence, and equilibrium indeterminacy” by L. Stracca