How do exchange rates co-move? A study on the currencies of five inflation-targeting countries

Journal of Banking & Finance 35 (2011) 418–429

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How do exchange rates co-move? A study on the currencies of five inflation-targeting countries Xiao-Ming Li ⇑ School of Economics and Finance (Albany), Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand

a r t i c l e

i n f o

Article history: Received 10 March 2010 Accepted 18 August 2010 Available online 24 August 2010 JEL classification: F31 C32 C51

a b s t r a c t This paper does three things. First, it explores the type of asymmetry in exchange rate correlation for five inflation-targeting countries. We show their currencies co-move more closely with the currencies of some influential foreign countries during joint appreciations than joint depreciations against a world currency. Second, it establishes empirically the linkage between interest rate differentials and exchange rate correlation. We find evidence that both widening and narrowing interest rate differentials will reduce the correlation. Third, it proposes a new version of the asymmetric dynamic conditional correlation model. The model proves to be capable of providing great insight into the two issues investigated. Ó 2010 Elsevier B.V. All rights reserved.

Keywords: Exchange rate correlation Interest rate differentials ADCCE model Inflation-targeting countries

1. Introduction Over recent years, interest in exchange rate co-movements has been growing rapidly out of that in univariate exchange rate movements. An often cited reason is the crucial importance of information on exchange rate co-movements in financial and economic applications. Examples of financial applications include pricing multivariate currency options (Salmon and Schleicher, 2007) and optimizing currency portfolios (Beine, 2004). Concerning economic applications, how exchange rates co-move matters for the real economy and inflation, hence for central banks to achieve desired appreciation/depreciation of the domestic currency against several foreign currencies (Benediktsdottir and Scotti, 2009). In gauging short-run exchange rate co-movements, researchers have used two popular measures: tail dependence and correlation. The former allows for multivariate non-normal distributions and focuses on the probability of joint extreme appreciation or depreciation. This is useful for capturing tail risk in a portfolio. The latter stays on the multivariate normality assumption and looks at how two currencies move together on average across the marginal distributions. This is relevant to investors seeking portfolios with a global minimum variance. Adopting a conditional copula approach,

⇑ Tel.: +64 9 414 0800x9471; fax: +64 9 441 8177. E-mail address: [email protected] 0378-4266/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2010.08.019

Patton (2006) examines tail dependence, while Benediktsdottir and Scotti (2009) investigate tail dependence and correlation, between exchange rates. This paper employs the concept of correlation to study how the currencies of five inflation-targeting countries co-move with some influential foreign currencies in terms of their exchange rates against a common world currency. We contribute to the intervention literature, the inflation-targeting literature, and the literature on modeling dynamic conditional correlation (DCC) or time-varying correlation among financial asset returns. In the intervention literature, the effects of central bank interventions (CBIs) on exchange rate dynamics have attracted tremendous attention of researchers. Early investigations mainly probed into the level and/or volatility of a given exchange rate to explore the effectiveness of CBIs. This literature is vast and has yielded mixed evidence (see Nikkinen and Vahamaa, 2009, and the references therein). More relevant to our study, however, are several recent papers that turn to exchange rate co-movements under CBIs. Beine (2004) applies a multivariate GARCH model to look at whether coordinated CBIs affect the variances and covariance between the yen-dollar and euro-dollar exchange rates. He documents that increases in the covariance (correlation) tend to be associated with concerted interventions. Nikkinen and Vahamaa (2009) take a different approach and examine implied correlation among the yen-dollar, euro-dollar and pound-dollar rates. They argue that, unlike ex post exchange rate correlation used in Beine

X.-M. Li / Journal of Banking & Finance 35 (2011) 418–429

(2004), ex ante exchange rate correlation implied by the prices of currency options incorporate all the information underlying market expectations about future exchange rate dynamics. Their results suggest that CBIs significantly affect the market expectations about future exchange rate co-movements through increasing ex ante correlations among major exchange rates. A common feature of the intervention studies is that they look at the effects of an event (i.e., an official intervention) on exchange rate movements and co-movements. Unlike them, we ask whether a particular monetary policy regime, namely inflation targeting (IT), would result in asymmetric dynamics in exchange rate correlation and, if so, what type of asymmetry it might be. Surprisingly, the literature on inflation targeting and exchange rates has so far neglected this issue.1 Because inflation targeting is a regime, not an event, approaches of an event-study nature are not relevant. Also, a regime is not quantifiable, and an inflation target does not change frequently enough to be an informative variable. Thus, in examining exchange rate co-movements under inflation targeting, our strategy is to test the conjecture that the currency of an IT country should demonstrate positive-type asymmetry (to be defined below) in the dynamics of its correlation with an influential foreign currency visà-vis a common world currency. To illuminate this conjecture, let us carry out simple economic reasoning as follows.2 Consider an IT country H (as the home country with currency CH) and an influential foreign country F (with currency CF), and denote their exchange rates against a world currency (CW) as SW/ H (the world currency price of CH) and SW/F (the world currency price of CF). Suppose SW/F rises (appreciates) due to some economic shocks. Given other economic variables, this would make F’s goods/services relatively dearer than H’s if measured by Cw, causing H’s exports hence aggregate demand to rise over time and thus pushing up H’s expected inflation. H’s central bank is likely to pursue a beggar-thy-neighbor policy through currency appreciation (a rise in SW/H), as this would help prevent inflation from rising above the target in H. Now suppose SW/F falls. Unlike the case of SW/F rising, this would not exert an upward pressure on expected and actual inflation but may reduce domestic output in H. However, as the monetary policy strategies of H’s central bank are geared at price stability, not output stabilization, the central bank is less likely to pursue currency depreciation (a fall in SW/H) for stimulating exports hence output. Thus, under the IT regime, the responses of H’s central bank to rises/falls in SW/F may be asymmetric in the way described above. Further, such asymmetric responses tend to lead to stronger correlation between SW/H and SW/F during their joint appreciations than joint depreciations. We term this asymmetry ‘‘positive-type asymmetry”. However, there also exists the possibility of ‘‘negative-type asymmetry” – exchange rates are more strongly correlated during joint depreciations than joint appreciations. Negative-type asymmetry is likely due to portfolio rebalancing (Patton, 2006). For instance, when CW appreciates so that both SW/H and SW/F fall, there may be a shift of funds from both CH and CF to CW, leading to high exchange rate correlation during joint depreciation of SW/H and SW/F. When CW weakens so that both SW/H and SW/F rise, if market participants consider CH to be more (less) desirable than CF, there will be a shift of funds from CW to CH (CF) rather than to CF (CH). As a result, SW/H (SW/F) is more likely to rise than 1 Some studies focus on the pass-through from exchange rates to inflation (e.g., Allsopp et al., 2006), some examine whether monetary policy should also react to the exchange rate in addition to the output gap and inflation deviations from the target (e.g., Taylor, 2001), and some probe into the connection between inflation targeting and floating exchange rates (e.g., Edwards, 2007). 2 To the best of our knowledge, no formal theoretical models are readily available for predicting asymmetric dynamics in exchange rate correlation under the IT regime. Thus, we base the economic reasoning on some macroeconomic commonsense as, e.g., Patton (2006) does, to motivate the investigation and offer possible explanations for the empirical findings about positive-type asymmetry.

419

SW/F (SW/H) or, equivalently, SW/H and SW/F will have low correlation when they are appreciating together. We hypothesize that the price stability preference of an IT central bank is strong enough to outweigh the portfolio-rebalancing effect, so positive-type asymmetry will prevail in the exchange rate correlation between SW/H and SW/F. Our main research task is to empirically test this hypothesis. By uncovering the type of asymmetry in exchange rate correlation and by linking the asymmetry to price stability featuring inflation targeting, one can learn how effective the IT regime is. If positive-type asymmetry is present, we consider the regime to be effective in tying the central bank to achieving price stability. This distinguishes our study from the recent intervention studies on exchange rate correlation: While they look at the effectiveness of CBI events by examining whether the magnitude of exchange rate correlation (ex post or ex ante) changes following CBIs, we look at the effectiveness of the IT regime by examining whether positive-type asymmetry characterizes the dynamics in exchange rate correlation. We find overwhelming evidence of positive-type asymmetry for the foreign exchange (FX) market correlations of IT currencies, as opposed to the overwhelming evidence of negative-type asymmetry for stock market correlations found in the literature (see Baele, 2005; Dennis et al., 2006; Ang and Chen, 2002, among others). In addition to uncovering a common pattern of asymmetric exchange rate correlation for IT countries, we further investigate the possible effects of interest rate differentials (IRDs) on the correlation. Such effects, if present, are not unique to IT countries. For instance, Benediktsdottir and Scotti (2009) find certain evidence that currencies (including non-IT currencies) with a higher interest rate differential with the US dollar tend to have their exchange rates against the dollar co-move less closely, in terms of both tail dependence and correlation. However, while Benediktsdottir and Scotti (2009) take the copula approach, we base empirical investigation on the DCC model; and more importantly, while they use absolute IRDs in the current period, we use absolute changes in IRDs in the previous period. Our results are therefore different: both widening and narrowing IRDs tend to lower exchange rate correlation, which is consistent with the prediction of the uncovered interest parity (UIP) condition (to be discussed in more detail in Section 4.3). Our third contribution lies in methodological innovations conceived to accomplish the proposed research tasks. The innovations contribute to the literature on the DCC analysis of co-movements among financial asset returns or economic variables.3 Specifically, we extend the standard DCC model of Engle (2002) to a new asymmetric one and add to it exogenous variables. In fact, Sheppard (2002) already extends the model to include asymmetric effects, but the asymmetric effects are characterized by differing slopes across joint negative and joint positive values of past shocks. Our proposed asymmetric DCC (ADCC) model is different: It captures asymmetry by appealing to ‘‘eccentricity”, i.e., by re-centering the news impact surface away from zero as in the spirit of the asymmetric GARCH (AGARCH) model (Engle and Ng, 1993). In addition, Sheppard (2002) does not consider incorporating exogenous variables in his ADCC model. The importance of incorporating exogenous variables is suggested by Cappiello et al. (2006), as this helps identify and assess potential determinants of time-varying correlation. As will become clear later on, our proposed model proves to be more capable, than Sheppard’s (2002) asymmetric model, of providing insight into the asymmetry pattern of exchange rate correlation for the

3 The DCC model and the concept of time-varying correlation have become increasingly popular in studying financial issues, macroeconomic problems, or their mixture. An incomplete list of recent studies include Chulia et al. (2010), You and Daigler (2010), Yang et al. (2009), Cai et al. (2009), Lee (2006), Crespo Cuaresma and Wojcik, 2006, and Fang et al. (2006).

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X.-M. Li / Journal of Banking & Finance 35 (2011) 418–429

IT currencies investigated, as well as establishing the empirical linkage between IRDs and the correlation. The rest of the paper proceeds as follows. The next section describes our choices of currency pairs and data. Section 3 outlines econometric methodology. We report and discuss empirical results in Section 4, and offer summary and conclusion in Section 5.

2. Currency pairs and data Taking an IT country as the domestic economy, we measure the values of its currency and a foreign currency using a common world currency which is from a non-IT economy (hence, either the US dollar, or the euro, or the yen). The foreign economy may or may not be an explicit inflation targeter, but must be open and should be of sufficient importance to the domestic economy – that is, ‘‘influential”, so that the domestic economy will take seriously shocks to the foreign currency’s value. We consider significant linkages of trade and flows of capital between the domestic and foreign economies to be an indication of such importance. But, we also confine our choices of currency pairs within a geographical region, to make the undertaking of empirical investigation manageable. Our study involves each of the following three geographical regions: Australasia, Europe and North America. We select from these regions five inflation-targeting countries including Australia, Canada, New Zealand, Sweden and the United Kingdom, for two reasons. First, they are ‘‘full-fledged” inflation targeters (with floating exchange rates and high capital mobility), as they were the earliest to adopt this monetary policy regime in the early 1990s. Second, the five countries have been subject to several empirical queries in the literature (see, e.g., Johnson, 2003; Rogers and Siklos, 2003). The present paper therefore extends these studies by shedding light on the key research questions as posed in the Introduction. Australasia includes Australia and New Zealand. Both countries are competitors in international goods and capital markets, and importers/recipients of each other’s goods and capital. So, we assume that their shocks affect each other through exchange rate correlation. New Zealand officially adopted inflation targeting in February 1990, while Australia in March 1993. To avoid possible effects of initial, unstable inflation-targeting stages in Australia on estimation results, our investigation period starts from July 2, 1993 (through to November 12, 2009) for the exchange rates of the Australian dollar (AD) and the NZ dollar (ND) against the US dollar (UD) and the yen (JY). As for the exchange rates of AD and ND against the euro (ER), the starting investigation date is January 4, 1999 when the euro came into being (and the ending date is November 12, 2009). The two countries in Europe, Sweden and the UK, were forced to adopt the inflation-targeting regime following the breakdown of their exchange-rate-based monetary policy frameworks during the European Monetary System crisis in 1992. Although Sweden introduced inflation targeting in January 1993, the Riksbank declared that the target (2%, ±1%) would be in effect only from 1995 on. The UK started, in October 1992, with a target band of 1–4%, but has since 1995 set a single target at 2.5%. However, since we take the EU as the most influential foreign economy for Sweden and the UK, our investigation of asymmetric exchange rate correlation between the Swedish krona (SK) and ER vis-à-vis UD and JY, and between GP and ER vis-à-vis UD and JY, has to use the sample period starting from January 4, 1999 (and ending November 12, 2009). For Canada in North America, the most closely-linked foreign economy is obviously the US. In February 1991, the Bank of Canada and the federal government announced a series of inflation-reduc-

tion targets with a time frame to achieve them. In December 1991, the announced inflation target was 3–5%, indicating that Canada had gone through the initial stage of shaping inflation expectations and could now formally embark on inflation targeting. In view of these, we truncate the data for 1991 and use the data over 1992 through to 2009 to estimate exchange rate correlations between the Canadian dollar (CD) and UD vis-à-vis JY. Again, the sample period for estimating the correlation between the ER/CD and ER/ UD rates has to start from January 4, 1999 (and ends November 12, 2009). We source all exchange rate data used in this paper from the Pacific Exchange Rate Service website (http://fx.sauder.ubc.ca/). We employ daily rather than weekly or monthly data, as high-frequency data embrace information about shocks to exchange rates which would otherwise be lost in low-frequency data. In addition, we obtain from DataStream data on 3-month interbank interest rates for each currency involved, again with daily frequency. Use of 3-month interest rates makes our results comparable with those of Benediktsdottir and Scotti (2009) that also use 3-month interest rates. 3. Econometric methodology Consider a bivariate case where rt = [r1t, r2t]0 is a 2  1 vector containing two exchange rate return series each defined as the log difference of an exchange rate. We fit an ARMA(m, n) model, P Pn rit ¼ ci þ m j¼1 /ij r itj þ zit þ k¼1 jik zitk ði ¼ 1; 2Þ, to each return ser0 ies to obtain zt = [z1t, z2t] , a 2  1 vector containing two filtered return series. We assume a bivariate normal distribution for zt conditional on the information set Xt14:

zt jXt1  Nð0; Ht Þ

ð1Þ

The covariance matrix Ht can be decomposed into

Ht ¼ Dt Rt Dt

ð2Þ

1=2 1=2 diag(h1t ; h2t )

where Dt = is the 2  2 diagonal matrix of conditional standard deviations, and Rt = (diag(Qt))1  Qt  (diag(Qt))1 is the 2  2 conditional correlation matrix of et = [e1t, e2t]0 which contains 1=2 two standardized residuals defined as e1t ¼ z1t =h1t and 1=2 e2t ¼ z2t =h2t . To make e1t and e2t as close to i.i.d. as possible, we determine the orders (m and n) of the ARMA(m, n) model, and estimate the GARCH(1, 1) model for the conditional variances hit5:

hit ¼ xi þ di z2it1 þ hi hit1 ;

i ¼ 1; 2

ð3Þ

where xi (P0), di (P0) and hi (P0) are parameters. Then, the typical element in Rt, q12t, represents conditional correlation between e1t and e2t. Qt is the 2  2 conditional covariance matrix of et, whose elements, q11t, q12t and q22t, are used to compute q12t = q12t/ (q11tq22t)1/2. Up to this point, everything is from the standard DCC model. Now we depart by proposing an asymmetric DCC model with an exogenous IRDs variable for the evolution of Qt. We term the model ADCCE. It is partly in the spirit of the AGARCH model of (Engle and Ng, 1993): F

H

  B0 QBÞ  þ A0 et1 e0 A þ B0 Q B þ gjDði  i Þj   A0 QA Q t ¼ ðQ t1 t1 t1 t1 ð4Þ

4 In the absence of conditional normality (which is true for our data), the results have a standard QMLE interpretation. So the assumption of conditional normality is not crucial. 5 As Balaban (2004) points out (while quoting a referee), unlike the equity returns, there is no theoretical reason for asymmetry or leverage effect in currency volatility. To avoid such a potential statistical artifact as asymmetry in currency volatility, we only model asymmetry in currency correlations which has a theoretical reason given in Section 1.

X.-M. Li / Journal of Banking & Finance 35 (2011) 418–429

¼ where Q F





q 12 1 q 12 1 ;A ¼



a1 0

     e þ c1 0 b1 0 ;B ¼ ; et ¼ 1t e2t þ c2 ; j 0 b2 a2

421

the theorems provided in Engle and Sheppard (2001) for the twostage procedure.

H

Dðit  it Þj  absolute changes in IRDs between the foreign and the  12 is the unconditional correlation domestic economy, and q between e1t and e2t. a1 (P0), a2 (P0), b1 (P0), b2 (P0), c1, c2 and g denote the parameters to be estimated. Note, absolute IRDs are often non-stationary, so we use absolute changes in IRDs to avoid this problem. Moreover, using absolute changes in IRDs makes more economic sense (see Section 4.3 for the discussion). The element version of (4) reads: F

H

F

H

q11t ¼ ð1  a21  b21 Þ þ a21 ðe1t1 þ c1 Þ2 þ b21 q11t1 þ gjDðit1  it1 Þj  12 ð1  a1 a2  b1 b2 Þ þ a1 a2 ðe1t1 þ c1 Þðe2t1 þ c2 Þ q12t ¼ q F

H

þ b1 b2 q12t1 þ gjDðit1  it1 Þj q22t ¼ ð1  a22  b22 Þ þ a22 ðe2t1 þ c2 Þ2 þ b22 q22t1 þ gjDðit1  it1 Þj where 1  a21  b21 > 0; 1  a1 a2  b1 b2 > 0 and 1  a22  b22 > 0. Some remarks regarding Eq. (4) are in order. First, when c1 and c2 both equal zero, (4) collapses to the DCC model with no asymmetry; when c1, c2 > 0 (c1, c2 < 0), positive-type (negative-type) asymmetry will surely result; and when c1 and c2 take different signs, the asymmetry type could be positive or negative, depending on the values of |ci|, ai and bi. F H Second, the exogenous variable jDðit1  it1 Þj affects the conditional correlation coefficient q12t in the following manner. According to the definition of q12t, we have

q12t C 12t þ gyt1 ffi q12t ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q11t q22t ½C 11t þ gyt1 ½C 22t þ gyt1 

ð5Þ

where F

H

yt1  jDðit1  it1 Þj C 11t  ð1  a21  b21 Þ þ a21 ðe1t1 þ c1 Þ2 þ b21 q11t1  12 ð1  a1 a2  b1 b2 Þ þ a1 a2 C 12t  q ðe1t1 þ c1 Þðe2t1 þ c2 Þ þ b1 b2 q12t1 C 22t  ð1  a22  b22 Þ þ a22 ðe2t1 þ c2 Þ2 þ b22 q22t1 Note, C11t, C12t and C22t do not depend on yt1. From these relations, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi we can derive @ q12t =@yt1 ¼ gð1  q12t =2Þ= q11t q22t . Clearly, both the sign of g and the sign of 1  q12t/2 determine the sign of pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi oq12t/oyt1, as q11t q22t is non-negative. Our estimation results show that q12t < 2 for all t and all currency pairs (and that the positive definiteness of Qt for all t and all pairs is not violated). Thus, if g < 0, a rise (fall) in the absolute change of IRDs in the previous period would reduce (increase) exchange rate correlation in the current period, given all other variables and parameters in (4); if g > 0, the reverse is true; and if g = 0, the absolute change of IRDs will have no effect on the correlation. We estimate all the GARCH and ADCCE model parameters in Eqs. (1)–(4) using the two-stage procedure proposed in Engle and Sheppard (2001). Specifically, in the first stage, we maximize the quasi-log-likelihood function,

" # 2 T  X z2it 1X LLF 1 ¼  T logð2pÞ þ logðhit Þ þ 2 i¼1 hit t¼1

ð6Þ

with respect to (x1, d1, h1, x2, d2, h2). In the second stage, condition^ 1; ^ ^ 2; ^ ing on (x d1 ; ^ h1 ; x d2 ; ^ h2 ) obtained from the first stage, we maximize the quasi-log-likelihood function

LLF 2 ¼ 

T 1X ½2 logð2pÞ þ 2 log jDt j þ logðjRt jÞ þ e0t R1 t et  2 t¼1

ð7Þ

with respect to (a1, b1, c1, a2, b2, c2, g) to obtain their estimates. We then modify the standard errors of the 13 parameters according to

4. Empirical results 4.1. Estimates of the GARCH and DCC parameters Table 1 compactly summarizes the estimation and test results for the 12 GARCH-ADCCE models. One can see from the table that ^ i; ^ all of the GARCH parameter estimates ðx di and ^ hi Þ are statistically significant at the 1% level and all of the sums ^ di þ ^ hi are close to unity. The latter suggests that all of the 24 filtered return series have a high degree of persistence in volatility. In addition, except for the ER/CD-vs-ER/UD pair, the modified Box-Pierce Q-statistics for ^eit and ^e2it are all statistically insignificant at the 5% level, allowing one to regard the 23 standardized residuals as i.i.d., or as carrying current, unpredictable information shocks. The only exception is the ER/CD rate, for which we try different orders of the ARMA(m, n) model up to m, n = 20 but fail to improve its Q 11 statistic. But, the simple GARCH(1, 1) specification seems to work reasonably well in capturing the dynamics of variances for at least 23 return series. ^i ^ i and b Turning to the DCC parameters, Table 1 indicates that a are also statistically significant at the 1% level for all the 12 pairs; that is, the 12 correlation series are not constant but time-varying. To confirm this, we employ the testing procedure proposed by Engle and Sheppard (2001). The resultant v2-test statistics allow one to reject the null of a constant correlation in favor of a dynamic structure for all the 12 pairs, at the 1% level. Moreover, all of the ^2 and a ^2 ; a ^1 b ^2 are also close to unity, sug^ 21 þ b ^2 þ b ^1a ^ 22 þ b sums a 1 2  12 ’s gesting a high degree of persistence in correlation. The 12 q show that 11 pairs have high unconditional correlations in each of them (ranging between 0.5601 and 0.8866), while one pair (ER/SK vs ER/GP) has the lowest unconditional correlation between  12 ¼ 0:0897Þ. However, although not the involved two rates (q shown in this paper, the conditional correlation between the ER/ SK and ER/GP rates swings quite widely over time between 0.2657 and 0.3579. 4.2. Evidence on positive-type asymmetry in dynamic exchange rate correlation As stated earlier, our first objective is to explore the type of asymmetry in the dynamics of exchange rate correlation. Thus, of more interest are the estimates and signs of the asymmetry parameters c1 and c2. A striking observation from Table 1 is that, for the 12 exchange rate pairs investigated, all the 24 estimated values of c1 and c2 are positive, and are significant at above the 5% level both individually (by the t-statistics) and jointly (by the LRT statistics). Overall, Table 1 provides overwhelming evidence in support of positive-type asymmetry for the five IT currencies. Note, it is eccentricity that features the asymmetry our model attempts to detect. Is there any evidence of the asymmetry (positive-type or negative-type) characterized by differing slopes? We consider this question by exploring Sheppard’s (2002) version of the ADCC model. Table 2 sets out the parameter estimates of the model. Eight of 12 pairs demonstrate that one cannot reject symmetry in slopes (i.e., g1 = g2 = 0) at the 5% level for both joint positive shocks (i.e., nt = I(et > 0) ° et) and joint negative shocks (i.e., nt = I(et < 0) ° et), based on the LRT statistics. This implies that evidence on asymmetry in slopes is rather weak. As far as the remaining four pairs (UD/ SK vs UD/ER, JY/SK vs JY/ER, UD/GP vs UD/ER, and UD/SK vs UD/GP) are concerned, one would favor both positive-type and negativetype asymmetries against symmetry. However, a problem arises.

422

Table 1 Parameter estimates of the GARCH-ADCCE model. UD/AD UD/ND Sample period Start 02/07/93 End 12/11/09

ER/AD ER/ND

JY/AD JY/ND

UD/SK UD/ER

JY/SK JY/ER

UD/GP UD/ER

JY/GP JY/ER

UD/SK UD/GP

ER/SK ER/GP

JY/SK JY/GP

ER/CD ER/UD

JY/CD JY/UD

04/01/99 12/11/09

02/07/93 12/11/09

04/01/99 12/11/09

04/01/99 12/11/09

04/01/99 12/11/09

04/01/99 12/11/09

03/01/95 12/11/09

04/01/99 12/11/09

03/01/95 12/11/09

04/01/99 12/11/09

02/01/92 12/11/09

0.0044** 0.0634** 0.9319** 0.0075** 0.0449** 0.9437**

0.0122** 0.0759** 0.9127** 0.0155** 0.0730** 0.9108**

0.0042** 0.0372** 0.9554** 0.0013** 0.0306** 0.9667**

0.0036** 0.0508** 0.9465** 0.0025** 0.0531** 0.9451**

0.0029** 0.0429** 0.9486** 0.0014** 0.0308** 0.9664**

0.0031** 0.0480** 0.9492** 0.0025** 0.0535** 0.9447**

0.0036** 0.0367** 0.9558** 0.0027** 0.0378** 0.9534**

0.0009** 0.0630** 0.9346** 0.0008** 0.0342** 0.9628**

0.0054** 0.0469** 0.9455** 0.0047** 0.0442** 0.9482**

0.0031** 0.0315** 0.9620** 0.0013** 0.0299** 0.9668**

0.0094** 0.0477** 0.9383** 0.0065** 0.0404** 0.9469**

ADCCE model parameters a1 0.1319** b1 0.9879** c1 0.2663** a2 0.1112** b2 0.9918** c2 0.1964** g 0.0029 q 0.7076

0.1283** 0.9862** 0.4179** 0.1081** 0.9881** 0.3787** 0.0404** 0.7457

0.1529** 0.9780** 0.3398** 0.1577** 0.9755** 0.3054** 0.0188** 0.8362

0.1347** 0.9906** 0.4206** 0.1127** 0.9922** 0.6605** 0.1709** 0.8535

0.1454** 0.9857** 0.3599** 0.1427** 0.9873** 0.3952** 0.1368** 0.8866

0.0944** 0.9898** 0.5865** 0.1472** 0.9886** 0.6237** 0.2771** 0.6919

0.1190** 0.9873** 0.3727** 0.1258** 0.9920** 0.3900** 0.1164* 0.7969

0.0841** 0.9942** 0.3373** 0.0749** 0.9946** 0.3653** 0.0330** 0.5601

0.1808** 0.9414** 0.5679* 0.0881** 0.9941** 0.5495** 0.1484** 0.0897

0.1498** 0.9686** 0.3275** 0.1161** 0.9834** 0.3796** 0.1048** 0.7271

0.1250** 0.9908** 0.4042** 0.1063** 0.9943** 0.3446** 0.1029** 0.6054

0.1376** 0.9905** 0.2164** 0.1339** 0.9899** 0.2379** 0.0046 0.8227

Statistics LRT Q 1 Q 11 Q 2 Q 22 v2-test LLF

26.810** 36.615 37.921 19.859 32.187 1234.0** 6737.6

39.229** 28.080 25.510 5.7024 14.934 851.59** 4641.4

45.802** 37.392 36.766 26.064 27.798 1553.2** 7942.9

18.003** 21.221 28.291 10.807 28.314 1322.0** 3559.5

57.131** 17.774 9.6640 15.514 16.803 1258.6** 3980.7

11.234** 17.479 17.867 13.336 27.469 931.97** 3787.5

33.402** 17.959 28.418 14.311 16.206 967.82** 4485.1

15.118** 33.515 30.866 33.175 18.722 887.73** 5914.1

37.044** 24.722 26.506 8.8677 26.522 23.194** 2792.3

22.924** 27.778 14.016 32.379 28.017 1237.2** 7217.8

39.229** 17.441 53.383** 10.131 28.616 702.03** 4242.5

30.112** 37.587 29.818 38.116 29.555 1561.6** 6812.2

Note: This table presents the parameter estimates of Eqs. (3) and (4) for 12 exchange rate pairs. The estimation (and the computation of modified standard errors) uses the two-stage procedure proposed in Engle and Sheppard (2001). LRT denotes the likelihood ratio test statistic testing the joint null c1 = c2 = 0. Q* represents the Box-Pierce Q-statistic adjusted for heteroskedasticity (see Lobato et al., 2001). Q 1 ; Q 11 ; Q 2 and Q 22 are associated with e1t ; e21t ; e2t ; e22t , respectively. We set their lag lengths to be 18 for the sample period 04/01/99–12/11/09, 25 for 03/01/95–12/11/09, and 28 for both 02/07/93–12/11/09 and 02/01/92–12/11/09. The v2-test, proposed by Engle and  against the alternative that vech ðRt Þ ¼ v echðRÞ  þ s1 vech(Rt1) +    + spvech(Rtp). LLF is the quasi-log-likelihood function evaluated at the maximum. Sheppard (2001), tests the null that Rt ¼ R * Significance at the 5% level. ** Significance at the 1% level.

X.-M. Li / Journal of Banking & Finance 35 (2011) 418–429

GARCH model parameters 0.0052** d1 0.0546** h1 0.9359** x2 0.0021** d2 0.0400** h2 0.9557**

x1

Table 2 Parameter estimates of Sheppard’s (2002) ADCC model (with the IRDs variable added). UD/AD UD/ND

JY/AD JY/ND

UD/SK UD/ER

JY/SK JY/ER

UD/GP UD/ER

JY/GP JY/ER

UD/SK UD/GP

ER/SK ER/GP

JY/SK JY/GP

ER/CD ER/UD

JY/CD JY/UD

Panel A: nt = I(et > 0) et 0.1588** b1 0.9840** g1 0.0671** a2 0.1319** b2 0.9864** g2 0.0633** g 0.0034** LRT 3.0729 LLF 6713.3

0.1525** 0.9767** 0.0000 0.1038** 0.9928** 0.0000 0.0767** 0.0003 4655.6

0.1704** 0.9735** 0.0830** 0.1700** 0.9727** 0.0821** 0.0178** 5.8040 7924.7

0.1626** 0.9777** 0.0662** 0.1140** 0.9803** 0.1095** 0.3774** 20.266** 3558.4

0.1919** 0.9733** 0.0268** 0.1910** 0.9647** 0.0747** 0.2859** 8.1323** 3975.5

0.0847** 0.9879** 0.0677** 0.0713** 0.9908** 0.1051** 0.2118** 15.068** 3785.5

0.1727** 0.9696** 0.0418** 0.1330** 0.9899** 0.0331** 0.3086 0.3432 4468.5

0.1996** 0.9773** 0.0460** 0.0875** 0.9825** 0.1204** 0.1774** 16.207** 5907.4

0.1215** 0.9926** 0.0000** 0.0564** 0.9984** 0.0000** 0.0044** 1.4842 2775.6

0.1997** 0.9595** 0.0035** 0.1151** 0.9852** 0.0374** 0.2951** 0.8202 7208.1

0.1685** 0.9823** 0.0391** 0.2053** 0.9787** 0.0000 0.0130* 0.7067 4228.8

0.1899** 0.9778** 0.0346** 0.1723** 0.9850** 0.0000 0.0078** 5.0816 6781.9

Panel B: nt = I(et < 0) et 0.1788** b1 0.9832** g1 0.0000 a2 0.1399** b2 0.9884** g2 0.0000 g 0.0141** LRT 0.0001 LLF 6714.8

0.1525*** 0.9767*** 0.0000 0.1038*** 0.9928*** 0.0000 0.0766*** 0.0001 4655.6

0.1853** 0.9753** 0.0000 0.1862** 0.9728** 0.0000 0.0218** 0.0011 7927.6

0.1065** 0.9821** 0.1203** 0.1147** 0.9846** 0.0770** 0.3143** 31.852** 3552.6

0.1306** 0.9740** 0.1498** 0.1462** 0.9736** 0.1222** 0.2715** 18.881** 3970.1

0.0523** 0.9902** 0.1028** 0.0855** 0.9891** 0.0779** 0.2244** 20.402** 3782.9

0.1749** 0.9692** 0.0344** 0.1354** 0.9894** 0.0274** 0.3137 0.1573 4468.6

0.1362** 0.9805** 0.1319** 0.0860** 0.9873** 0.0631** 0.1534** 16.947** 5907.0

0.0828** 0.9944** 0.0000 0.0756** 0.9960** 0.0000 0.0034** 0.0158 2776.3

0.1911** 0.9593** 0.0755** 0.1122** 0.9858** 0.0405** 0.2479** 0.4668 7208.3

0.1739** 0.9821** 0.0000 0.1990** 0.9790** 0.0444** 0.0134* 0.8603 4228.8

0.1992** 0.9772** 0.0000 0.1788** 0.9839** 0.0000 0.0255 0.0000 6784.4

a1

a1

Note: This table presents the parameter estimates, for 12 exchange rate pairs, of Sheppard’s (2002) version of the ADCC model (but with the IRDs variable added) as follows:  A  B0 Q  B  G0 NGÞ   A0 Q  þ A0 et1 e0 A þ B0 Q t1 B þ G0 nt1 n0 G þ gjDðiF  iH Þj Q t ¼ ðQ t1 t1 t1 t1  ¼ T 1 PT nt n0 with T being the sample size, and nt = I(et > 0) ° et with ° denoting the Hadamard product. All other matrices, parameters and variables are defined where G = diag(g1, g2) with g1 (P0) and g2 (P0) being parameters, N t t¼1 the same as in (4). The estimation (and the computation of modified standard errors) uses the two-stage procedure proposed in Engle and Sheppard (2001). LRT denotes the likelihood ratio test statistic testing the joint hypothesis that g1 = g2 = 0. LLF is the quasi-log-likelihood function evaluated at the maximum. * Significance at the 5% level. ** Significance at the 1% level.

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ER/AD ER/ND

423

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Table 3 Final estimation results of the ADCCE model (4) with structural change. UD/AD UD/ND

a1 b1

c1pre-euro c1post-euro a2 b2

c2pre-euro c2post-euro g  pre-euro q  post-euro q LRT LLF

0.1369** 0.9870** 0.5083** 0.2130** 0.1100** 0.9939** 0.5617** 0.1275** 0.0250** 0.5362 0.7823 37.122** 6719.1

JY/AD JY/ND 0.1529* 0.9780** 0.3398** 0.3398** 0.1577** 0.9755** 0.3054** 0.3054** 0.0188** 0.8362 0.8362 7942.9

UD/SK UD/GP 0.0870** 0.9942** 0.6736* 0.3404** 0.0727** 0.9902** 0.5835** 0.4533** 0.0653** 0.4087 0.6126 23.479** 5902.4

JY/SK JY/GP 0.1501** 0.9686** 0.2246* 0.3388** 0.1155** 0.9861** 0.2214* 0.4258* 0.0946** 0.7273 0.7273 7.2738** 7214.2

JY/CD JY/UD 0.1556** 0.9758** 0.3507** 0.3507** 0.1288** 0.9858** 0.3428** 0.3428** 0.0401** 0.9256 0.7535 90.072** 6767.2

Note: This table presents the parameter estimates, for five exchange rate pairs, of Eq. (4) but with a structural break assumed to take place on the advent of the euro. The estimation (and the computation of modified standard errors) uses the two-stage procedure proposed in Engle and Sheppard (2001). LRT denotes the likelihood ratio test  ; c1 and c2. statistic. The ‘‘null” model under the likelihood ratio test is one in Table 1 – i.e., with no break in q * Significance at the 5% level. ** Significance at the 1% level.

The model for positive-type asymmetry does not nest the model for negative-type asymmetry, nor vice versa, although they all nest the model for symmetry. So, it is difficult to determine which, the positive- or the negative-type asymmetry model, we should favor by using the LRT test. To sum up, Sheppard’s (2002) version of the ADCC model is irrelevant to asymmetry featured by eccentricity, and does not lend us a helping hand in ascertaining the type of asymmetry if it is characterized by differing slopes. On the contrary, our ADCC model nests symmetry, and positive-type and negative-type asymmetry in the form of eccentricity, and does a good job in revealing that the positive-type asymmetry for the five IT currencies is the eccentricity-induced asymmetry. It is also interesting to note Patton’s (2006) study on asymmetric dependence between the yen-dollar and the mark-dollar exchange rate over the period of January 1991–December 2001. Based on a copular approach, he finds strong evidence of what we refer to as negative-type asymmetry for the pre-euro period but weak evidence of positive-type asymmetry for the post-euro period. A natural question is: Would one obtain qualitatively the same results if applying our ADCCE model to the correlation between the same two exchange rates over the same sample period while allowing for the same structure break date (January 4, 1999) as in Patton (2006)? The answer is affirmative. To save space, we only report estimates of the asymmetry parameters and their ^1preeuro ¼ 0:5898 (t-value = 6.4715), related test results here: c c^2preeuro ¼ 0:0725 (t-value = 2.4218), c^1posteuro ¼ 0:1438 (t^2posteuro ¼ 0:4948 (t-value = 0.2876). The value = 0.3976), and c LRT statistics allow us to reject the joint null of c^1preeuro ¼ c^2preeuro ¼ c^1posteuro ¼ c^2posteuro ¼ 0 and the joint null ^1preeuro ¼ c ^2preeuro ¼ 0 at the 5% level, but not the joint null of of c c^1posteuro ¼ c^2posteuro ¼ 0 at the 10% level. So, our approach also suggests strong evidence of negative-type asymmetry in the preeuro period, and weak evidence of positive-type asymmetry in the post-euro period, for the yen-dollar and the mark-dollar exchange rate, consistent with Patton’s (2006) findings. This brings out an important point that our detection of positive-type asymmetry for the five IT currencies is not due to employing a DCC approach instead of a copula approach, but due to a reason proposed by Patton (2006) as follows. Since the advent of the euro, the dominance of export competitiveness preference and/or the portfoliorebalancing effect has given way to the dominance of price stability preference, for the Bank of Japan and/or the Bundesbank. By the same token, we can explain the findings of positive-type asymmetry for the five IT economies in this way: Under inflation targeting,

the five central banks have their price stability preference constantly outweigh both output stabilization (i.e., export competitiveness) preference and the portfolio-rebalancing effect put together.6 However, to be able to uphold this explanation or argument, one must address another question: Has the introduction of the euro also caused structural change that is significant enough to turn positive-type into negative-type asymmetry for the five IT currencies? If so, our proposed link between the dominance of price stability preference and positive-type asymmetry would be broken. Thus, as a robustness check, we estimate the ADCCE model with structural change for those exchange rate correlations which involve the pre-euro and post-euro samples. We consider five pos c1 , and c2; (2) q  sibilities: Structural change takes place in (1) q  and c1; and (5) q  and c2. From the five coronly; (3) c1 and c2; (4) q responding break models, we pick the one with the highest value of the log likelihood function and then, via the likelihood ratio test, compare it with its no-break counterpart reported in Table 1. The final results appear in Table 3. Four pairs reject the no-break model in favor of the break model. Among them, the UD/AD-vs-UD/ND  c1 , and c2; the JY/ and UD/SK-vs-UD/GP pairs show a break in q SK-vs-JY/GP pair has a break in c1 and c2 only; and the JY/CD-vs only. Regarding the JY/ADJY/UD pair demonstrates a break in q vs-JY/ND pair, we cannot reject the ‘‘null”, no-break model in favor of the five alternative break models under consideration. The advent of the euro has lowered the asymmetry parameters c1 and c2 for the UD/AD-vs-UD/ND and the UD/SK-vs-UD/GP correlation, increased the parameters for the JY/SK-vs-JY/GP correlation, and left unchanged the parameters for the JY/AD-vs-JY/ND and the JY/CD-vs-JY/UD correlation. More importantly, however, none of the five exchange rate correlations have changed from positivetype to negative-type asymmetry. Thus, unlike the two non-IT banks (i.e., the Bank of Japan and/or the Bundesbank) that could change their policy preferences following an event like the introduction of the euro, the five IT central banks could not. The inflation-targeting regime confines their ‘‘policy room” to maneuver.

6 We also estimate the ADCCE model for the correlation between the yen-euro and dollar-euro rates over 04/01/99–12/11/09. Our results again suggest negative-type asymmetry for the currencies of the two non-IT countries, Japan and the US, whose central banks do not always tie their monetary policies to maintaining price stability. We take this as circumstantial evidence to establish that positive-type asymmetry exists for currencies under inflation targeting where price stability is the steadfast, paramount monetary policy objective of their central banks.

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As a result, while the exchange rate correlation between the two non-IT currencies has undergone a shift from negative-type to positive-type asymmetry, the exchange rate correlations involving the five IT currencies have adhered firmly to positive-type asymmetry.

4.3. Evidence on the effects of interest rate differentials on exchange rate correlation Our second objective is to establish the empirical linkage between IRDs and the evolution of exchange rate correlation. We achieve this by estimating the parameter g associated with the F H exogenous variable (jDit1  it1 j). According to Table 1, Moorthy ^ ’s are negative. Among 11 out of 12 pairs demonstrate that their g ^ ’s, 10 are statistically significant with nine at the 1% level the 11 g and one at the 5% level, and one (for the UD/AD-vs-UD/ND pair) is both statistically and economically insignificant. In addition, the only positive estimate of g appears with the JY/CD-vs-JY/UD pair, but it is also both statistically and economically insignificant. However, when we take into account a structural break due to the introduction of the euro for, especially, the four relevant pairs (UD/AD-vs-UD/ND, UD/SK-vs-UD/GP, JY/SK-vs-JY/GP and JY/CDvs-JY/UD), a new picture emerges. Comparing Table 3 with Table ^ ’s now become more, and significantly, 1, one can see that three g negative, including those for the UD/AD-vs-UD/ND and JY/CD-vsJY/UD pairs as mentioned above; and one (for the JY/SK-vs-JY/GP pair) remains about the same. Therefore, all of the 12 pairs show strong evidence on the negative linkage between IRDs and the dynamics of exchange rate correlation. Recalling from Section 3, g < 0 means that, other things being equal, conditional exchange rate correlation will decline (rise) if the absolute change of IRDs in the previous period rises (falls). This is consistent with the UIP theory, as detailed below. F H The UIP theory suggests Dðit1  it1 Þ ¼ DðEt1 r Ht  Et1 r Ft Þ,7 where Et1 r Ft and Et1 r Ht are the expected exchange rate returns on, respectively, foreign and domestic currencies. Consider F H F H Dðit1  it1 Þ > 0 first. This means that it1 rises more than it1 does, F H F H F H or it1 falls less than it1 does, or it1 rises while it1 falls. If it2 > it2 , the interest rate differentials in t  1 will increase (i.e., F H F H F H it1  it1 > it2  it2 ); and if it2 < it2 , the interest rate differenF H F H tials in t  1 will decrease (again, it1  it1 > it2  it2 ). Meanwhile, it follows from the UIP condition that DðEt1 r Ht  Et1 rFt Þ > 0 : Et1 rHt rises more than Et1 rFt does, or Et1 rHt falls less than Et1 rFt does, or Et1 r Ht rises while Et1 r Ft falls. Similarly, if Et2 r Ht1 > Et2 r Ft1 , the gap between the two expected returns for the current period t will widen (i.e., Et1 rHt  Et1 r Ft > Et2 rHt1  Et2 r Ft1 ); and if Et2 r Ht1 < Et2 r Ft1 , the gap will narrow (again, Et1 rHt  Et1 r Ft > Et2 r Ht1  Et2 r Ft1 ). In either of the two circumstances, the FX markets expect r Ht and r Ft to move less likely in the same direction but more likely in the opposite directions (i.e., to co-move less closely) than in the circumstance where DðiFt1  iHt1 Þ ¼ 0. Next, consider F H Dðit1  it1 Þ < 0. Via similar reasoning to the above, the conclusion remains the same: The correlation will be lower than for F H F H Dðit1  it1 Þ ¼ 0. Therefore, as long as jDðit1  it1 Þj > 0 (i.e., it F H F H does not matter whether Dit1 > Dit1 or Dit1 < Dit1 ), we expect that correlation between two exchange rate returns is smaller than F H when jDðit1  it1 Þj ¼ 0, so g is negative. These theoretical predictions seem to be well supported by the empirical results reported in Tables 1 and 3. F 7 The UIP conditions for foreign and domestic currencies are iW t1  it1 ¼ H W Et1sW=F;t sW=F;t1 and iW is the interest rate on the t1  it1 ¼ Et1sW=H;t sW=H;t1 , where i world currency and s denotes the logarithm of the exchange rate. It is straightforward H F to show iFt1  iH t1 ¼ ðEt1sw=H;t1 sw=H;t1 Þ  ðEt1sW=F;t1 sW=F;t1 Þ ¼ Et1 r t  Et1 r t .

425

Our idea to establish empirically the linkage between interest rate differentials and the evolution of exchange rate correlation is not completely new. Benediktsdottir and Scotti (2009) also examine this issue. However, there are several differences between our study and theirs. Firstly, whereas they employ a time-varying normal copula to model conditional correlation, we resort to the DCC model. Secondly, while they use absolute IRDs in the current period, we opt for the absolute change of IRDs lagged by one period, as an exogenous variable. While their results imply that widening (narrowing) IRDs will reduce (increase) the correlation, our results suggest that both widening and narrowing IRDs will reduce exchange rate correlation – which is more consistent with the UIP theory. Thirdly, although both studies show that the impacts of IRDs on exchange rate correlation can be negative, our evidence is much stronger hence much more affirmative. 4.4. Graphical representation of the results To appreciate the financial and economic implications of the estimation results, this section presents and discusses the news impact surfaces and time-series plots of exchange rate correlation. However, for the sake of space conservation, we use the UD/GP-vsUD/ER pair as an example for illustration; the conclusions drawn from the pair apply qualitatively to the remaining 11 pairs. We treat current exchange rate shocks (i.e., eit) as ‘‘news” – positive/negative shocks as ‘‘good/bad news”, and examine the impact of such news on exchange rate correlation using the notion of the ‘‘news impact surface” of Kroner and Ng (1998). Focusing on the asymmetric impacts of e1t and e2t on q12t, we hold the exogF H enous variable jDðit1  it1 Þj at zero. Thus, for our ADCCE model, the correlation news impact surface is:

~c12 þ a1 a2 ðe1 þ c1 Þðe2 þ c2 Þ þ b1 b2 q  12 f ðe1 ; e2 Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½~c11 þ a21 ðe1 þ c1 Þ2 þ b21 ½~c22 þ a22 ðe2 þ c2 Þ2 þ b22 

ð8Þ

The value of ~c12 determines the vertical location, not the shape, of the surface in a three-dimensional plot. For e1 = c1 and e2 = c2,  12 . In we force the surface to be f(0, 0) = 0 and so ~c12 to be – b1 b2 q addition, we set ~c11 and ~c22 to 1  a21  b21 and 1  a22  b22 , respectively. We evaluate the surface in the domain ei = [3, 3] (i = 1, 2), ^i) and use the parameter estimates of the ADCCE model (except g for the UD/GP-vs-UD/ER correlation from Table 1 to construct its news impact surface. Fig. 1 depicts the surface by giving three different looks at the surface. The positive-type asymmetry is apparent in Panels (2) and (3). They demonstrate that the surface is centered at a point (0.5865, 0.6237) in the ‘‘, ” standardized-residual quadrant, away from the origin (0, 0), resulting in a greater surface value for joint positive than joint negative standardized residuals of equal magnitudes. This implies a larger response to joint good news (in the ‘‘+, +” quadrant) than to joint bad news (in the ‘‘, ” quadrant) of the correlation between the UK sterling and the euro against the US dollar. To be more concrete, consider the scenario that joint positive shocks e1 = e2 = 3 hit the FX markets, and another scenario for joint negative shocks e1 = e2 = 3.8 The former leads to f(3, 3) = 0.1527, while the latter yields f(3, 3) = 0.0743, about half of the former. An argument naturally follows: Given that the conditional correlation series between the UD/GP and UD/ER rates declines significantly when bad news hits the markets, diversification sought by investing in the UK sterling and the euro is likely to be high. It is worth noting that Cappiello et al. (2006) and Li and Zou (2008) also apply news impact surfaces in modeling bond–bond, 8 The actual maximum (minimum) values of e1 and e2 are 4.498 (4.178) and 4.872 (4.069), respectively.

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Fig. 1. The news impact surface for the UD/GP-vs-UD/ER correlation. Note: This figure depicts the news impact surface by giving its three different looks for the UD/GP-vs-UD/ ^ i ) taken from Table 1 in constructing the surface based on Eq. (8). ER correlation. We use the parameter estimates of the ADCCE model (except g

stock–stock and stock–bond asymmetric dynamic correlations. The differences between our and their news impact surfaces are not because we deal with currency co-movements, but because we use a different version of the ADCC model. While their models yield news impact surfaces that capture asymmetries via a slope change, ours differs in that asymmetry in the news impact surface comes through re-centering of the surface. This way, we are able to reveal, for the first time in the literature, that asymmetric dynamics in the correlations of currencies could be of a positive type and eccentricity-induced, different than in the correlations of other asset classes like bonds and stocks. Whereas Fig. 1 gives a static picture describing a ‘‘snapshot” of positive-type asymmetry, Fig. 2 presents a ‘‘dynamic movie” of the asymmetry based on the estimated ADCC model for the UD/GP-vsUD/ER pair. Simulating dynamic conditional correlations under asymmetry, we consider two extreme scenarios: (1) joint good news, i.e., e1t > 0 and e2t > 0, for all t; and (2) joint bad news, i.e., e1t < 0 (but of the same magnitude as e1t > 0) and e2t < 0 (but of the same magnitude as e2t > 0), for all t. We also simulate the correlations under symmetry (by imposing c1 = c2 = 0) for the two scenarios. The top, solid line ‘‘rho_pos” (the bottom, dashed line ‘‘rho_neg”) represents the simulated dynamic correlations where joint positive (negative) shocks hit the FX markets over the entire

sample period. It is evident that the differences between ‘‘rho_pos” and ‘‘rho_neg” are economically significantly large. The middle, dotted line ‘‘rho_sym” corresponds to two correlation series for, respectively, joint positive and negative shocks but under symmetry. The differences between ‘‘rho_pos” and ‘‘rho_sym” and between ‘‘rho_sym” and ‘‘rho_neg” are also economically significantly large. When negative-type asymmetry is present, the value of diversification will be overstated if one does not take into account the increase in downside correlation. Conversely, when positive-type asymmetry is present, the value of diversification will be understated if one does not take into account the fall in downside correlation. The dynamic pictures in Fig. 2 shed further light on this insight provided by the static pictures in Fig. 1. Next, we assess the actual extent to which positive-type asymmetry contributes to historical total correlation; that is, how much of historical total correlation at each t can be attributed to the asymmetry. In doing so, we simply impose a zero value on both c^1 and c^2 , while retaining the estimates of all other parameters, ^ 12t ” and compare it with to generate what we term as ‘‘restricted q ^1 ¼ c ^2 ¼ 0). Note, ^ 12t ” (which does not impose c the ‘‘unrestricted q re-estimating the ADCCE model with c1 and c2 set to zero would lead to changes in other parameter estimates, and such a restricted model is decisively rejected by the likelihood ratio tests for all the

X.-M. Li / Journal of Banking & Finance 35 (2011) 418–429

427

Fig. 2. Simulated correlations for the UD/GP-vs-UD/ER pair. Note: This figure plots the simulated dynamic conditional correlations for the UD/GP-vs-UD/ER pair under asymmetry and symmetry. The top, solid line ‘‘rho_pos” (the bottom, dashed line ‘‘rho_neg”) represents the simulated correlation series where joint positive (negative) shocks hit the FX markets over the entire sample period. The middle, dotted line ‘‘rho_sym” corresponds to two correlation series for, respectively, joint positive and negative shocks but under symmetry.

Fig. 3. The UD/GP-vs-UD/ER correlations: unrestricted vs restricted. Note: This figure plots the simulated dynamic conditional correlations for the UD/GP-vs-UD/ER pair based on the historical data on all the variables involved, under two different scenarios: (1) We consider all the parameter estimates of the GARCH-ADCCE models taken from Table 1; and (2) we impose a zero restriction on the c1 and c2 parameters while retaining all other parameter estimates. The solid, ‘‘unrestricted” line represents the correlation series for (1), and the dotted, ‘‘restricted” line corresponds to the correlation series for (2).

12 pairs (see the LRT statistics in Table 1). Moreover, using the favored, unrestricted model’s parameter estimates except setting c^i ¼ 0 allows us to gauge the actual contribution of positive-type ^ 12t ” (i.e., the historical correlation asymmetry to the ‘‘unrestricted q series). We plug the required data in the GARCH-ADCCE model, first ^1 ¼ 0:5865 and c ^2 ¼ 0:6237, and then with c ^1 ¼ c ^2 ¼ 0, with c while keeping all other parameter estimates for the UD/GP-vsUD/ER correlation unchanged as they are in Table 1. These exercises yield two series of conditional correlation estimates labeled ‘‘unrestricted” and ‘‘restricted” in Fig. 3. The immediate observation is that the UD/GP-vs-UD/ER correction is time-varying (as are the other 11 correlation series), confirming the v2-test results in Table 1. That exchange rate correlation is time-varying is consistent with previous findings on currencies and other asset classes such as stocks and bonds (see Patton, 2006; Cappiello et al.,

2006), and so is not new. What make our study novel are the differences between the correlation under positive-type asymmetry (the ‘‘unrestricted” curve) and that under symmetry (the ‘‘restricted” curve). Fig. 3 illustrates that the ‘‘unrestricted” curve always lies above its ‘‘restricted” counterpart. The differences measure the contribution of positive-type asymmetry to historical total correlation. In other words, ignoring positive-type asymmetry would lead to underestimating of the correlation and understating of diversification benefits.9 This underestimation is quite serious in ^1 ¼ c ^2 ¼ 0 clearly accenthe UD/GP-vs-UD/ER case where imposing c tuates the downturns of correlation. For example, the ‘‘unrestricted” correlation indicates a fall from 0.69 to about 0.38 over the first half 9 In the presence of negative-type asymmetry, it is the increase in downside ^ unrestricted ^ restricted correlation that contributes to q q > 0, and the underestimation of 12 12 correlation should lead to overstating of diversification benefits.

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Fig. 4. The effects of interest rate differentials on the UD/GP-vs-UD/ER correlation. Note: This figure plots the simulated dynamic conditional correlations for the UD/GP-vsUD/ER pair using all the parameter estimates of the GARCH-ADCCE model taken from Table 1, under two different scenarios: (1) We consider historical data on all the variables involved; and (2) we increase the historical absolute change of IRDs by 0.02 while retaining historical data on all other variables involved. The solid, ‘‘factual” line represents the correlation series for (1), and the dotted, ‘‘counterfactual” line corresponds to the correlation series for (2).

of 1999, while the ‘‘restricted” correlation indicates a fall from 0.69 to approximately 0.16 over the same period: a difference of some 0.22. Such a discrepancy due to neglecting positive-type asymmetry could result in, say, mispricing of multivariate currency options used to hedge against several currencies. Fig. 4 turns to the graphical representation of the effects of IRDs on the evolution of the UD/GP-vs-UD/ER correlation. What also make our study novel are the ‘‘factual” and ‘‘counterfactual” correlation series and their differences presented therein. The upper, solid line labeled ‘‘factual” uses the historical absolute change of IRDs F H (Recally  jDði  i Þj), and the lower, dotted line labeled ‘‘counterfactual” uses the perturbed absolute change of IRDs. The perturbation is a permanent increase of 0.02 in y right from the beginning of the sample period. Though arbitrarily chosen, the size of the increase has to be of a plausible magnitude to ensure the positive definiteness of Qt or the non-negativity and non-zero of q11t and q22t. Provided a perturbation is plausible, slightly changing its size does not change the conclusion qualitatively. A rise in y allows us to see the degree to which widening/narrowing the historical IRDs would impact negatively on the correlation,10 as predicted by the ADCCE model (4) and the discussion in Sections 3 and 4.3. One can see clearly from Fig. 4 that the ‘‘counterfactual” correlation series always lies below its ‘‘factual” counterpart (and this is also true for the other 11 pairs). In other words, had the IRDs between the pound and the euro been greater or smaller than their historical values, the UD/ GP-vs-UD/ER correlation would have been lower than its historical levels. This confirms visually that the absolute change of IRDs has a negative effect on exchange rate correlation, for all the 12 exchange rate pairs under investigation. A policy implication is clear: The central banks of the five IT countries can use the interest rate as a policy instrument to regulate relevant exchange rate correlations should such a need arise.

correlation, for five IT currencies. To this end, we propose a new version of the asymmetric DCC model with the news impact surface re-centered away from zero and with exogenous variables added. We term the model ADCCE. Employing the GARCH-ADCCE model, we are able to deliver several interesting results. First, correlations between exchange rates are dynamic and time-varying. This may not necessarily be unique to IT countries, however. Second, and as a novel result, we show that asymmetry in dynamic exchange rate correlations is of a positive type: The currency of an IT country has a higher correlation with the currency of an influential foreign country during joint appreciations than joint depreciations against any one of the three world currencies (the US dollar, the euro and the Japanese yen). We attribute this phenomenon to a particular monetary policy regime – inflation targeting – which obliges the five central banks to maintain price stability as their paramount policy goal. Third, and as a novel result too, we provide strong evidence that, other things being equal, both widening and narrowing interest rate differentials will lower exchange rate correlations. This observation is consistent with the prediction of the UIP theory. Our results have implications for portfolio management. For example, an investor seeking to optimize currency portfolios that contain the currencies of the five IT countries may estimate more accurately the diversification benefits by taking into account the positive-type asymmetry in the exchange rate correlations. The investor may also predict the changing directions of exchange rate co-movements using the information on past changes in IRDs. Our results are useful for IT policymakers too, regarding the effectiveness of their policies to achieve price stability as necessitated by the IT regime, and in terms of managing exchange rate correlations by an appropriate use of interest rates. Acknowledgements

5. Summary and conclusion The focus of this paper is on exploring the type of asymmetry in the dynamics of exchange rate correlation and establishing an empirical linkage between IRDs and the evolution of exchange rate

I thank seminar participants at the 11th New Zealand Finance Colloquium and Nanjing University, and an anonymous referee for comments. References

We also consider the counterfactual scenario that yt ¼ jDðiFt  iH t Þj is set to zero for all t. The simulation results show that the ‘‘counterfactual” correlation curves lie above their ‘‘factual” counterparts. 10

Ang, A., Chen, J., 2002. Asymmetric correlations of equity portfolios. Journal of Financial Economics 63, 443–494.

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