Relationship between stock and currency markets conditional on the US stock returns: A vine copula approach

Accepted Manuscript Title: Relationship between stock and currency markets conditional on the US stock returns: A vine copula approach Author: Minoru Tachibana PII: DOI: Reference:

S1042-444X(17)30300-6 https://doi.org/doi:10.1016/j.mulfin.2018.05.001 MULFIN 557

To appear in:

J. of Multi. Fin. Manag.

Received date: Revised date: Accepted date:

3-12-2017 30-4-2018 18-5-2018

Please cite this article as: Minoru Tachibana, Relationship between stock and currency markets conditional on the US stock returns: A vine copula approach, (2018), https://doi.org/10.1016/j.mulfin.2018.05.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Relationship between stock and currency markets conditional on the US stock returns: A vine copula approach#

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Minoru Tachibana∗

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Graduate School of Economics, Osaka Prefecture University, Japan

Abstract

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Ignoring the co-movement of international stock markets might lead to a biased estimate for the relationship between domestic stock and currency markets. We address this issue by using the US stock returns as a proxy for the movement of foreign

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stock markets and applying a vine copula approach to 21 economies over the period 2003--2017. We find that both stock and currency markets in these economies are

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highly correlated with the US stock market. As a result, taking no account of the international stock market co-movement leads to an upward bias in the estimate for the correlation between domestic stock and currency returns, although the bias is not

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of great magnitude. Finally, the estimate for the correlation between domestic stock and currency returns conditional on the US stock returns tends to be positive in

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emerging economies, whereas it tends to be negative in developed economies.

Keywords: Vine copula, Stock return, Currency return. JEL Classification: C58, F31, G15.

I amgrateful to three anonymous referees for valuable comments and suggestions. I also acknowledge financial support from JSPS KAKENHI (grant number: 16K03746). ∗ E-mail address: [email protected] #

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Highlights We examine the stock-currency relationship conditional on the US stock returns.

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Athree-variate vine copula is applied to 21 economies over the period 2003-2017. Both stock and currency markets are highly correlated with the US stock market.

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Estimates for the stock-currency relation are smaller relative to a non-vine copula.

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Relationship between stock and currency markets conditional

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May 21, 2018

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on the US stock returns: A vine copula approach

Abstract

Ignoring the co-movement of international stock markets might lead to a biased esti-

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mate for the relationship between domestic stock and currency markets. We address this issue by using the US stock returns as a proxy for the movement of foreign stock markets

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and applying a vine copula approach to 21 economies over the period 2003–2017. We find that both stock and currency markets in these economies are highly correlated with

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the US stock market. As a result, taking no account of the international stock market co-movement leads to an upward bias in the estimate for the correlation between domes-

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tic stock and currency returns, although the bias is not of great magnitude. Finally, the estimate for the correlation between domestic stock and currency returns conditional on the US stock returns tends to be positive in emerging economies, whereas it tends to be negative in developed economies.

Keywords: Vine copula, Stock return, Currency return. JEL Classification: C58, F31, G15.

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1

Introduction

Understanding the relationships between stock and currency markets within countries is an

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important issue for international investors who manage risks in their portfolios as well as for policymakers who are responsible for financial and macroeconomic stability. The literature on the subject has relied on two classical theories of exchange rate determination to explain

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different types of linkages between domestic stock and currency markets. The “flow-oriented”

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or “international-trading model” (Dornbusch and Fischer, 1980) suggests that changes in exchange rates affect the international competitiveness of firms, consequently influencing their profits and stock prices. Thus, whether the correlation between stock prices and currency

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values is negative or positive might depend on whether a country under study is an exportdominant or import-dominant country. On the other hand, the “stock-oriented” or “portfolio-

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balance model” (Branson, 1983; Frankel, 1983) predicts that increases in stock prices in a country raise investors’ wealth, leading in turn to increases in money demand and interest

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rates, which induce appreciation of the domestic currency. Hence if this effect is dominant,

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we should find positive relationship between stock prices and currency values. Another and more plausible explanation from the viewpoint of international investment is that a positive

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shock to a country’s stock market would attract capital flows from foreign investors, resulting in appreciation of the currency to buy the stocks. Building on these theoretical insights, a vast number of empirical studies have attempted to clarify the linkages between stock and currency markets for various countries and periods. See, for instance, a review article by Bahmani-Oskooee and Saha (2015) and references therein.1 Most of the previous studies, however, have not considered the co-movement of international stock markets, which has been investigated by many authors in another strand of literature (e.g., Ang and Bekaert, 2002; Erb et al., 1994; Forbes and Rigobon, 2002; Ramchand 1

Bahmani-Oskooee and Saha (2015) conclude that although the link between stock prices and exchange rates is dependent on the data frequency and period chosen, the countries studied, and other macroeconomic variables, most of the previous studies find that the two variables are related in the short-run but not in the long-run.

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and Susmel, 1998; Kasa, 1992; King et al., 1994; Longin and Solnik, 1995, 2001; Solnik et al., 1996). Ignoring this factor might lead to a biased estimate for the domestic stock-currency relationship, because a common shock to international stock markets would influence a lo-

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cal country’s stock and currency markets as well, generating a spurious positive correlation among them that is not explained by the theories mentioned above. Therefore, one needs to

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control for the effect of foreign stock markets on both domestic stock and currency markets to obtain an unbiased estimate of the country-specific stock-currency relationship that the

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theories can account for.

The aim of this paper is to bridge the two strands of literature and disentangle the country-

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specific dependence structure between stock and currency markets from the co-movement of international stock markets. To this end, we employ a vine copula approach which has been

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recently developed in statistics and applied to financial data. More specifically, we construct a three-variate vine copula model that consists of a local economy’s stock and currency returns and the US stock returns, and apply it to 21 economies over the period 2003–2017. Here the

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US stock return is used as a proxy for the movement of foreign markets, since the US stock

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market is largest in the world and has played a leading role in the evolution of international stock markets. The vine copula enables us to assess the dependence structure between stock

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and currency returns conditional on the state of the US stock market. We compare the result from a vine copula with that from a non-vine bivariate copula (which does not contain the US stock returns) in order to see if there is bias in the estimate of the domestic stock-currency relationship when the latter model is estimated. One of the interests of the analysis is whether the bias becomes larger in times of financial turbulence than in normal times, since domestic stock and currency markets might be more strongly correlated with the US stock market or foreign stock markets during volatile times. Many recent studies show that interdependence among stock markets in the world had been intensified during the 2007–2009 global financial crisis due to contagion effects (see, e.g., Aloui et al., 2011; Bekiros, 2014; Dimitriou et al., 2013; Karanasos et al., 2016; Kenourgios and

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Padhi, 2012; Kenourgios and Samitas, 2011; Kim et al., 2015; Samarakoon, 2011; Syllignakis and Kouretas, 2011; Yang and Hamori, 2013). It might also be true during the episode of the European debt crisis beginning at the end of 2009. To allow for such possible structural

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changes in the dependence structure among international stock markets, we divide our full sample period into three sub-samples: the pre-crisis period (2003–2007), the crisis period

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(2007–2012), and the post-crisis period (2013–2017). The crisis period includes two devastating events of the global financial crisis and the European debt crisis during which the US stock

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market experienced much higher volatility than during other two periods. Thus comparing the results between the crisis and the two tranquil periods gives us useful information on how

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large the estimation bias for a stock-currency relationship is in times of financial turmoil. A few studies have taken into account the impact of foreign stock markets on the stock-

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currency relationship. Phylaktis and Ravazzolo (2005) incorporate the US stock price into the cointegration system of stock prices and exchange rates for five Asian countries (Hong Kong, Malaysia, the Philippines, Singapore, and Thailand). The evidence suggests that stock

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and foreign exchange markets are positively related and that the US stock market acts as a

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conduit for these links. Diamandis and Drakos (2011) apply the same cointegration model to four Latin American countries (Argentina, Brazil, Chile, and Mexico), obtaining similar

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results to those in Phylaktis and Ravazzolo (2005). Kubo (2012) adds two variables of the US stock price index and the stock price index of the US information technology industry to the cointegration systems of five Asian countries (Indonesia, Korea, the Philippines, Singapore, and Thailand). He finds that the two US stock price indices are positively related to the stock prices of all these countries. Moreover, he shows evidence that the relationships between domestic stock and foreign exchange markets in Indonesia, Korea, and Thailand are consistent with the portfolio-balance model. Sui and Sun (2016) estimate vector autoregressive (VAR) models with the US stock return for BRICS countries. They find significant spillover effects from exchange rates to stock returns in the short-run, but not vice versa. They also find that shocks to the US stock market significantly influence stock markets in Brazil, China, and

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South Africa. This paper contributes to the literature by adopting a vine copula approach, which dates back to Joe (1996) and is further studied by Bedford and Cooke (2001, 2002), Kurowicka

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and Cooke (2006), Aas et al. (2009), among others. The advantage of using the vine copula approach is that it allows a great deal of flexibility and complexity in specifying a model for

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the joint distribution of three or more variables. More specifically, a vine copula structure decomposes a multivariate density into products of respective marginal densities and bivariate

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copulas, the latter characterizing dependence structures for some pairs of the variables under study. Although the class of multivariate copulas is quite restricted, a huge number of bivariate

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copulas have been proposed. Therefore, we can construct a flexible and complex model for a multivariate joint distribution through the vine copula approach.

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Michelis and Ning (2010), Ning (2010), Reboredo et al. (2016), and Wang et al. (2013) have also adopted copula approaches to investigate the relationship between stock and currency markets. However, they estimate bivariate copula models with only two variables of

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stock and exchange rate returns. Meanwhile, this study extends the bivariate copula to a

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three-variate vine copula that includes the US stock returns in order to control for the effect of foreign stock markets on the domestic stock-currency relationship.

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Another contribution of the paper is to provide a relatively large set of assessment for the complicated dependence structure of international financial markets. Previous work typically examines either the relationship between international stock markets or the relationship between domestic stock and currency markets with a dataset of less than 10 countries. This study, on the other hand, reveals both of the relationships for 21 economies. The knowledge obtained here would be useful to international investors and policymakers. The remainder of the paper proceeds as follows. In Section 2 we introduce a vine copula approach. In Section 3 we describe the data, report the results, and discuss the implications of the results. Section 4 concludes.

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2

Empirical methodology

2.1

Vine copula

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Consider a vector of three random variables X = (X1 , X2 , X3 ) with a joint distribution F (x1 , x2 , x3 ) and respective marginal distributions F1 (x1 ), F2 (x2 ), and F3 (x3 ), where x =

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(x1 , x2 , x3 ) is a vector of realizations. In our application, X1 , X2 , and X3 denote the US stock returns and a local country’s stock and currency returns, respectively. According to

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Sklar’s theorem, the joint distribution can be expressed as

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F (x1 , x2 , x3 ) = C (F1 (x1 ), F2 (x2 ), F3 (x3 )) ,

(1)



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where C : [0, 1]3 → [0, 1] is a copula function.2 The copula can also be written as 

C(u1 , u2 , u3 ) = F F1−1 (u1 ), F2−1 (u2 ), F3−1 (u3 ) ,

(2)

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where Fi−1 (ui ) (i = 1, 2, 3) are inverse distribution functions of the margins. Thus the copula

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function can be considered a joint distribution function of U1 = F1 (X1 ), U2 = F2 (X2 ), and U3 = F1 (X3 ), that is, C(u1 , u2 , u3 ) = Pr(U1 ≤ u1 , U2 ≤ u2 , U3 ≤ u3 ), where Ui (i = 1, 2, 3)

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are shown to follow a standard uniform distribution, Ui ∼ U (0, 1), from probability integral transformation.

The probability density function of X is obtained by taking the third-order cross-partial derivative of Eq.(1):

f (x1 , x2 , x3 ) = f1 (x1 ) · f2 (x2 ) · f3 (x3 ) · c (F1 (x1 ), F2 (x2 ), F3 (x3 )) ,

2

(3)

See Joe (1997, 2015) and Nelsen (2006) for a comprehensive exposition of copulas.

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where c denotes a copula density function: ∂ 3 C(u1 , u2 , u3 ) ∂ 3 C (F1 (x1 ), F2 (x2 ), F3 (x3 )) = . ∂F1 (x1 )∂F2 (x2 )∂F3 (x3 ) ∂u1 ∂u2 ∂u3

(4)

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c (F1 (x1 ), F2 (x2 ), F3 (x3 )) =

From Eqs.(3) and (4), we can see that the copula describes the dependence structure between variables, being completely separate from their marginal distributions.

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A difficult problem in treating multivariate copulas is that while the list of bivariate

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copulas is long and varied, the set of higher-dimensional copulas is very limited. To overcome this problem, a vine copula approach is proposed by Joe (1996) and further investigated by, among others, Bedford and Cooke (2001, 2002), Kurowicka and Cooke (2006), and Aas et al.

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(2009). This approach decomposes a multivariate joint density into respective margins and a set of bivariate copulas, thus enabling us to construct many different forms of multivariate

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distributions.3

More specifically, in the case of our three-dimensional system, a vine representation of

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Eq.(3) is

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f (x1 , x2 , x3 ) = f1 (x1 ) · f2 (x2 ) · f3 (x3 )

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·c12 (F1 (x1 ), F2 (x2 )) · c13 (F1 (x1 ), F3 (x3 )) 



·c23|1 F2|1 (x2 |x1 ), F3|1 (x3 |x1 ) ,

(5)

where cij is a bivariate copula density for the pair of transformed variables Fi (xi ) and Fj (xj ), and c23|1 is a conditional copula density with two arguments defined by Fi|j (xi |xj ) =

∂Cij (ui , uj ) ∂Cij (Fi (xi ), Fj (xj )) = . ∂Fj (xj ) ∂uj

(6)

In our application, the conditional copula c23|1 is the most important component in Eq.(5) since it characterizes the dependence structure between a local country’s stock returns (X2 ) 3

See Kurowicka and Joe (2011) for an overview and summarizing results of the vine copula approach.

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and currency returns (X3 ), conditional on the values of the US stock returns (X1 ).4 The parameters of marginal models and bivariate copulas are estimated through maximum

i=1 t=1 T 

+ +

t=1 T  t=1

log fi (xit ; θim )

c c12 (F1 (x1t ; θ1m ), F2 (x2t ; θ2m ); θ12 )+

T  t=1

c c13 (F1 (x1t ; θ1m ), F3 (x3t ; θ3m ); θ13 )



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3  T 



c c c c23|1 F2|1 (x2t |x1t ; θ1m , θ2m , θ12 ), F3|1 (x3t |x1t ; θ1m , θ3m , θ13 ); θ23|1 ,

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l(θm , θc ; x) =

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likelihood (ML) estimation. The log-likelihood of Eq.(5) is given by

(7)

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where θm = ((θ1m ) , (θ2m ) , (θ3m ) ) denotes a vector of parameters in three marginal modc ) , (θ c ) , (θ c ) ) a vector of parameters in three bivariate copulas, and x = els, θc = ((θ12 13 23|1

(x1 , ..., xT ) where xt = (x1t , x2t , x3t ) are all observations. Because of computationally dif-

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ficulty in jointly estimating all the parameters by ML, we rely on a sequential estimation procedure that has often been used in the literature applying a vine copula approach to fi-

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nancial data (e.g., Reboredo and Ugolini, 2015a,b). First, we estimate parameters of each

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of marginal models separately. Second, given pseudo-sample observations for copula, u ˆi for i = 1, 2, 3, we estimate parameters of each of unconditional bivariate copulas in the first

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tree of a vine copula structure (corresponding to the second line in Eq.(7)). Finally, given pseudo-sample observations, Fˆ2|1 and Fˆ3|1 , which are obtained by using Eq.(6), we estimate parameters of a conditional bivariate copula in the second tree of the vine copula structure (corresponding to the last line in Eq.(7)).

2.2

Specification of marginal models

We next need to specify both marginal models and bivariate copulas in Eq.(5). In this study, marginal distributions are characterized by an ARMA(p,q)–GJR–GARCH(1,1) model with a 4

Aas et al. (2009) popularize two classes of vines, namely, canonical vines (C-vines) and drawable vines (D-vines), which are more tractable than the general class of vines called regular vines (R-vines). But, in the case of a three-dimensional vine, both C- and D-vines have the same expression, see Aas et al. (2009).

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disturbance term following the normal, Student’s t, or skewed t distribution: p 

βl Xi,t−l +

l=1

q 

γl εi,t−l + εit ,

(8)

l=1

εit = σit ηit ,

(9) (10)

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2 2 = φ0 + φ1 σi,t−1 + φ2 ε2i,t−1 + φ˜2 Di,t−1 ε2i,t−1 , σit

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Xit = α +

for i = 1, 2, 3 and t = 1, ..., T . The ARMA model (8) and the GARCH model (10) represent

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conditional mean and conditional variance of the marginal distribution of Xit , respectively. The so-called GJR term, suggested by Glosten et al. (1993), appears in the last of the right-

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hand side of Eq.(10), where the dummy variable Di,t−l takes the value of 1 if εi,t−l is negative and 0 otherwise. Hence the coefficient on the GJR term quantifies the leverage effect, namely, the effect that a negative shock to financial returns causes higher volatility of the returns in

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the future than a positive shock does. It is assumed that the standardized disturbance ηit in Eq.(9) is a variable that follows an independently and identically distributed (i.i.d.) normal,

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Student’s t, or skewed t distribution. The degrees of freedom parameter ν of the Student’s t

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distribution controls thickness of the tails, which enables us to describe well-known fat tails of financial return data. The skewed t distribution proposed by Hansen (1994) characterizes

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asymmetry by a skewness parameter ζ ∈ (−1, 1) as well as fat tails by a degrees of freedom parameter ν. It reduces to the Student’s t distribution when ζ = 0, to the skewed normal distribution when ν → ∞, and to the normal distribution when ζ = 0 and ν → ∞. The best marginal model for each series is selected according to the Akaike information criterion (AIC).

2.3

Specification of copulas

Our three-variate vine copula model consists of three kinds of bivariate copulas, i.e., C12 , C13 , and C23|1 . As specifications of them, we consider eight different forms of bivariate copula functions: Gaussian, Student’s t, Clayton, Gumbel, BB7, Clayton rotated by 90 degrees,

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Gumbel rotated by 90 degrees, and BB7 rotated by 90 degrees. The second column in Table 1 presents functional forms of the first five copulas, followed by corresponding functions of Kendall’s τ and of the lower and upper tail dependence, which are all defined as a function

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of copula parameter. While Kendall’s τ is a rank correlation measure indicating the overall dependence between two variables of interest, the lower (upper) tail dependence means the

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probability that two variables jointly take extreme negative (positive) values. As the last two columns in Table 1 show, the five copulas have different structures of tail dependence:

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Gaussian copula has no tail dependence; Student’s t copula has the same degree of lower and upper tail dependence; Clayton copula has only lower tail dependence; Gumbel copula

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has only upper tail dependence; and BB7 copula has both upper and lower tail dependence, which are allowed to be different. Whereas Gaussian and Student’s t copulas are able to

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describe both positive and negative dependence between two variables, Clayton, Gumbel, and BB7 copulas only model positive dependence. Therefore, we additionally estimate 90-degree rotated versions of these three copulas to consider negative dependence. As in the selection

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of the best marginal model, we use AIC to choose the best copula model for each of the three

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kinds of bivariate copulas, C12 , C13 , and C23|1 . [Table 1 around here]

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In this study we estimate a static and a dynamic vine copula model, the difference coming from different specifications of the dependence measures. The static vine copula is a model where all of the three bivariate copulas are assumed to have dependence measures that are constant over time. The estimation of each bivariate copula is implemented by first estimating its copula parameter and then by computing dependence measures of the Kendall’s τ and the lower and upper tail dependence using the estimated copula parameter. As described in more detail in the next section, we estimate not only a static vine copula whose parameters (and dependence measures) are constant over the full sample period, but also divide the sample into three sub-periods and estimate a static vine copula for each of the sub-periods. The dynamic vine copula is a model where all of the dependence measures are assumed

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to change over time. Here we follow Patton (2006) and directly specify the evolution of dependence measures as ARMA(1, r)-type process. More specifically, for bivariate copulas of Gaussian and Student’s t, the dynamic model of the Kendall’s τ rank correlation between

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variables i and j is given by 

(11)

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τij,t



r 1 = Λ ω0 + ω1 τij,t−1 + ω2 Φ−1 (ui,t−l ) · Φ−1 (uj,t−l ) , r l=1

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where Λ(x) = (1−e−x )(1+e−x )−1 is the modified logistic transformation, designed to keep τt in (−1, 1) at all times. Φ−1 (x) denotes the inverse of the standard normal distribution function

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and is replaced with the inverse of the standard Student’s t distribution when Student’s t copula is estimated.

Clayton and Gumbel copulas can only describe positive dependence between variables,

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and hence a different evolution equation of the Kendall’s τ is considered: 

(12)

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τij,t



r  ˜ ω0 + ω1 τij,t−1 + ω2 1 =Λ |ui,t−l − uj,t−l | , r l=1

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the space of τt to (0, 1).

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˜ where Λ(x) = (1 + e−x )−1 is the logistic transformation, employed instead of Λ(x) to restrict

The Kendall’s τ of BB7 is a function of two copula parameters (see notes in Table 1), which makes it impossible to estimate the same dynamic equation as Eq.(12). Thus we first estimate two evolution equations for the lower and upper tail dependence of BB7, defined as 

λL ij,t

L1 ˜ ω L + ω L λL =Λ 0 1 ij,t−1 + ω2 r



λU ij,t

U1 ˜ ω U + ω U λU =Λ 0 1 ij,t−1 + ω2 r

r  l=1 r 



|ui,t−l − uj,t−l | , 

|ui,t−l − uj,t−l | ,

(13)

l=1

U where λL ij,t and λij,t denote the lower and upper tail dependence, respectively, between vari-

ables i and j. After that, time-varying estimates for the two copula parameters of BB7 are

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computed using estimates for the lower and upper tail dependence obtained above. Lastly, time-varying estimates for the Kendall’s τ are calculated from these copula parameter esti-

Data and results

3.1

Data

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3

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mates.

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We analyze dependence structures between stock and currency markets by applying a vine copula approach to the following 21 developed and emerging economies: Australia, Brazil,

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Chile, Colombia, the Czech Republic, the Euro area, Hungary, India, Indonesia, Japan, Korea, New Zealand, Norway, the Philippines, Poland, South Africa, Sweden, Switzerland, Taiwan, Turkey, and the UK.5 For each economy, our data set consists of three variables, namely, stock

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and currency returns of the economy and the US stock return. We use weekly data of the MSCI stock market indices and the WM/Reuters exchange rates, both sourced from Datastream.

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The stock market indices are expressed in their own local currencies. Each of the exchange

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rates is expressed as the amount of units of the US dollar per local currency, implying that increase in the exchange rate means appreciation in the local economy’s currency. The use

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of weekly frequency data is appropriate for our analysis, since it avoids the problem arising from time zone differences between the US and each of local economies as well as the problem related to drifts and noises that would be present in daily or high-frequency data. We calculate time series of the three returns, that is, the US stock returns (X1t ), a local economy’s stock returns (X2t ), and its currency returns (X3t ), as 100 times the log-difference of respective variables in level.

Our full sample period spans from May 2, 2003 to September 29, 2017. The start of the 5

Our data set initially includes Canada, Mexico, and Thailand. However, all of the estimated marginal models for currency returns of Canada and Thailand fail to pass the specification tests introduced in the next subsection. For the data of Mexico, some coefficients of a dynamic vine copula model are estimated to be very small with p-values near one. For these reasons, we exclude the three countries from our data set. Our study also excludes other large- and medium-scale economies because their exchange rate systems are not a floating one during a part or the whole of our sample period.

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sample is chosen so as not to include relatively volatile periods of the early 2000s in which the crash of the dot-com bubble and the 9/11 attacks occurred in the US. By so doing, periods of high volatility in the US stock market mostly correspond to the episodes of the global financial

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crisis and the subsequent European debt crisis occurring around 2007 to 2012, which makes easier the interpretation of our empirical results.

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Table 2 presents descriptive statistics of the return data used in this study. Stock returns in all economies have positive means but negative skewness (except for South Africa), a

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negative skewness meaning a long tail in the negative direction. Further, standard deviations of the stock returns are larger than those of currency returns, showing higher risk in the stock

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markets. Skewness, kurtosis, and Jarque–Bera test statistics imply that the use of normal distribution might not be appropriate for modeling conditional marginal distributions of both

addition to the normal distribution.

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stock and currency returns, supporting the use of Student’s t and skewed t distributions in

Results for marginal models

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3.2

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[Table 2 around here]

We first estimate several variants of the marginal models for each of our return series data and

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select its best marginal model. More specifically, the following procedure is taken to select the best marginal model. First, we estimate several ARMA(p,q)–GJR–GARCH(1,1) models (8)–(10) which have different specifications in conditional mean, conditional variance, and error distribution. Here we consider four conditional mean models (ARMA(0,0), ARMA(1,0), ARMA(0,1), and ARMA(1,1)); two conditional variance models (GARCH(1,1) models with and without a GJR term); and three distributions for the standardized disturbance (standard normal, Student’s t, and skewed t distributions). As a result, we estimate 24 marginal models in total for each of our return series data. Second, a candidate for the best marginal model is chosen according to AIC. Third, we implement four diagnostic tests for that candidate: the Ljung–Box serial correlation test applied to standardized residuals ηˆit , the same test applied

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2 (setting the lag length of the two tests equal to 12 to squared standardized residuals ηˆit

weeks), and the Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests applied to the probability integral transforms of standardized residuals u ˆit . If the candidate model is well

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2 would exhibit no serial correlation and u ˆit would be generated from an specified, ηˆit and ηˆit

i.i.d. uniform (0, 1) distribution. Thus, if it passes all of the four tests at the 5% significance

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level, we regard it as the best marginal model that is correctly specified. If it fails any of the four tests, we return to and repeat the second and third steps until obtaining the best

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marginal model.

Tables 3 and 4 report results on the best marginal models for stock returns (including the

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US stock return) and currency returns, respectively.6 All of the return data except for the Swedish currency return are specified by either the Student’s t or the skewed t distribution.

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The estimate of the degrees of freedom parameter is statistically significant in most of the return series, confirming fat tail features of stock and currency returns. The skewness parameter of the skewed t distribution is estimated to be negative and statistically significant in

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almost all of the return series, which means that while the mode of the conditional probability

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density is positive, the probability of taking negative returns is larger than the probability of taking positive returns. The coefficient on the GJR term is significantly positive only for

Ac ce p

six stock and two currency returns, suggesting that the leverage effect is present in a limited number of economies, especially for currency returns. Finally, from p-values of four diagnostic tests reported in the last four columns, we confirm that all the marginal models are correctly specified, although this is obvious from our procedure of selecting the best marginal model. [Tables 3 & 4 around here]

3.3

Results for static vine copulas with and without structural changes

We next estimate three-variate vine copula models by which the dependence structure among the US stock returns and a local economy’s stock and currency returns is characterized. 6 To save space, we do not report the estimates of ARMA and GARCH coefficients, which are likely to be less informative. These results are available from the authors upon request.

13

Page 16 of 54

The vine copula considered in this subsection is a static one with and without structural changes. That is, it is not only a vine copula whose parameters are assumed to be constant over the whole sample period, but also a vine copula which allows for structural changes in

ip t

the parameters. The latter model is useful because dependence structure among the three variables might vary in times of financial turbulence due to stronger co-movement among

cr

international stock markets. More precisely, it is expected that the US stock market is more closely connected with both stock and currency markets in a local economy during a financially

us

stressful period, which would increase estimation bias for the country-specific relationship between domestic stock and currency returns.

an

We allow for such structural breaks by dividing our full sample period into three subsamples: the pre-crisis period (May 2003 to July 2007), the crisis period (August 2007 to

M

December 2012), and the post-crisis period (January 2013 to September 2017). Here the crisis period contains episodes of the global financial crisis and the subsequent European debt crisis, with the start of the period, August 2007, corresponding to BNP Paribas’s announcement

d

regarding the US securitization market. We select December 2012 as the end of the crisis

te

period according to the movement of the US stock market volatility. Fig.1 plots a time series of the US stock market volatility, computed from the marginal model of the US stock returns

Ac ce p

estimated in the previous subsection. It is found that large fluctuations in the US stock returns, beginning from the middle of 2007 and reaching a peak in October 2008, cease at the end of 2012. Therefore, December 2012 seems to be appropriate for the end of the crisis period. It is also seen from Fig.1 that the US stock market is relatively stable in the pre- and post-crisis periods except around 2016. [Figure 1 around here]

In what follows, we first present results from the first tree of a three-variate vine copula model. This is composed of two kinds of relationships: one is the relationship between the US stock returns and a local economy’s stock returns and the other is the relationship between the US stock returns and a local economy’s currency returns. Then we provide results from

14

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the second tree of a vine copula model where domestic stock and currency markets in a local economy are connected conditional on the US stock returns. Dependence structures between US and local economies’ markets

ip t

3.3.1

Table 5 reports results for the pairs of the US stock returns and each of local economies’ stock

cr

returns (one component of the first tree in the three-variate vine copula model). Column (1) shows estimation results of the bivariate copulas whose parameters are assumed to be

us

constant over the whole sample period, while Columns (2) to (4) present the results for three sub-sample periods, namely, the pre-crisis period, the crisis period, and the post-crisis period,

an

respectively. The contents reported in each economy–period part of the table include the name of a selected best copula; the estimate of copula parameter7 ; the estimate of Kendall’s

M

τ rank correlation computed from the estimated copula parameter8 ; and the estimates of the lower and upper tail dependence which are also obtained by using the estimated copula parameter.9 The bottom rows of the table show average values of the Kendall’s τ and the

d

lower and upper tail dependence across all of the 21 economies.

te

[Table 5 around here]

The estimates of Kendall’s τ reported in Column (1) indicate strong evidence on the co-

Ac ce p

movement of international stock markets over the full sample period. They are all positive and statistically significant at the 1% level, ranging from 0.198 for the US–New Zealand pair to 0.563 for the US–Euro area pair. Furthermore, the results from a sub-sample analysis given in Columns (2) to (4) show that the interdependence between two stock markets is higher in the crisis period than in the pre- and post-crisis periods for all of the economies except for Japan and Switzerland. This implies the presence of contagion effects between international stock markets during episodes of the global financial crisis and the subsequent European debt 7 Estimated parameters reported in “Parameter” are ρ for Gaussian, ρ and ν (reported in this order) for Student’s t, δ for Clayton and Gumbel, and δ and θ (reported in this order) for BB7. 8 The delta method is used to compute standard errors for Kendall’s τ and tail dependence. 9 The first row in “Tail” indicates the estimate of the lower tail dependence and the second row the upper tail dependence.

15

Page 18 of 54

crisis.10 Surprisingly, however, such evidence cannot be seen from the estimates of the lower tail dependence as only seven economies exhibit the highest estimate in the crisis period. This means that interdependence between stock markets was intensified during the crisis period

ip t

regardless of the level of stock returns, which is represented by a higher value of the overall association measure of Kendall’s τ rather than by the lower tail dependence.

cr

[Table 6 around here]

Table 6 presents results for the pairs of the US stock returns and each of local economies’

us

currency returns (the other component of the first tree in the three-variate vine copula model). Note first that all of the estimates of Kendall’s τ reported in Column (1), which are assumed

an

to be constant over the whole sample period, are positive and statistically significant at the 1% level, except for Japan and Switzerland. This implies that the values of almost all of the local

M

currencies are positively connected with each other. Moreover, combining this evidence with that from Table 5 above suggests that stock returns of many economies which are denominated in dollars, that is, the sum of stock returns expressed in local currency (X2 ) and the currency

d

returns (X3 ), are highly positively correlated with each other.

te

The sub-sample results reported in Columns (2) to (4) show that the interdependence among currency values of the local economies has strengthened particularly during the crisis

Ac ce p

period. All of the Kendall’s τ estimates in the crisis period are positive and statistically significant other than Japan and Switzerland, and they are greater than those in other two periods except for Brazil. Again, combined with the result from Table 5 above, it means that interdependence among international stock markets (in terms of stock returns expressed in dollars) became stronger during the crisis period, compared with that during other two tranquil periods.

As already noted, however, the Japanese yen and the Swiss franc have an exceptional relationship with the US stock market. Fatum and Yamamoto (2016), Hossfeld and MacDonald (2015), Ranaldo and S¨oderlind (2010), and Tachibana (2018) show that international 10

See articles cited in the Introduction for evidence on contagion effects during the global financial crisis.

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investors have regarded either or both of the two currencies as safe-haven and/or hedge currency.11 In particular, Tachibana (2018) allows for different patterns of safe-haven and hedge behavior across three major stock markets (US, UK, and Euro area stock markets) and find

ip t

that the Japanese yen has become the most important currency both as a safe-haven and as a hedge for the US stock market since the 2007 global financial crisis. The same evidence is

cr

obtained in this study: A finding that the Kendall’s τ correlation between the US stock and Japanese yen returns is significantly negative in last two sub-periods means that the Japanese

us

yen has served as a hedge currency for the US stock market. Furthermore, the 90-degree rotated Gumbel is selected as the best copula for the two sub-periods, supporting evidence

an

that the Japanese yen has been a safe-haven currency for the US stock market, since that copula implies that higher probability is assigned to the region of large negative returns on

M

the US stock market and large positive returns on the Japanese yen. The Swiss franc, on the other hand, qualifies merely as a hedge currency for the US stock market in the post-crisis period, because the Kendall’s τ correlation between the US stock and Swiss franc returns is

d

significantly negative in that period, but because Gaussian copula, which has no tail depen-

te

dence, is selected as the best copula. This finding on the Swiss franc is again the same as

Ac ce p

that shown in Tachibana (2018). 3.3.2

Dependence structures between domestic stock and currency markets con-

ditional on the US stock returns

Here we report results regarding the main subject of our analysis: the dependence structure between domestic stock and currency markets conditional on the US stock returns (which corresponds to the second tree of the three-variate vine copula model). Table 7 presents the estimates of copula parameters in this stage of the vine copula construction as well as the implied estimates of the Kendall’s τ and the lower and upper tail dependence. The latter three measures indicate the conditional dependence between domestic stock and currency returns 11 A safe-haven currency is defined as one that appreciates in times of market stress or turmoil, while a hedge currency is defined as one that is negatively correlated with an asset in normal times.

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given the values of the US stock return, and therefore their estimates are of our main interest in this study. [Table 7 around here]

ip t

First, it is found that positive relationship between stock and currency markets is concentrated in emerging economies. The estimate of Kendall’s τ is positive and statistically

cr

significant for the full sample and three sub-sample periods in Brazil, Colombia, Hungary, India, Indonesia, Korea, the Philippines, Poland, Taiwan, and Turkey. The positive relation

us

is predictable from both the portfolio-balance model and the international-trading model for an import-dominant country. The latter model, however, seems to contradict the data on

an

trade balance given in Table 8.12 Among the above-mentioned economies, Brazil, Hungary, Indonesia, and Korea are trade-surplus countries, which would have negative relationships

M

between stock and currency returns if such export-dominant countries were affected by the international-trading effect. The portfolio-balance model, on the other hand, only predicts positive correlations regardless of international trade structure. Hence we can state that the

d

portfolio-balance model is a more plausible theory than the international-trading model to

te

explain positive correlations in the emerging economies. The finding on the dominance of the portfolio-balance effect in emerging economies is consistent with the results of previous

Ac ce p

studies (Chkili and Nguyen, 2014; Diamandis and Drakos, 2011; Kubo, 2012; Lee et al., 2011; Phylaktis and Ravazzolo, 2005; Reboredo et al. 2016; Tsai, 2012; and Yang et al., 2014). [Table 8 around here]

Second, in contrast to the result above, advanced economies tend to have negative correlations between stock and currency returns. In the Euro area, Japan, Sweden, Switzerland, and the UK, the estimate of Kendall’s τ is negative and statistically significant for the full sample period and at least two sub-sample periods. This suggests that international-trading effect surpasses portfolio-balance effect in these five advanced economies, confirming the results of Alagidede et al. (2010), Inci and Lee (2014), Kollias et al. (2012), and Tsagkanos 12 The source of the data is World Development Indicators, the World Bank. Taiwan is excluded from the table due to unavailability of the data.

18

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and Siriopoulos (2013), all of which find international-trading effect in developed economies. One caveat of our result is that among these five developed economies, the UK is a net import country as seen from Table 8. This might imply that at least for advanced economies,

ip t

international-trading model always predicts a negative relationship regardless of trade surplus or deficit.

cr

Even in the advanced economies, however, there are cases where international-trading effect is overtaken by portfolio-balance effect: the sign of Kendall’s τ turns to be positive in the

us

Euro area, Sweden, and the UK during the crisis period. This corroborates the finding of Kollias et al. (2012) and Tsagkanos and Siriopoulos (2013) that portfolio-balance effect emerged

an

in the European Union during the recent crisis period (2008 in Kollias et al. (2012) and 2008–2012 in Tsagkanos and Siriopoulos (2013)) whereas international-trading effect mainly

M

worked during normal times.

[Table 9 around here] We next compare the dependence structure estimated by a vine copula with that estimated

d

by a non-vine bivariate copula. The latter model uses only two variables of domestic stock and

te

currency returns, meaning that it does not control for the effect of international stock market co-movement on these two markets. Table 9 presents estimation results for this non-vine

Ac ce p

copula model. As will be discussed in detail later, the Kendall’s τ rank correlation between the two variables increases in almost all of the economies and periods, compared with that from a vine copula. As a result, each of the two groups, one having positive values of Kendall’s τ and the other having negative values, has different members from those found by a vine copula. Australia and Chile additionally enter the group of having positive relationship. On the other hand, the Euro area, Sweden, and the UK are no longer a member of the group of having negative relationship as their estimates of Kendall’s τ are not a significantly negative one for the full sample period. Hence, controlling for the effect of international stock market co-movement with a vine copula is crucial to these economies. [Tables 10 & 11 around here]

19

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To look more closely at the differences of dependence measures between a vine and a non-vine copula, Table 10 summarizes them for every dependence measure and period, with average values across economies being shown in the bottom row.13 In addition, to see how

ip t

statistically large the difference is, Table 11 provides 90-percent confidence intervals for the dependence measures from a vine copula (presented in the first row) and from a non-vine

cr

copula (presented in the second row).14 The set of two confidence intervals in bold means that they do not overlap each other.

us

First, controlling for the impact of the US stock market with a vine copula reduces the Kendall’s τ rank correlation between domestic stock and currency returns. As seen from

an

the first column of Table 10, the difference of the Kendall’s τ between a vine and a nonvine copula is negative in all of the economies except for Japan over the full sample period. Moreover, as noted from the first column of Table 11, two confidence intervals for the Kendall’s

M

τ do not overlap each other in 11 economies. The evidence suggests that researchers would be confronted with an issue of having an upward bias in the estimate for the relationship between

d

domestic stock and currency returns if they ignore the co-movement of international stock

te

markets. However, note also that the bias is not of great magnitude: the average difference of Kendall’s τ across economies is -0.071 with a minimum of -0.026 in the Philippines and a

Ac ce p

maximum of -0.149 in the UK. This implies that the bias might have a limited influence on the estimate for the relationship between the two markets. Second, the differences of Kendall’s τ are more remarkable for the crisis period relative to other two sub-periods. Table 10 shows that there are 16 economies in which the difference of Kendall’s τ is the largest in the crisis period. Furthermore, Table 11 shows that there are 13 economies where two confidence intervals for the Kendall’s τ do not overlap each other during the crisis period, which is the much larger number compared with only three economies in the pre-crisis period and no economy in the post-crisis period. This result is attributable to the 13

Blanks for tail dependence in the table mean that both a vine and a non-vine copula show no tail dependence between domestic stock and currency returns. 14 Confidence intervals for tail dependence are restricted to [0, 1]. When there is no tail dependence, its confidence interval is denoted as [0] in the table.

20

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fact that a non-vine copula model ignores higher correlations between the US stock returns and each of local economies’ stock and currency returns during the crisis period, which has already been shown in Tables 5 and 6.

ip t

Third, it is not clear whether the lower and upper tail dependence differ between a vine and a non-vine copula. Table 10 shows evidence that as with Kendall’s τ , both measures of

cr

tail dependence from a vine copula are generally smaller than those from a non-vine copula. However, it is noted from Table 11 that two confidence intervals for the tail dependence do

us

not overlap each other only in a few economies, which is a different finding from Kendall’s τ correlation. Therefore, controlling for the effect of the US stock market on the domestic

Results for dynamic vine copulas

M

3.4

an

stock-currency relationship is likely to be less important for the tail dependence.

We now turn to an alternative specification of the three-variate vine copula in which dependence measures are allowed to change over time. Specifically, their dynamics are modeled

te

being set to 12 weeks.15

d

by Eqs.(11)–(13), choices among them depending on copula functions, with the lag order, r,

[Table 12 around here]

Ac ce p

Table 12 presents all of the estimated coefficients in the dynamic equations. The first to third columns report the estimates for the vine copula, while the last column provides the results from the non-vine copula. Note that only less than half of the coefficients are estimated to be statistically significant. This suggests that the ARMA-type specifications (11)–(13) might not be appropriate to characterize the dynamic dependence between three variables under consideration. However, the purpose here is to confirm robustness of main results found in the previous subsection by extending a static vine copula to a dynamic one. For this reason, we proceed with the robustness analysis here without determining whether the dynamic specification is appropriate or not, or whether it is more suitable than the static 15

We attempted alternative orders (r = 1, 4, 8) as well, but results did not essentially change.

21

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model or not. Before that, main findings in the previous subsection are summarized below. (i) Local economies’ stock returns are positively correlated with the US stock returns. In

ip t

particular, it is intensified during the crisis period.

In particular, it is intensified during the crisis period.

cr

(ii) Local economies’ currency returns are positively correlated with the US stock returns.

us

(iii) As a result of (i) and (ii), Kendall’s τ correlations between domestic stock and currency returns conditional on the US stock returns become smaller compared with those from

an

non-vine copulas (but the decreases are not remarkable in size). In particular, the differences are relatively large in the crisis period.

M

(iv) The Kendall’s τ correlation between domestic stock and currency returns conditional on the US stock returns tends to be positive in emerging economies, whereas it tends

d

to be negative in developed economies.

te

[Figures 2 & 3 around here]

We first establish robustness of (i) and (ii). Fig.2 plots the estimated evolution of the

Ac ce p

Kendall’s τ correlations between the US and local economies’ stock returns.16 It shows that the two stock returns are highly correlated with each other over time for all of the US-local economy pairs, supporting evidence described in the first sentence of (i). Fig.3 displays the estimated evolution of the Kendall’s τ correlations between the US stock and local economies’ currency returns. Although the correlations are generally lower than those in Fig.2, they are positive over the whole period or most of the period in many economies. Exceptional 16

The estimated dynamics of the lower and upper tail dependence are not reported here, since estimation results regarding the static tail dependence presented in the previous subsection are not important enough to test the robustness. In addition, even when examining the robustness using the tests introduced below (not reported), the dynamic tail dependence estimated from dynamic vine copulas is shown to be as important as the Kendall’s τ , which means no robust evidence between a static and a dynamic vine copula in terms of the tail dependence. This test result and the figures of the dynamic tail dependence are available from the authors upon request.

22

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economies are the Czech Republic, the Euro area, Japan, and Switzerland, in which the correlation takes a negative value many times and particularly for Japan it has been negative since 2007. These results associated with the relationship between the US stock and local

Table 6 and thus support evidence in the first sentence of (ii).

ip t

economies’ currency returns are consistent with those from static vine copulas reported in

us

in volatile times, we estimate the following equation by OLS:

cr

To test for the second sentences of (i) and (ii), that is, the existence of stronger correlation

σ1t − σ ¯ 1 ) + ξt , τˆ1i,t = c + b(ˆ

(14)

an

where τˆ1i,t denotes the estimated time-varying Kendall’s τ between the US stock returns and a local economy’s stock returns (when i = 2) or between the US stock returns and a local

M

economy’s currency returns (when i = 3). σ ˆ1t is the estimated time-varying volatility of the US stock market, which is obtained from a marginal model estimation of the US stock returns

d

and displayed in Fig.1. The average value of the volatility, denoted by σ ¯1 , is 2.06 and it is

te

subtracted from σ ˆ1t to make the constant term of Eq.(14) interpreted as the level of Kendall’s τ when the US stock market is in an average situation. The most focus is on the coefficient

Ac ce p

b because b > 0 means that Kendall’s τ correlation becomes larger as the US stock market is more volatile, which is consistent with the evidence described in the second sentences of (i) and (ii).

[Table 13 around here]

The results are reported in Table 13. The left two columns show the results for the relationships between the US and local economies’ stock returns, while the middle two columns correspond to the relationships between the US stock and local economies’ currency returns. The last row reports the results estimated by pooling data across economies. The estimates of the coefficient b are all positive and statistically significant except for Japan of the fourth column, implying that when the US stock market is volatile, the two kinds of relationships

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strengthen, which confirms robustness of the second sentences of (i) and (ii). Only the estimate for Japan of the fourth column is significantly negative, but this is consistent with the result of Table 6 and represents a characteristic of safe-haven currency.

ip t

[Figure 4 around here] We next establish robustness of (iii). Fig.4 plots the movements of the Kendall’s τ cor-

cr

relations between stock and currency returns in local economies. The blue and the red lines represent the dynamic correlation estimated from a vine and a non-vine copula, respectively.

us

The figure shows that the former correlation is generally lower than the latter, implying the existence of upward bias when the co-movement of international stock markets is ignored. To

an

quantify the difference between the two lines and to see if it becomes wider when the US stock market is more volatile, Eq.(14) is modified as follows:

M

σ1t − σ ¯ 1 ) + ξt , τˆ23,t − τˆ˜23,t = c + b(ˆ

(15)

d

where τˆ23,t denotes the time-varing Kendall’s τ between domestic stock and currency returns

te

estimated from a vine copula, and τˆ˜23,t is the corresponding estimate from a non-vine copula. The last two columns in Table 13 show the estimation results. The constant term is negative

Ac ce p

and statistically significant in all of the economies except for Japan, suggesting that one would be confronted with an issue of having an upward bias for the evaluation of the relationship between the two markets if ignoring the co-movement of international stock markets. The coefficient b is also estimated to be negative and statistically significant in all economies other than Japan, which indicates that the upward bias is more serious when the US stock market is unstable. These results on both constant and coefficient terms, therefore, suggest robustness of the evidence stated in (iii). However, it should be noted that the bias is not very large in size even with a dynamic vine copula specification. As the bottom row of the table shows, the bias is 0.078 on average across economies and increases by 0.018 as the volatility of the US stock market increases by one percentage point.

24

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Finally, we examine robustness of the evidence described in (iv). Turning back to Fig.4, time-varying Kendall’s τ correlations (plotted as blue lines) are positive over the whole period in Australia, Brazil, Colombia, Hungary, India, Indonesia, Korea, the Philippines, Poland,

ip t

Taiwan, and Turkey. On the other hand, Japan, Switzerland, and the UK exhibit negative correlation throughout the period, and the Euro area shows negative correlation during the

cr

pre- and post-crisis periods defined in the previous subsection. Hence, we can find the similar

3.5

us

evidence to the one stated in (iv), even when estimating dynamic vine copulas.

Implications of the results

an

The results of this study have important implications in the following three directions. First, empirical evidence in previous related studies might change if the co-movement of international

M

stock markets is considered. More specifically, one would find a downward estimate for the relationship between domestic stock prices and currency values if controlling for the effect of international stock market co-movement on the two markets. However, given the evidence in

d

this paper that most of the estimates for the bias are not very large (about 0.07 reduction

te

in Kendall’s τ on average across economies for the full sample period), the influence on the results of previous studies might be limited to some economies or a particular period in which

Ac ce p

the bias is found to be relatively large. To verify whether the bias is significant or not, more studies need to be done by using the same empirical models as previous work used, with a consideration of international stock market co-movement. Second, our results would be useful to international investors. The analysis in this paper disentangled the complex dependence structure between the US stock market and domestic stock and currency markets for a relatively large set of economies. Thus the information on the dependence structure would help international investors diversify their assets and reduce the risks by investing in weakly or negatively correlated markets. It would be also helpful for international investors to predict market returns in response to certain kinds of shocks. The results of this paper imply that a positive (negative) common shock to global stock markets

25

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would induce increases (decreases) in both stock prices and currency values around the world except for a few assets (the Japanese yen, the US dollar, and possibly the Swiss franc), while a country-specific shock could move domestic stock prices and currency values in the same or

ip t

opposite direction, depending on the economy considered. Third, our results would be also useful to policymakers, especially monetary authorities

cr

who are responsible for stabilizing the domestic macroeconomy and financial markets. As discussed in the previous paragraph, a relatively long list of the dependence structure this

us

study provide facilitates the prediction of market returns when a common global shock or a country-specific shock occurs. Hence monetary authorities can use this information to pursue

an

more optimal policies in response to these shocks. For example, our estimation results imply that a negative shock to global stock markets leads to declines in stock prices and appreciation

M

in currency values for Japanese economy, which justifies aggressive monetary easing in Japan since the policy can potentially succeed in stabilizing both stock prices and currency values. On the other hand, for the economies in which the global negative shock induces falls in both

d

stock prices and currency values, the same degree of monetary easing as Japan would not be

Conclusion

Ac ce p

4

te

supported because it might accelerate the depreciation of currency.

Ignoring the co-movement of international stock markets might lead to a biased estimate for the relationship between domestic stock and currency markets. To take into account the possible effect of the international stock market co-movement, this paper uses the US stock returns as a proxy for the movement of foreign stock markets and applies a vine copula approach to 21 economies over the period 2003–2017. The vine copula model employed here consists of three variables, namely the US stock returns and a local economy’s stock and currency returns. We first estimate static vine copulas for the full sample period and three sub-sample periods. The latter sub-sample analysis is conducted in order to consider

26

Page 29 of 54

the possibility that the bias might become larger in times of financial turbulence. Then, to confirm robustness of the results from static vine copulas, we estimate dynamic vine copulas in which all of the dependence measures are allowed to change over time.

ip t

We find several interesting results. First, each of local economies’ stock returns is highly correlated with the US stock returns, indicating the co-movement of international stock mar-

cr

kets. In particular, it is shown that the interdependence is intensified in volatile times. Second, each of local economies’ currency returns is positively correlated with the US stock returns

us

as well, and the relationship becomes stronger when the US stock market is highly volatile. Combining the first finding with the second suggests that the co-movement of international

an

stock markets would be very remarkable if stock returns are all expressed in US dollar. Third, taking no account of the international stock market co-movement leads to an upward bias in

M

the estimated correlation between domestic stock and currency returns, although most of the estimates for the bias are not very large in size. We also find evidence that the upward bias increases during times of financial turmoil. Finally, the resulting estimates for the correla-

d

tion between domestic stock and currency returns conditional on the US stock returns show

te

that the correlation tends to be positive in emerging economies, which is consistent with the portfolio-balance model, whereas it tends to be negative in developed economies, which is

Ac ce p

explained by the international-trading model. One of the implications of our results is that if previous studies had considered the comovement of international stock markets, they would have found lower estimates for the relationship between domestic stock and currency markets than they actually found. However, it is not clear whether the influence is significant or not, since our estimates for the bias seem to be small for most of the economies. To explore this point, in future research we need to adopt the same empirical models as previous work used, with a consideration of international stock market co-movement. Our results also have important implications for international investors and monetary authorities. The paper provides a relatively large list of the complex dependence structure between international financial markets. Thus this information would be

27

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useful for international investors to diversify their portfolios appropriately and for monetary

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ip t

authorities to conduct more optimal policies.

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cr

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us

[2] Alagidede, P., Panagiotidis, T., & Zhang, X. (2010). Causal Relationship between Stock Prices and Exchange Rates. Journal of International Trade and Economic Development, 20, 67–86.

an

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M

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d

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te

Rates: A Review Article. Journal of Economic Studies, 42, 707–732. [6] Bedford, T., & Cooke R.M. (2001). Probability Density Decomposition for Conditionally Depen-

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dent Random Variables Modeled by Vines. Annals of Mathematics and Artificial Intelligence, 32, 245–268.

[7] Bedford, T., & Cooke R.M. (2002). Vines–A New Graphical Model for Dependent Random Variables The Annals of Statistics, 30, 1031–1068. [8] Bekiros, S.D. (2014). Contagion, Decoupling and the Spillover Effects of the US Financial Crisis: Evidence from the BRIC Markets. International Review of Financial Analysis, 33, 58–69. [9] Branson, W.H. (1983). Macroeconomic Determinants of Real Exchange Rate Risk. In: Herring, R.J. (Ed.), Managing Foreign Exchange Rate Risk. Cambridge University Press.

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[10] Chkili, W. & Nguyen, D.K. (2014). Exchange Rate Movements and Stock Market Returns in a Regime-Switching Environment: Evidence for BRICS Countries. Research in International Business and Finance, 31, 46–56.

ip t

[11] Diamandis, P.F., & Drakos, A.A. (2011). Financial Liberalization, Exchange Rates and Stock Prices: Exogenous Shocks in Four Latin America Countries. Journal of Policy Modeling, 33,

cr

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us

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[56] Yang, Z., Tu, A.H., & Zeng, Y. (2014). Dynamic Linkages between Asian Stock Prices and

Ac ce p

te

d

M

an

us

cr

ip t

Exchange Rates: New Evidence from Causality in Quantiles. Applied Economics, 46, 1184–1201.

33

Page 36 of 54

i cr us an M

ed

Table 1: Bivariate copulas constituting vine copula models Copula CDF

Gaussian Student’s t Clayton

CN (u1 , u2 ; ρ) = Φ2 Φ−1 (u1 ), Φ−1 (u2 ); ρ
CT (u1 , u2 ; ρ, ν) = T2,ν Tν−1 (u1 ), Tν−1 (u2 ); ρ −δ −1/δ CC (u1 , u2 ; δ) = (u−δ 1 + u2 − 1)

BB7




h

CG (u1 , u2 ; δ) = exp − (− log u1 )δ + (− log u2 )δ

ce

Gumbel

pt

Name



h

i1/δ 

CBB7 (u1 , u2 ; δ, θ) = 1 − 1 − (1 − (1 − u1 )θ )−δ + (1 − (1 − u2 )θ )−δ − 1

i−1/δ

Kendall’s τ

Lower tail

2π −1 arcsin(ρ) 2π −1 arcsin(ρ) δ/(δ + 2)

0

0 See notes below 2−1/δ 0

(δ − 1)/δ

0

2 − 21/δ

See notes below

2−1/δ

2 − 21/θ

1/θ

Upper tail

Ac

Notes: The second column in the table presents cumulative distribution functions (CDFs) of the bivariate copulas used to construct vine copula models. Φ and Φ2 (Tν and T2,ν ) denote the CDFs of the standard univariate and bivariate normal (Student’s t) distributions, respectively. The third column shows functions to compute Kendall’s τ . The Kendall’s τ of BB7 copula is: τ = 1 − 2δ −1 (2 − θ)−1 + 4δ −1 θ−2 B(δ + 2, 2/θ − 1), where B(·, ·) denotes the beta function. The last two columns present the lower and upper tail dependence of  p each copula. The tail dependence of Student’s t copula is: λL = λU = 2Tν+1 − (ν + 1)(1 − ρ)/(1 + ρ) . In addition to the five bivariate copulas above, we use the 90-degree rotated versions of Clayton, Gumbel, and BB7, which are defined as C90 (u1 , u2 ) = u2 − C(1 − u1 , u2 ).

Page 37 of 54

Table 2: Descriptive statistics Min

SD

Skewness

Kurtosis

JB

11.526 9.733 16.892 16.662 11.474 18.285 10.820 17.746 13.660 13.012 9.642 18.819 7.148 15.341 12.523 16.078 16.264 12.603 12.299 9.448 13.482 12.549

-20.116 -16.490 -21.357 -22.956 -22.037 -27.484 -24.472 -35.012 -19.000 -22.383 -22.318 -21.403 -13.429 -24.610 -19.600 -16.703 -9.695 -22.670 -24.788 -11.478 -28.601 -23.430

2.297 2.208 3.468 2.486 2.983 3.039 2.765 3.745 3.079 3.489 2.869 2.956 1.933 3.223 2.891 3.067 2.581 2.850 2.407 2.682 3.129 2.368

-1.027 -0.900 -0.330 -1.010 -0.822 -1.022 -1.333 -1.335 -0.571 -0.627 -1.020 -0.652 -0.671 -1.216 -0.591 -0.375 0.140 -0.955 -1.872 -0.638 -1.094 -1.382

13.409 8.684 7.254 15.702 10.338 14.937 12.593 15.097 6.791 7.136 8.818 9.528 6.835 11.349 7.571 6.004 6.234 10.131 22.321 4.763 13.065 18.607

3531.75*** 1115.18*** 581.34*** 5190.20*** 1774.15*** 4601.62*** 3110.74*** 4814.71*** 491.76*** 586.08*** 1192.55*** 1390.38*** 518.07*** 2372.69*** 699.22*** 300.69*** 330.70*** 1709.76*** 12152.46*** 148.65*** 3328.84*** 7881.65***

Panel B: Currency returns Australia 0.032 7.040 Brazil -0.006 9.141 Chile 0.014 6.527 Colombia -0.001 9.177 Czech Rep. 0.035 6.193 Euro area 0.009 5.331 Hungary -0.022 7.518 India -0.043 4.706 Indonesia -0.057 8.718 Japan 0.009 8.466 Korea 0.010 9.816 New Zealand 0.036 6.716 Norway -0.015 7.009 Philippines 0.006 2.642 Poland 0.009 7.989 South Africa -0.083 11.337 Sweden 0.002 6.537 Switzerland 0.046 17.329 Taiwan 0.019 2.368 Turkey 0.034 5.448 UK -0.023 5.328

-17.805 -12.579 -11.706 -13.129 -7.586 -5.623 -9.992 -4.489 -8.543 -5.421 -6.988 -11.990 -6.400 -3.770 -12.923 -11.285 -6.557 -12.096 -2.757 -6.340 -8.664

1.867 2.093 1.600 1.758 1.693 1.365 2.082 0.927 1.097 1.449 1.390 1.922 1.690 0.747 2.011 2.379 1.649 1.628 0.588 0.801 1.378

-1.716 -0.829 -0.945 -0.674 -0.444 -0.301 -0.524 -0.228 -0.002 0.370 0.059 -0.888 -0.328 -0.035 -0.933 -0.533 -0.214 1.075 -0.054 -0.341 -0.762

16.455 8.229 9.210 9.224 4.009 4.073 4.856 6.050 17.460 5.076 10.995 6.983 3.769 4.942 7.136 5.343 4.097 23.126 5.144 13.574 7.294

6049.71*** 944.12*** 1321.79*** 1272.51*** 56.69*** 47.51*** 142.52*** 298.41*** 6559.86*** 152.40*** 2006.08*** 596.53*** 32.11*** 118.50*** 645.96*** 207.90*** 43.50*** 12854.18*** 144.65*** 3522.86*** 651.23***

Ac ce p

te

d

cr

us

an

Panel A: Stock returns US 0.139 Australia 0.085 Brazil 0.207 Chile 0.160 Colombia 0.296 Czech Rep. 0.078 Euro area 0.087 Hungary 0.148 India 0.296 Indonesia 0.342 Japan 0.099 Korea 0.197 New Zealand 0.048 Norway 0.157 Philippines 0.248 Poland 0.101 South Africa 0.247 Sweden 0.172 Switzerland 0.098 Taiwan 0.100 Turkey 0.193 UK 0.081

ip t

Max

M

Mean

Notes: Weekly stock and currency returns for the period May 2, 2003 to September 29, 2017. SD denotes the standard deviation. JB is the Jarque–Bera statistics for the test of normality. *** indicates rejection of the null hypothesis of normality at the 1% level.

Page 38 of 54

Table 3: Estimation results for best marginal models of stock returns p

q

GJR

DoF

Skewness

Q(12)

Q2 (12)

KS

AD

US

S

1

1

[0.204]

[0.648]

1

1

[0.492]

[0.969]

[0.357]

[0.604]

Brazil

S

0

0

[0.368]

[0.898]

[0.942]

[0.912]

Chile

S

1

1

[0.682]

[0.936]

Colombia

S

0

0

[0.131]

[0.984]

Czech Rep.

S

0

0

[0.585]

[0.584]

[0.819]

[0.814]

Euro area

S

0

1

-0.421 *** (0.050) -0.325 *** (0.060) -0.213 *** (0.054) -0.146 *** (0.055) -0.097 ** (0.048) -0.179 *** (0.053) -0.367 *** (0.054)

[0.062]

S

[0.911]

[0.988]

[0.633]

[0.853]

Hungary

T

0

0

India

S

0

0

Indonesia

S

1

0

Japan

S

0

1

Korea

S

1

1

New Zealand

S

0

0

Norway

S

0

0

Philippines

S

1

0

Poland

S

0

0

South Africa

S

1

Sweden

S

0

Switzerland

S

0

1

Taiwan

S

0

1

Turkey

T

1

1

UK

S

1

1

12.127 ** (5.308) 10.703 *** (3.979) 11.647 *** (3.531) 10.685 *** (3.408) 3.966 *** (0.638) 5.491 *** (1.014) 10.547 *** (2.788) 6.020 *** (0.870) 15.511 ** (6.478) 4.682 *** (0.913) 11.609 ** (5.140) 10.739 ** (4.584) 15.708 ** (7.913) 5.292 *** (1.169) 6.545 *** (1.343) 8.431 *** (2.193) 24.451 (17.254) 6.843 *** (1.542) 6.220 *** (0.993) 9.531 *** (3.401) 9.274 *** (3.020) 7.106 *** (1.425)

[0.089]

Australia

0.161 * (0.083) 0.132 (0.101) 0.111 (0.079) 0.181 * (0.094)

0

Ac ce p

1

0.137 * (0.082)

-0.314 *** (0.054)

[0.896]

[0.682]

[0.801]

us

cr

[0.840]

[0.386]

[0.999]

[0.396]

[0.477]

[0.623]

[0.741]

[0.796]

[0.773]

[0.355]

[0.985]

[0.978]

[0.979]

[0.732]

[0.381]

[0.987]

[0.998]

[0.582]

[0.504]

[0.949]

[0.992]

[0.747]

[0.464]

[0.911]

[0.953]

[0.965]

[0.599]

[0.979]

[0.977]

[0.926]

[0.936]

[0.907]

[0.902]

[0.856]

[0.904]

[0.999]

[0.989]

[0.912]

[0.518]

[0.955]

[0.963]

[0.840]

[0.974]

[0.951]

[0.976]

[0.889]

[1.000]

[0.535]

[0.829]

[0.651]

[0.080]

[0.822]

[0.958]

[0.557]

[0.355]

[0.681]

[0.624]

[0.170]

[0.921]

[0.900]

[0.909]

an

-0.202 *** (0.050) -0.073 (0.052) -0.233 *** (0.051) -0.274 *** (0.053) -0.133 ** (0.059) -0.244 *** (0.050) -0.125 ** (0.051) -0.088 (0.060) -0.173 *** (0.056) -0.274 *** (0.052) -0.300 *** (0.052) -0.240 *** (0.053)

M

te

d

0.185 ** (0.080) 0.065 (0.098) 0.112 (0.125) 0.148 (0.127) 0.237 ** (0.096) 0.127 (0.084) 0.061 (0.071) 0.166 (0.101) 0.061 (0.094) 0.044 (0.091) 0.150 (0.097) 0.130 (0.100) 0.300 ** (0.119) 0.059 (0.099)

ip t

Dist.

Notes: The table reports results on the best marginal models of stock returns, selected from the class of ARMA(p,q)–GJR–GARCH(1,1) models. The sample period is from May 2, 2003 to September 29, 2017. The first column (Dist.) shows selected distribution functions for the standardized disturbance, where N, T, and S denote the standard normal, Student’s t, and skewed t distributions, respectively. The second and third columns (p, q) present the numbers of lag length for the AR and MA terms, respectively. The fourth to sixth columns (GJR, DoF, Skewness) report estimates of the coefficient of the GJR term, estimates of the degrees of freedom parameter for the Student’s t and skewed t distributions, and estimates of the skewness parameter for the skewed t distribution, respectively. Standard errors are reported in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Q(12) and Q2 (12) denote the Ljung–Box serial correlation tests applied to standardized residuals and squared standardized residuals, respectively, with lag length of 12 weeks. KS and AD denote the Kolmogorov–Smirnov and Anderson–Darling tests, respectively, for the adequacy of the marginal distribution. For these four tests, p-values are reported in brackets.

Page 39 of 54

Table 4: Estimation results for best marginal models of currency returns Dist.

p

q

GJR

DoF

Skewness

Q(12)

Q2 (12)

Australia

S

1

1

0

0

[0.668]

[0.940]

Chile

S

0

0

[0.550]

[0.957]

[0.974]

[0.992]

Colombia

S

1

1

[0.860]

[0.994]

[0.748]

[0.883]

Czech Rep.

S

0

0

Euro area

S

0

0

Hungary

S

0

0

-0.322 *** (0.051) -0.197 *** (0.053) -0.132 ** (0.054) -0.162 *** (0.055) -0.186 *** (0.059) -0.183 *** (0.058) -0.223 *** (0.057)

[0.558]

S

India

T

1

1

Indonesia

T

1

1

Japan

T

0

0

Korea

S

1

1

New Zealand

S

0

0

Norway

S

0

0

Philippines

T

0

Poland

S

0

South Africa

S

0

1

8.879 *** (2.753) 7.344 *** (1.971) 8.393 *** (2.178) 5.483 *** (1.046) 38.486 (52.882) 54.706 (95.222) 17.865 ** (8.761) 3.664 *** (0.664) 2.619 *** (0.317) 9.153 *** (2.760) 8.323 *** (2.193) 11.074 ** (4.343) 23.507 (15.930) 6.112 *** (1.849) 11.137 *** (3.737) 12.252 *** (4.621)

[0.091]

Brazil

0.091 (0.100) 0.129 (0.110)

Sweden

N

0

0

Switzerland

T

0

0

Taiwan

T

1

0

Turkey

S

0

0

UK

S

1

1

te

d

0.222 ** (0.113) 0.067 (0.084) 0.061 (0.081)

0

Ac ce p

0

0.040 (0.085) 0.057 (0.086)

0.141 (0.093) 0.073 (0.075)

8.229 *** (0.956) 4.868 *** (1.183) 7.747 *** (2.433) 28.273 (26.168)

-0.131 ** (0.051) -0.297 *** (0.052) -0.252 *** (0.055)

-0.250 *** (0.055) -0.314 *** (0.054)

-0.226 *** (0.055) -0.222 *** (0.058)

[0.610]

[0.585]

[0.893]

[0.958]

us

cr

ip t

AD

[0.585]

[0.636]

[0.940]

[0.992]

[0.504]

[0.441]

[0.973]

[0.986]

[0.851]

[0.939]

[0.955]

[0.977]

[0.332]

[0.881]

[0.514]

[0.561]

[0.149]

[0.862]

[0.462]

[0.622]

[0.289]

[0.115]

[0.995]

[0.970]

[0.164]

[0.677]

[0.738]

[0.967]

[0.821]

[0.388]

[0.665]

[0.970]

[0.909]

[0.997]

[0.993]

[0.999]

[0.116]

[0.958]

[0.956]

[0.932]

[0.391]

[0.973]

[0.682]

[0.954]

[0.263]

[0.998]

[0.981]

[0.956]

[0.950]

[0.705]

[0.221]

[0.474]

[0.493]

[1.000]

[0.397]

[0.290]

[0.110]

[0.660]

[0.491]

[0.501]

[0.671]

[0.589]

[0.682]

[0.577]

[0.813]

[0.807]

[0.078]

[0.277]

an

M

0.049 (0.085) 0.054 (0.089) 0.112 (0.133)

KS

Notes: The table reports results on the best marginal models of currency returns. See also notes in Table 3.

Page 40 of 54

Table 5: Estimation results for static vine copulas (first tree): dependence between US and local economies’ stock returns

Student-t

Chile

BB7

Colombia

BB7

Czech Rep.

Gaussian

Euro area

Student-t

Hungary

Gaussian

0.361 *** (0.018)

0.774 *** (0.015) 7.191 *** (1.261) 0.436 *** (0.027)

0.563 *** (0.015)

0.417 *** (0.021)

0.259 *** (0.019)

0.205 *** (0.021)

0.257 *** (0.020)

0.428 *** (0.034) 0.295 *** (0.045) 0.191 *** (0.054) 0.191 *** (0.054) 0.282 *** (0.040) 0.162 *** (0.053) 0.216 *** (0.047) 0.076 * (0.046) 0

Clayton

0.846 *** (0.129)

0.297 *** (0.032)

0.441 *** (0.055) 0

BB7

Student-t

0.656 *** (0.043) 5.358 *** (1.768) 0.374 *** (0.053)

0.456 *** (0.036)

0.292 *** (0.083) 0.292 *** (0.083) 0

Student-t

Gaussian

0.244 *** (0.036)

0.287 *** (0.019)

BB7

0.462 *** (0.135) 1.066 *** (0.056) 0.596 *** (0.117)

0.211 *** (0.041)

Gaussian

0.783 *** (0.020)

0.572 *** (0.020)

Gaussian

0.416 *** (0.053)

0.273 *** (0.037)

Clayton

0.229 *** (0.035)

Student-t

Indonesia

Gaussian

Japan

BB7

Korea

BB7

New Zealand

Student-t

0.480 *** (0.033) 10.550 ** (4.386) 0.342 *** (0.030)

0.319 *** (0.024)

0.868 *** (0.077) 1.174 *** (0.061) 0.769 *** (0.070) 1.095 *** (0.052) 0.307 *** (0.039) 9.286 ** (3.751) 0.615 *** (0.025) 10.267 *** (3.260) 0.522 *** (0.055)

0.344 *** (0.019)

0.222 *** (0.020)

0.068 (0.051) 0.068 (0.051) 0

Gaussian

0.433 *** (0.046)

0.285 *** (0.032)

0.421 *** (0.020)

Clayton

0.207 *** (0.017)

Poland

Gaussian

0.505 *** (0.024)

0.337 *** (0.018)

South Africa

Gaussian

0.532 *** (0.023)

0.357 *** (0.017)

0

Student-t

Switzerland

Student-t

Taiwan

Gaussian

Turkey

Student-t

0.711 *** (0.019) 5.404 *** (0.833) 0.710 *** (0.019) 13.087 *** (4.152) 0.470 *** (0.024)

0.503 *** (0.017)

0.404 *** (0.036) 15.919 (10.197) 0.767 *** (0.015) 8.246 *** (1.648)

0.265 *** (0.025)

0.502 *** (0.017)

0.311 *** (0.018)

0.336 *** (0.040) 0.336 *** (0.040) 0.144 ** (0.063) 0.144 ** (0.063) 0

UK

Average of: Kendall’s τ Lower tail Upper tail

Student-t

0.343 0.172 0.114

0.556 *** (0.015)

Gaussian

0.500 *** (0.029)

0.329 *** (0.028)

0

BB7

Clayton

1.011 *** (0.166)

0.336 *** (0.037)

0.504 *** (0.057) 0

Clayton

0.815 *** (0.128)

0.289 *** (0.032)

0.427 *** (0.057) 0

Student-t

Gaussian

0.212 *** (0.066)

0.136 *** (0.043)

0

Student-t

Gaussian

Clayton

M

0

0

Clayton

0.871 *** (0.123)

0.303 *** (0.030)

Clayton

0.639 *** (0.108)

0.313 0.235 0.074

0.327 *** (0.026)

0.273 *** (0.032)

0.973 *** (0.111)

0.327 *** (0.025)

0.567 *** (0.044) 9.430 ** (4.010) 0.423 *** (0.055) 9.429 ** (4.079) 0.710 *** (0.022)

0.384 *** (0.034)

0.278 *** (0.039)

Student-t

0.572 *** (0.041) 9.781 *** (3.480) 0.582 *** (0.033)

0.388 *** (0.032)

0

1.444 *** (0.196) 1.439 *** (0.158)

0.806 *** (0.111) 1.159 *** (0.073) 0.416 *** (0.046)

0.256 *** (0.032)

0.348 *** (0.032)

BB7

0.376 *** (0.026)

0.392 *** (0.046)

0.520 *** (0.043)

Clayton

0.650 *** (0.019)

Gaussian

Gaussian

BB7

0.853 *** (0.015) 6.861 *** (1.410) 0.557 *** (0.034)

0.338 *** (0.062) 0 0

Student-t

0.285 *** (0.032)

0.242 *** (0.031)

0.297 *** (0.038)

1.168 *** (0.155) 1.367 *** (0.123) 0.703 *** (0.037) 5.963 ** (2.404) 0.585 *** (0.127) 1.126 *** (0.089) 0.392 *** (0.103)

0.239 *** (0.032)

Gaussian

0.449 *** (0.054)

BB7

0.496 *** (0.103) 1.120 *** (0.077) 0.433 *** (0.045)

0.451 *** (0.051) 0

Gaussian

0.502 *** (0.020)

0.265 *** (0.037)

0.164 *** (0.036)

0.479 *** (0.029)

0.587 *** (0.039)

0.399 *** (0.031)

Gaussian

0.418 *** (0.046)

0.275 *** (0.032)

0.247 *** (0.072) 0.143 * (0.079) 0

0.453 *** (0.053) 0.453 *** (0.053) 0

0.423 *** (0.050) 0.182 *** (0.068) 0

Gaussian

0.395 *** (0.026)

Student-t

0.619 *** (0.040) 0.381 *** (0.086)

Student-t

BB7

Student-t

Clayton

0.761 *** (0.025) 5.678 *** (1.078) 1.408 *** (0.127) 1.407 *** (0.138) 0.498 *** (0.050) 11.797 * (6.835) 0.772 *** (0.096)

0.857 *** (0.015) 8.354 *** (1.955) 0.391 0.214 0.133

0.551 *** (0.025)

0.470 *** (0.022)

0.332 *** (0.037)

0.278 *** (0.025)

0.655 *** (0.018)

0 0

Clayton

0.669 *** (0.115)

0.251 *** (0.032)

0.355 *** (0.063) 0

Clayton

0.371 *** (0.097)

0.156 *** (0.035)

0.154 ** (0.076) 0

Gaussian

0.336 *** (0.060)

0.218 *** (0.041)

0

1.350 *** (0.154) 1.275 *** (0.112) 0.276 *** (0.066)

0.445 *** (0.025)

BB7

Gaussian

0

0.178 *** (0.044)

0.598 *** (0.035) 0.278 *** (0.082) 0 0

Gaussian

0.463 *** (0.045)

0.307 *** (0.032)

0 0

Clayton

0.282 *** (0.101)

0.124 *** (0.039)

0.086 (0.075) 0

0.491 *** (0.040) 0

Gaussian

0.590 *** (0.036)

0.402 *** (0.028)

0

0.119 (0.076) 0.119 (0.076) 0.066 (0.054) 0.066 (0.054) 0

Clayton

0.718 *** (0.124)

0.264 *** (0.034)

0.381 *** (0.063) 0

Student-t

0.222 *** (0.072) 8.089 (7.936) 0.617 *** (0.046) 13.149 (8.593) 0.353 *** (0.054)

0.143 *** (0.047)

0.230 *** (0.037)

0.039 (0.074) 0.039 (0.074) 0.088 (0.101) 0.088 (0.101) 0

Gaussian

0.474 *** (0.048)

0.314 *** (0.035)

Gaussian

0.482 *** (0.045)

0.320 *** (0.033)

0

0

Student-t

0

Gaussian

0.423 *** (0.038)

0.115 * (0.063) 0.115 * (0.063) 0

0

0.374 *** (0.053) 0.374 *** (0.053) 0.611 *** (0.027) 0.363 *** (0.079) 0.059 (0.068) 0.059 (0.068) 0.407 *** (0.046) 0 0.417 *** (0.061) 0.417 *** (0.061)

0 0

0

0.553 *** (0.044) 0.340 *** (0.076) 0.307 *** (0.097) 0.307 *** (0.097) 0.306 *** (0.078) 0.149 (0.091) 0.171 ** (0.079) 0.000

0 0

0

0

0.496 *** (0.033)

Gaussian

0

0

0.432 *** (0.027)

0.520 *** (0.041) 0.324 *** (0.069) 0.185 * (0.099) 0.185 * (0.099) 0

0

0

0 0.016 (0.029) 0.016 (0.029) 0.297 *** (0.050) 0.297 *** (0.050)

0

0.227 *** (0.034)

0

Sweden

0.411 *** (0.024)

Copula

0

0.349 *** (0.051)

0

0

Student-t

Gaussian

Gaussian

Ac ce p

Philippines

0

d

Student-t

0.198 *** (0.026)

BB7

0

te

Norway

0.303 *** (0.019)

0.223 ** (0.098) 0.084 (0.066) 0.312 *** (0.071) 0

0

0 0.450 *** (0.032) 0.195 *** (0.055) 0.406 *** (0.033) 0.117 ** (0.057) 0.041 (0.034) 0.041 (0.034) 0.129 ** (0.058) 0.129 ** (0.058) 0.265 *** (0.037) 0

1.061 *** (0.129) 1.342 *** (0.107) 0.707 *** (0.032) 10.582 ** (4.690) 0.495 *** (0.038)

(4) Post-crisis period Parameter Kendall Tail

Tail

0

0

0 India

Gaussian

(3) Crisis period Parameter Kendall

0

0 0.336 *** (0.045) 0.336 *** (0.045) 0

Copula

ip t

Brazil

0.817 *** (0.076) 1.300 *** (0.065) 0.609 *** (0.026) 7.337 *** (1.803) 0.548 *** (0.061) 1.139 *** (0.054) 0.452 *** (0.064) 1.059 *** (0.038) 0.393 *** (0.029)

(2) Pre-crisis period Parameter Kendall Tail

cr

BB7

Copula

us

Australia

(1) Full sample period Parameter Kendall Tail

an

Copula

0 0

Student-t

0.700 *** (0.037) 5.457 *** (2.076) 0.706 *** (0.028)

0.493 *** (0.033)

Clayton

0.774 *** (0.125)

0.279 *** (0.032)

0.408 *** (0.059) 0

Gaussian

0.378 *** (0.051)

0.247 *** (0.035)

0

Gaussian

0.499 *** (0.025)

0.324 *** (0.093) 0.324 *** (0.093) 0 0

0 BB7

1.538 *** (0.158) 1.254 *** (0.147)

0.468 *** (0.025)

0.637 *** (0.030) 0.262 ** (0.113)

0.306 0.146 0.047

Notes: The table reports estimation results for the static relationship between the US stock returns and each of local economies’ stock returns, which corresponds to one component of the first tree of the three-variate vine copula model. (1) Full sample period is from May 2, 2003 to September 29, 2017. (2) Pre-crisis period is from May 2, 2003 to July 27, 2007. (3) Crisis period is from August 3, 2007 to December 28, 2012. (4) Post-crisis period is from January 4, 2013 to September 29, 2017. “Parameter” reports the estimates of copula parameters: ρ for Gaussian, ρ and ν (in this order) for Student’s t, δ for Clayton and Gumbel, and δ and θ (in this order) for BB7. “Tail” reports the estimates of the lower and upper tail dependence (in this order). Standard errors are reported in parentheses. The delta method is used to compute standard errors for Kendall’s τ and tail dependence. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

Page 41 of 54

Table 6: Estimation results for static vine copulas (first tree): dependence between US stock and local economies’ currency returns

Student-t

Chile

BB7

Colombia

Gaussian

0.232 *** (0.020)

0.255 *** (0.026)

0.203 *** (0.020)

0.210 *** (0.022)

0.170 *** (0.046) 0.211 *** (0.047) 0.013 (0.023) 0.013 (0.023) 0.167 *** (0.044) 0.133 *** (0.049) 0

Clayton

0.384 *** (0.105)

0.161 *** (0.037)

0.164 ** (0.081) 0

BB7

Gaussian

0.451 *** (0.055)

0.298 *** (0.039)

0

BB7

Clayton

0.576 *** (0.109)

0.223 *** (0.033)

0.300 *** (0.068) 0

Student-t

Clayton

0.425 *** (0.127)

0.175 *** (0.043)

0.196 ** (0.095) 0

Gaussian

0.069 (0.064) 0

Student-t

0

0

Euro area

Clayton

Hungary

Student-t

India

Student-t

Indonesia

Japan

Student-t

90◦ rotated Gumbel

0.161 *** (0.042) 7.211 ** (3.173) 0.201 *** (0.043)

0.103 *** (0.027)

0.257 *** (0.040) 5.625 *** (1.554) 0.349 *** (0.038) 15.228 (11.819) 0.271 *** (0.040) 15.258 (11.803) 1.170 *** (0.030)

0.165 *** (0.027)

0.091 *** (0.018)

0.227 *** (0.026)

0.175 *** (0.026)

-0.145 *** (0.022)

0.040 (0.033) 0.040 (0.033) 0.032 (0.024) 0 0.091 ** (0.036) 0.091 ** (0.036) 0.013 (0.029) 0.013 (0.029) 0.007 (0.019) 0.007 (0.019) 0

Clayton

0.255 *** (0.091)

0.113 *** (0.036)

0.066 (0.064) 0

Clayton

Student-t

0.244 *** (0.078) 5.571 (4.071) 0.331 *** (0.061)

0.157 *** (0.051)

0.088 (0.090) 0.088 (0.090) 0

BB7

Gaussian

Gaussian

BB7

Norway

BB7

Philippines

Poland

BB7

Student-t

South Africa

Student-t

Sweden

BB7

Switzerland

Taiwan

Student-t

Student-t

Turkey

BB7

UK

Clayton

Average of: Kendall’s τ Lower tail Upper tail

0.212 *** (0.027)

0.180 *** (0.020)

0.153 *** (0.020)

0.166 *** (0.021)

0.060 (0.042) 0.060 (0.042) 0.151 *** (0.044) 0.081 (0.050) 0.071 * (0.038) 0.107 ** (0.045) 0.122 *** (0.047) 0.079 (0.049) 0.043 (0.035) 0.043 (0.035) 0.106 ** (0.047) 0.106 ** (0.047) 0.067 * (0.036) 0.109 ** (0.050) 0.013 (0.022) 0.013 (0.022) 0.041 (0.041) 0.041 (0.041) 0.251 *** (0.045) 0.170 *** (0.048) 0.056 * (0.032) 0

0.260 *** (0.060)

0.158 0.072 0.063

0.183 *** (0.026)

0.225 *** (0.026)

0.151 *** (0.021)

0.010 (0.025)

0.175 *** (0.027)

0.249 *** (0.020)

0.107 *** (0.019)

0.168 *** (0.039)

0 0

Student-t

Clayton

Clayton

0.160 ** (0.078) 4.765 (3.975) 0.323 *** (0.110)

0.102 ** (0.050)

0.139 *** (0.041)

0.323 *** (0.101)

0.139 *** (0.038)

te

New Zealand

0.327 *** (0.040) 8.081 ** (3.186) 0.367 *** (0.056) 1.064 *** (0.043) 0.263 *** (0.053) 1.086 *** (0.040) 0.329 *** (0.060) 1.062 *** (0.042) 0.283 *** (0.039) 8.694 ** (3.650) 0.347 *** (0.038) 6.062 *** (1.979) 0.256 *** (0.051) 1.088 *** (0.045) 0.016 (0.039) 8.661 (6.406) 0.272 *** (0.040) 8.700 ** (4.374) 0.502 *** (0.065) 1.147 *** (0.050) 0.240 *** (0.048)

0.215 *** (0.041)

0

Clayton

Clayton

0.178 ** (0.084)

0.341 *** (0.111)

Ac ce p

Student-t

0.115 *** (0.035)

Clayton

0 Korea

0.259 *** (0.090)

Gaussian

Student-t

Student-t

Gumbel

BB7

Gaussian

0.089 (0.088) 0.089 (0.088) 0.117 (0.085) 0

0.269 *** (0.064)

0.168 ** (0.080) 4.773 (3.424) 0.223 *** (0.076) 7.613 (7.785) 1.056 *** (0.044)

0.082 ** (0.035)

0.146 *** (0.040)

0.173 *** (0.042)

Gaussian

Student-t

90◦ rotated Gumbel

Student-t

0.117 (0.079) 0

BB7

0.020 (0.037) 0

BB7

0.131 (0.087) 0

Gaussian

0

Student-t

0.143 *** (0.049)

0.053 (0.039)

0.306 *** (0.107) 1.080 *** (0.063) 0.444 *** (0.054)

0.165 *** (0.037)

0.230 ** (0.092)

0.103 *** (0.037)

0.293 *** (0.038)

0.091 (0.084) 0.091 (0.084) 0.045 (0.083) 0.045 (0.083) 0 0.072 (0.052) 0.104 (0.082) 0.100 (0.072) 0

Student-t

BB7

Student-t

Gaussian

0.156 0.078 0.023

0.049 (0.059) 0

0.354 *** (0.027)

0.296 *** (0.031)

0.261 *** (0.039)

0.211 *** (0.034)

Copula

0.227 *** (0.073) 0.449 *** (0.050) 0.214 *** (0.079) 0.333 *** (0.066) 0.105 * (0.062) 0.105 * (0.062) 0

Clayton

0.297 *** (0.099)

0.129 *** (0.038)

0.097 (0.076) 0

Clayton

0.328 *** (0.086)

0.141 *** (0.032)

0.121 * (0.067) 0

Gaussian

0.244 *** (0.060)

0.157 *** (0.039)

0

Clayton

0.444 *** (0.105)

0.182 *** (0.035)

0.305 *** (0.061) 6.494 ** (2.668) 0.355 *** (0.075)

0.197 *** (0.041)

0.461 *** (0.103) 1.181 *** (0.080) 0.440 *** (0.042)

0.248 *** (0.030)

0.151 *** (0.027)

0.290 *** (0.030)

0.366 *** (0.062) 12.352 (10.456) 1.223 *** (0.052)

0.238 *** (0.042)

-0.124 * (0.070)

-0.079 * (0.045)

Gaussian

Gaussian

-0.098 (0.069)

-0.063 (0.044)

0.222 *** (0.075) 0.202 *** (0.072) 0

Student-t

0.047 (0.077) 7.072 (7.662) 0.360 *** (0.084)

0.030 (0.049)

0.153 *** (0.030)

0.167 *** (0.058)

0.107 *** (0.038)

-0.182 *** (0.035)

0

0 0

Clayton

Gaussian

0.304 *** (0.039)

0.291 *** (0.028)

0.252 *** (0.028)

0.255 *** (0.030)

0.049 (0.061) 0.049 (0.061) 0.278 *** (0.065) 0.264 *** (0.065) 0.194 *** (0.067) 0.240 *** (0.062) 0

0.425 *** (0.053) 9.708 ** (4.757) 0.500 *** (0.047) 7.299 ** (3.214) 0.387 *** (0.092) 1.206 *** (0.089) 0.088 (0.062) 6.715 (5.560) 0.363 *** (0.044)

0.279 *** (0.037)

0.333 *** (0.035)

0.235 *** (0.032)

0.056 (0.039)

0.237 *** (0.030)

0.062 (0.058) 0.062 (0.058) 0.133 * (0.078) 0.133 * (0.078) 0.167 ** (0.071) 0.223 *** (0.075) 0.036 (0.053) 0.036 (0.053) 0

Student-t

Clayton

0.517 *** (0.047) 8.564 ** (4.009) 0.321 *** (0.072)

0.228 0.103 0.110

0.346 *** (0.035)

0.138 *** (0.027)

0.113 (0.078) 0.113 (0.078) 0.115 ** (0.056) 0

0.026 (0.054) 0.026 (0.054) 0.146 ** (0.065) 0 0 0

90◦ rotated Gumbel

1.351 *** (0.066)

-0.260 *** (0.036)

Student-t

0.223 *** (0.076) 5.282 (4.193) 0.066 (0.076) 6.995 (7.659) 0.133 * (0.069)

0.143 *** (0.050)

0 0.460 *** (0.054) 11.825 * (6.974) 0.541 *** (0.099) 1.256 *** (0.085) 0.423 *** (0.089) 1.226 *** (0.077) 0.390 *** (0.043)

0.210 *** (0.077) 0

0

0 0.027 (0.055) 0.027 (0.055) 0

Tail

0

0.083 (0.055) 0.083 (0.055) 0.142 ** (0.059) 0

0 0

Student-t

Gaussian

0.042 (0.049)

0.085 * (0.044)

0.091 (0.096) 0.091 (0.096) 0.029 (0.059) 0.029 (0.059) 0 0

Clayton

0.260 *** (0.097)

0.115 *** (0.038)

0.069 (0.069) 0

Student-t

0.087 (0.076) 7.912 (9.828) 0.289 *** (0.073) 7.286 (6.287) 0.033 (0.073)

0.056 (0.049)

0.023 (0.059) 0.023 (0.059) 0.064 (0.091) 0.064 (0.091) 0

Student-t

Gaussian

0.187 *** (0.048)

0.021 (0.046)

0 Gaussian

-0.190 *** (0.071)

-0.121 *** (0.046)

0 0

Student-t

0

0 Clayton

0.467 *** (0.101) 1.580 *** (0.116) 0.450 *** (0.108) 1.357 *** (0.105) 0.398 *** (0.056) 6.789 ** (2.725) 0.325 *** (0.050)

(4) Post-crisis period Parameter Kendall

Tail

0

0 0.108 ** (0.052)

(3) Crisis period Parameter Kendall

0

M

Student-t

d

Czech Rep.

Copula

ip t

Brazil

0.391 *** (0.060) 1.192 *** (0.053) 0.390 *** (0.037) 16.330 * (9.295) 0.387 *** (0.057) 1.110 *** (0.047) 0.324 *** (0.033)

(2) Pre-crisis period Parameter Kendall Tail

cr

BB7

Copula

us

Australia

(1) Full sample period Parameter Kendall Tail

an

Copula

Clayton

Gaussian

0.173 ** (0.072) 5.407 (4.093) 0.389 *** (0.092)

0.111 ** (0.047)

0.152 ** (0.066)

0.097 ** (0.042)

0.163 *** (0.032)

0.075 (0.079) 0.075 (0.079) 0.169 ** (0.071) 0 0 0

0.066 0.053 0.015

Notes: The table reports estimation results for the static relationship between the US stock returns and each of local economies’ currency returns, which corresponds to one component of the first tree of the three-variate vine copula model. See also notes in Table 5.

Page 42 of 54

Table 7: Estimation results for static vine copulas (second tree): dependence between stock and currency returns in local economies

Australia

Brazil

Chile

BB7

Student-t

Clayton

(1) Full sample period Parameter Kendall 0.101 * (0.053) 1.064 *** (0.036) 0.387 *** (0.036) 11.159 *** (4.196) 0.075 * (0.039)

0.080 *** (0.023)

0.253 *** (0.025)

0.036 ** (0.018)

Tail

Copula

0.001 (0.004) 0.081 * (0.043) 0.039 (0.032) 0.039 (0.032) 0.000 (0.000) 0

Clayton

Student-t

Gaussian

(2) Pre-crisis period Parameter Kendall 0.124 (0.095)

0.300 *** (0.077) 15.765 (14.703) -0.043 (0.065)

0.058 (0.042)

0.194 *** (0.052)

-0.027 (0.041)

Tail

Copula

0.004 (0.016) 0

Gaussian

0.008 (0.026) 0.008 (0.026) 0

Gaussian

(3) Crisis period Parameter Kendall 0.222 *** (0.050)

0.142 *** (0.033)

0.418 *** (0.044)

0.274 *** (0.031)

0.000 (0.000) 0

Gaussian

0.003 (0.009) 0

Gaussian

Clayton

0.201 ** (0.085)

0.091 *** (0.035)

0.032 (0.046) 0

Clayton

0.117 * (0.068)

0.055 * (0.030)

Czech Rep.

Gumbel

1.024 *** (0.019)

0.024 (0.018)

0

Student-t

0.028 (0.075) 4.784 (3.852) 0.617 *** (0.099)

0.018 (0.048)

0.059 (0.064) 0.059 (0.064) 0

Gaussian

0.114 * (0.061)

0.073 * (0.039)

India

Gaussian

0.431 *** (0.027)

0.284 *** (0.019)

0

Indonesia

BB7

0.239 *** (0.020)

Japan

Student-t

0.419 *** (0.059) 1.188 *** (0.053) -0.352 *** (0.038) 7.092 *** (2.432) 0.361 *** (0.038) 18.417 (15.179) -0.062 (0.039) 11.192 (8.640) 0.135 *** (0.046)

0.191 *** (0.045) 0.208 *** (0.047) 0.003 (0.003) 0.003 (0.003) 0.007 (0.020) 0.007 (0.020) 0.003 (0.007) 0.003 (0.007) 0.006 (0.010) 0

0.297 *** (0.032)

0.192 *** (0.021)

0.361 *** (0.104)

0.153 *** (0.037)

0.147 * (0.081) 0

Student-t

Clayton

0.422 *** (0.114)

0.174 *** (0.039)

0.193 ** (0.086) 0

Gaussian

Clayton

0.512 *** (0.107)

0.204 *** (0.034)

0.259 *** (0.073) 0

Student-t

Student-t

-0.069 (0.081) 5.354 (5.340) 0.150 ** (0.063)

-0.044 (0.052)

0.034 (0.053) 0.034 (0.053) 0

90◦ rotated BB7

Student-t

Norway

Clayton

Philippines

Gaussian

-0.039 (0.025)

0.063 *** (0.020)

0

M

Gaussian

0.096 ** (0.040)

Gaussian

-0.115 (0.070)

-0.073 (0.045)

BB7

South Africa

Student-t

Sweden

Student-t

Switzerland

Student-t

Taiwan

Gaussian

0.275 *** (0.066) 1.074 *** (0.038) 0.123 *** (0.040) 6.017 ** (2.769) -0.066 * (0.039) 13.881 (12.751) -0.322 *** (0.035) 14.228 *** (3.916) 0.418 *** (0.026)

0.152 *** (0.023)

0.078 *** (0.026)

-0.042 * (0.025)

-0.209 *** (0.024)

0.274 *** (0.018)

0.081 * (0.049) 0.093 ** (0.044) 0.052 (0.037) 0.052 (0.037) 0.001 (0.003) 0.001 (0.003) 0.000 (0.000) 0.000 (0.000) 0

0.094 (0.076)

-0.045 (0.035)

Gaussian

0.256 *** (0.061)

0.165 *** (0.040)

UK

Average of: Kendall’s τ Lower tail Upper tail

Student-t

90◦ rotated BB7

0.499 *** (0.031) 5.898 *** (1.074) 0.179 *** (0.050) 1.163 *** (0.052) 0.082 0.036 0.034

0.333 *** (0.023)

-0.154 *** (0.022)

0.174 *** (0.038) 0.174 *** (0.038) 0

0.092 ** (0.036)

0.316 *** (0.067) 7.622 (6.271) 0.502 *** (0.037)

0.205 *** (0.045)

0.456 *** (0.055) 9.889 (7.083) 0.429 *** (0.091) 1.097 *** (0.059) 0.502 *** (0.038)

0.301 *** (0.039)

0.335 *** (0.027)

-0.212 *** (0.030)

Student-t

0.162 ** (0.076) 9.400 (12.023) -0.124 * (0.073) 6.175 (4.074) 0.334 *** (0.103)

0.104 ** (0.049)

Gaussian

-0.379 *** (0.058)

-0.247 *** (0.040)

Gaussian

0.372 *** (0.047)

0.243 *** (0.032)

Student-t

90◦ rotated Clayton

-0.079 * (0.047)

-0.143 *** (0.038)

0.335 *** (0.028)

Gaussian

0.479 *** (0.062) 3.999 ** (1.649) -0.354 *** (0.052)

0

Student-t

0

Gaussian

-0.073 (0.063) 9.046 (8.664) 0.311 *** (0.051)

-0.047 (0.040)

0.201 *** (0.034)

0.365 *** (0.087)

0.154 *** (0.031)

0 0

0.020 (0.060) 0.020 (0.060) 0.018 (0.022) 0.018 (0.022) 0

Gaussian

0.323 *** (0.049)

0.209 *** (0.033)

0

0.082 (0.055) 0.133 (0.086) 0.308 *** (0.079) 0

0.343 *** (0.110) 1.318 *** (0.116) 0.226 *** (0.067)

0.258 *** (0.037)

0.336 *** (0.057)

0.218 *** (0.039)

0

-0.062 (0.070)

-0.039 (0.045)

0

0.145 *** (0.044)

0

0

Student-t

0

0

0.242 *** (0.088) 0.242 *** (0.088) 0

0 -0.265 *** (0.072) 5.304 (3.478) 0.237 ** (0.094)

0.106 *** (0.037)

Gaussian

0.485 *** (0.049)

0.322 *** (0.036)

BB7

0.358 *** (0.096) 1.251 *** (0.103) 0.827 *** (0.122) 1.303 *** (0.113) 0.381 *** (0.050)

0.242 *** (0.036)

-0.363 *** (0.030)

0.249 *** (0.035)

0

90◦ rotated Clayton

0.115 (0.084)

-0.054 (0.038)

0

Gumbel

1.052 *** (0.049)

0.049 (0.045)

0.150 ** (0.068) 0

Gaussian

0.369 *** (0.057)

0.241 *** (0.039)

0

Gaussian

0.065 (0.090) 0.065 (0.090) 0

Clayton

-0.171 *** (0.047)

0

0 0.069 (0.087) 0.069 (0.087) 0

0

0.007 (0.016) 0.007 (0.016) 0

0.015 (0.017) 0.015 (0.017) 0.054 (0.062) 0

0

90◦ rotated BB7

Gaussian

0.145 * (0.075) 0.260 *** (0.080) 0 0

0

0 0 0.067 (0.060) 0 0 0.247 *** (0.063)

0.159 *** (0.042)

0 0

Clayton

0.374 *** (0.084)

0.158 *** (0.030)

0.157 ** (0.065) 0

Gumbel

1.194 *** (0.055)

0.162 *** (0.039)

Clayton

0.187 ** (0.077)

0.086 *** (0.032)

0.025 (0.038) 0

90◦ rotated Gumbel

1.154 *** (0.056)

-0.133 *** (0.042)

Gaussian

-0.175 *** (0.053)

-0.112 *** (0.035)

0

90◦ rotated Gumbel

1.410 *** (0.075)

-0.291 *** (0.038)

0

Gaussian

0.418 *** (0.045)

0.274 *** (0.032)

0

0

Gaussian

0.425 *** (0.044)

0.280 *** (0.031)

0

0

0 Gaussian

0.468 *** (0.043)

0.310 *** (0.031)

0

0 Student-t

0 Clayton

0.041 (0.057)

0.138 0.023 0.007

0.020 (0.027)

0.000 (0.000) 0

0.213 *** (0.048) 0 0

0

0

0.033 0.048 0.018

0

0

0

-0.230 *** (0.035)

Tail

0.060 (0.042)

0 Clayton

0

0.318 *** (0.045)

1.064 *** (0.047)

0

0 Student-t

0

0

0

0 Turkey

Gaussian

0

90◦ rotated Clayton

0

Poland

0.144 ** (0.056)

0

d

New Zealand

0.235 *** (0.026)

te

Student-t

Gaussian

0

Clayton

Ac ce p

Korea

-0.229 *** (0.026)

Gaussian

0

0

0

us

Clayton

-0.236 *** (0.029)

(4) Post-crisis period Parameter Kendall

0

an

0.148 *** (0.019)

Hungary

rotated Clayton

cr

0.059 * (0.033) 0

-0.108 *** (0.026)

BB7

0.033 (0.028)

0.109 *** (0.019)

-0.169 *** (0.041) 6.412 ** (3.150) 0.346 *** (0.053)

0

0.069 (0.060)

0.245 *** (0.048)

Student-t

Gumbel

Clayton

Clayton

Euro area

0

0

0

90◦

Copula

0

Colombia

0.032 (0.025) 0.013 (0.013) 0.013 (0.013) 0.135 *** (0.041) 0

Tail

ip t

Copula

Gaussian

0.580 *** (0.047) 4.725 *** (0.994) -0.359 *** (0.055)

0.394 *** (0.037)

-0.234 *** (0.037)

0.266 *** (0.055) 0.266 *** (0.055) 0 0

0.076 0.029 0.058

Notes: The table reports estimation results for the static relationship between stock and currency returns in each local economy, which corresponds to the second tree of the three-variate vine copula model. See also notes in Table 5.

Page 43 of 54

d

te

an

us

12.5 9.71 5.88 5.51 3.32 3.04 2.69 2.49 1.99 0.77 0.29 0.25 -0.53 -1.22 -1.26 -2.35 -3.03 -3.58 -3.82 -4.02

cr

Net exports (% of GDP)

Norway Switzerland Sweden Chile Czech Rep. Korea Hungary Indonesia Euro area New Zealand Japan Brazil South Africa Poland Australia UK Colombia Philippines India Turkey

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Economy

M

Ranking

ip t

Table 8: Net exports (% of GDP)

Notes: The table reports the ratio of net exports to GDP, averaged over the period 2003 to 2015 for each economy and ranked in descending order. The data source is World Development Indicators, the World Bank. Taiwan is excluded from the table due to unavailability of the data.

Page 44 of 54

Table 9: Estimation results for non-vine bivariate copulas (not including the US stock returns)

0.201 *** (0.021)

Clayton

Brazil

Student-t

Chile

Clayton

Colombia

Clayton

0.380 *** (0.050)

0.159 *** (0.018)

0.161 *** (0.038) 0

Czech Rep.

Clayton

0.117 *** (0.044)

0.055 *** (0.019)

Euro area

Student-t

-0.006 (0.041) 5.300 *** (1.811) 0.413 *** (0.061) 1.075 *** (0.052) 0.521 *** (0.023)

-0.004 (0.026)

Hungary

BB7

India

Gaussian

0.352 *** (0.023)

0.152 *** (0.047) 0.143 *** (0.047) 0.066 (0.046) 0.066 (0.046) 0.096 *** (0.035) 0

0.129 *** (0.017)

0.199 *** (0.021)

0.349 *** (0.017)

Student-t

(2) Pre-crisis period Parameter Kendall 0.297 *** (0.106)

0.129 *** (0.040)

New Zealand

Student-t

Clayton

Norway

BB7

Philippines

BB7

Poland

BB7

South Africa

Student-t

Sweden

Student-t

Switzerland

90◦ rotated Gumbel

Taiwan

Student-t

0.265 *** (0.055) 1.076 *** (0.041) 0.473 *** (0.062) 1.076 *** (0.045) 0.358 *** (0.066) 1.158 *** (0.048) 0.279 *** (0.039) 4.771 *** (1.497) 0.104 ** (0.041) 5.459 *** (1.348) 1.165 *** (0.029)

0.306 *** (0.024)

0.057 *** (0.015)

0.149 *** (0.021)

0.218 *** (0.021)

0.211 *** (0.021)

0.180 *** (0.026)

0.066 ** (0.026)

-0.142 *** (0.021)

Turkey

UK

Average of: Kendall’s τ Lower tail Upper tail

Student-t

Student-t

0.153 0.091 0.069

0.326 *** (0.023)

0.406 *** (0.021)

-0.004 (0.025)

0.593 *** (0.108) 1.259 *** (0.099) 0.604 *** (0.043) 10.653 (7.467) 0.230 *** (0.063) 6.937 ** (2.890) 0.278 *** (0.071)

0.304 *** (0.030)

0.311 *** (0.066) 0.266 *** (0.075) 0.117 (0.119) 0.117 (0.119) 0.057 (0.042) 0.057 (0.042) 0.083 (0.053) 0

Gaussian

Gaussian

0.399 *** (0.053)

0.261 *** (0.037)

0

90◦ rotated Gumbel

1.073 *** (0.053)

-0.068 (0.046)

0

Student-t

-0.278 *** (0.073) 6.512 (5.371) 0.286 *** (0.097)

-0.180 *** (0.049)

0.125 *** (0.037)

0.007 (0.012) 0.007 (0.012) 0.088 (0.073) 0

Gaussian

0.537 *** (0.044)

0.361 *** (0.034)

0

BB7

0.430 *** (0.111) 1.245 *** (0.107) -0.664 *** (0.030)

0.259 *** (0.037)

0.200 ** (0.083) 0.255 *** (0.083) 0

0.152 *** (0.033)

0.145 ** (0.072) 0

Clayton

0.003 (0.006) 0

Student-t

0.054 (0.047)

0.240 *** (0.055)

0.154 *** (0.036)

0

90◦ rotated Clayton

0.068 (0.073) 0.068 (0.073) 0

Gaussian

0.043 * (0.023) 0.043 * (0.023) 0.187 *** (0.046) 0.094 (0.059) 0

0.084 (0.074) 4.899 (3.976) 0.176 * (0.091)

Gaussian

0.326 *** (0.048)

0.211 *** (0.032)

0

-0.081 ** (0.038)

0.413 *** (0.107)

0.171 *** (0.037)

0.187 ** (0.081) 0

Student-t

Clayton

0.572 *** (0.129)

0.222 *** (0.039)

0.298 *** (0.081) 0

Gaussian

0.316 *** (0.073) 0.114 (0.080) 0.089 (0.062) 0.089 (0.062) 0.165 ** (0.074) 0

Student-t

0.073 * (0.040) 0.095 ** (0.046) 0.231 *** (0.045) 0.096 * (0.052) 0.144 *** (0.051) 0.181 *** (0.045) 0.123 *** (0.045) 0.123 *** (0.045) 0.059 ** (0.023) 0.059 ** (0.023) 0

Clayton

0.075 (0.070)

0.036 (0.032)

Clayton

0.566 *** (0.123)

Student-t

Clayton

Gaussian

0.602 *** (0.121) 1.092 *** (0.073) -0.003 (0.085) 3.595 (2.398) 0.385 *** (0.095)

0.260 *** (0.034)

-0.002 (0.054)

0.161 *** (0.034)

0.122 *** (0.028)

0.463 *** (0.052) 8.261 *** (2.718) 0.614 *** (0.028)

0.306 *** (0.037)

0.421 *** (0.023)

Student-t

Gaussian

0.532 *** (0.049) 7.302 ** (3.674) -0.452 *** (0.053) 6.477 *** (2.362) 0.624 *** (0.027)

0.357 *** (0.037)

-0.298 *** (0.038)

0.429 *** (0.022)

Student-t

Student-t

Gaussian

Gaussian

Gaussian

Gaussian

0.501 *** (0.128) 1.324 *** (0.123) 0.311 *** (0.061)

0.299 *** (0.036)

0.201 *** (0.041)

0.097 * (0.054) 0.097 * (0.054) 0

Clayton

0

0

Gaussian

-0.463 *** (0.025)

0 Gaussian

0.454 *** (0.047)

0.300 *** (0.034)

0.258 *** (0.060)

0.114 *** (0.024)

0.068 (0.043) 0

rotated Clayton

0.075 (0.076)

-0.036 (0.035)

0.000 (0.001) 0

Gaussian

0.490 *** (0.041)

0.326 *** (0.030)

0

Gumbel

1.092 *** (0.052)

0.085 * (0.044)

0.221 *** (0.037)

0.294 *** (0.078) 0

BB7

0.230 *** (0.032)

0.400 *** (0.056)

0.262 *** (0.039)

0.171 *** (0.040)

0.117 (0.095) 0.098 (0.063) 0.057 (0.036) 0.057 (0.036) 0.031 (0.044) 0.031 (0.044) 0

Gaussian

0.215 *** (0.070) 0.156 * (0.081) 0

Gaussian

0.323 *** (0.123) 1.078 *** (0.056) -0.025 (0.073) 4.474 ** (2.072) -0.065 (0.073) 5.551 (4.941) -0.240 *** (0.060)

0.450 *** (0.096) 1.133 *** (0.082) 0.488 *** (0.037)

BB7

0.158 (0.099) 1.200 *** (0.092) 1.275 *** (0.064)

0.161 *** (0.042)

0.424 *** (0.045)

0.279 *** (0.032)

-0.043 (0.044)

0

-0.016 (0.047)

-0.042 (0.046)

-0.154 *** (0.039)

0.547 *** (0.056) 5.978 ** (2.946) -0.124 * (0.063)

0.369 *** (0.043)

-0.079 * (0.041)

0.196 * (0.105) 0.196 * (0.105) 0

Student-t

BB7

90◦ rotated Gumbel

0.491 *** (0.051) 4.775 ** (2.009) 0.363 *** (0.083) 1.215 *** (0.083) 1.055 *** (0.032)

0.327 *** (0.037)

0

0.521 *** (0.037)

0.349 *** (0.027)

0.231 *** (0.031)

-0.053 * (0.029)

0.212 ** (0.084) 0.212 ** (0.084) 0.148 ** (0.065) 0.231 *** (0.069) 0

0

Gumbel

Student-t

90◦ rotated Gumbel

0.216 *** (0.039)

-0.124 (0.079) 5.802 (5.977) 1.377 *** (0.072)

-0.079 (0.050)

0.501 *** (0.057) 6.470 (4.136) 0.619 *** (0.044) 4.942 *** (1.478) -0.182 *** (0.061)

0.334 *** (0.042)

-0.274 *** (0.038)

0.619 *** (0.030)

0.425 *** (0.024)

0

Student-t

0 Clayton

0.295 *** (0.072)

0.237 0.074 0.061

0.129 *** (0.027)

0.096 * (0.055) 0

0.012 (0.034) 0.218 *** (0.079) 0 0.278 *** (0.047) 0.022 (0.039) 0.022 (0.039) 0 0

Student-t

0 Gaussian

0.114 ** (0.057) 0 0

0 Gaussian

0

0.107 0.104 0.032

0

0

0 0

0

0

0.325 *** (0.027)

0 0

Clayton

-0.068 (0.070)

0.251 *** (0.089) 0.312 *** (0.082) 0

0

0 0.149 (0.094) 0.149 (0.094) 0.003 (0.002) 0.003 (0.002) 0

Tail 0

0

90◦

0 Student-t

BB7

0

0

BB7

0.114 *** (0.042)

0

0

Clayton

BB7

0.148 *** (0.041)

0.178 *** (0.065)

0

0

0.266 *** (0.042) 0.249 *** (0.046) 0.010 *** (0.004) 0.010 *** (0.004) 0.057 (0.050) 0.057 (0.050) 0.003 (0.005) 0

0.039 (0.052) 0.039 (0.052) 0.185 *** (0.052) 0.185 *** (0.052) 0.006 (0.013) 0.006 (0.013)

Student-t

0.413 *** (0.034)

Copula

0.359 *** (0.092)

0.130 *** (0.034)

0

0.489 *** (0.032) 13.984 * (8.411) 0.596 *** (0.027) 7.243 *** (1.749) -0.007 (0.040) 10.425 (8.792)

Student-t

M

Korea

-0.276 *** (0.025)

0.024 (0.055) 0.024 (0.055) 0.098 (0.069) 0

d

Student-t

0.281 *** (0.019)

BB7

(4) Post-crisis period Parameter Kendall

Tail

Clayton

Clayton

te

Japan

0.523 *** (0.063) 1.238 *** (0.058) -0.420 *** (0.036) 4.728 *** (1.050) 0.463 *** (0.034) 11.073 ** (5.002) 0.121 *** (0.034)

0.097 (0.081) 0

(3) Crisis period Parameter Kendall

0.318 *** (0.047)

Ac ce p

BB7

Copula

0.479 *** (0.064) 16.322 (13.433) 0.298 *** (0.090)

0 Indonesia

Tail

ip t

0.368 *** (0.061) 1.120 *** (0.046) 0.526 *** (0.030) 11.944 *** (4.318) 0.296 *** (0.046)

Copula

cr

BB7

Tail

us

Australia

(1) Full sample period Parameter Kendall

an

Copula

Gaussian

0.425 *** (0.036)

-0.116 *** (0.040)

0.157 (0.117) 0.157 (0.117) 0.282 *** (0.073) 0.282 *** (0.073) 0 0

0.104 0.049 0.078

Notes: The table reports estimation results for the static relationship between stock and currency returns in each local economy, which are estimated from the non-vine bivariate copula model (not including the US stock returns). See also notes in Table 5.

Page 45 of 54

i cr us an

Table 10: Differences of dependence measures between a vine and a non-vine copula

Post-crisis

Full

-0.121 -0.100 -0.093 -0.050 -0.032 -0.105 -0.051 -0.065 -0.042 0.048 -0.071 -0.097 -0.086 -0.026 -0.059 -0.102 -0.108 -0.067 -0.051 -0.073 -0.149 -0.071

-0.071 -0.124 -0.157 -0.061 -0.036 -0.155 -0.018 -0.048 -0.056 -0.042 -0.065 -0.030 -0.081 -0.056 -0.067 -0.064 -0.101 -0.093 -0.036 -0.051 -0.151 -0.074

-0.054 -0.041 -0.056 -0.043 0.029 0.009 -0.019 -0.038 -0.018 0.100 -0.051 -0.018 -0.035 -0.021 -0.002 -0.053 -0.054 -0.017 -0.055 -0.031 -0.118 -0.028

-0.151 -0.028 -0.096 -0.102 -0.003 -0.030 -0.052

Ac

M

Kendall’s τ Pre-crisis Crisis

-0.161 -0.139 -0.115 -0.067 -0.081 -0.119 -0.102 -0.086 -0.056 0.087 -0.094 -0.161 -0.125 -0.076 -0.115 -0.169 -0.146 -0.060 -0.075 -0.115 -0.109 -0.099

ed

pt

ce

Australia Brazil Chile Colombia Czech Rep. Euro area Hungary India Indonesia Japan Korea New Zealand Norway Philippines Poland South Africa Sweden Switzerland Taiwan Turkey UK Average

Full

-0.075 -0.007 -0.050 0.000 -0.067 -0.231 -0.063 -0.072 -0.058 0.000 -0.039 -0.012 -0.006 -0.057

Lower tail Pre-crisis Crisis -0.093 -0.016 -0.098 -0.113 -0.008 -0.040 -0.105 -0.058 -0.056 -0.165

-0.311 -0.117 -0.057 -0.080

-0.033 -0.080 -0.003

Post-crisis

Full

Upper tail Pre-crisis Crisis

-0.118

-0.062 -0.028

-0.016

0.032 -0.030 -0.094

-0.008

0.008 -0.035

-0.041 -0.007 -0.050 0.003 -0.095 -0.096 -0.088 -0.072 -0.058 0.000 -0.039 -0.012 -0.006 -0.041

-0.114 -0.056

-0.055

-0.061 0.000 -0.294 -0.097 -0.039 -0.031

-0.065 -0.012 -0.055 -0.123

-0.157 -0.016

0.046 -0.073

-0.022

-0.096 -0.090

-0.051

-0.266 -0.117 -0.057

Post-crisis 0.082 -0.004

0.008 -0.033 -0.080 -0.003

0.005

0.007 -0.046 -0.156 -0.078 -0.039 -0.031

-0.212 -0.231

-0.157 -0.016

0.046 -0.037

-0.218 -0.065 -0.022

-0.115

-0.043

Notes: The table reports differences of dependence measures between a vine (presented in Table 7) and a non-vine copula (presented in Table 9). The dependence measures are Kendall’s τ and the lower and upper tail dependence between domestic stock and currency returns. Blanks for tail dependence mean that both a vine and a non-vine copula show no tail dependence between the two returns.

Page 46 of 54

i cr us

Czech Rep. Euro area Hungary India Indonesia Japan Korea New Zealand Norway Philippines Poland South Africa Sweden Switzerland Taiwan Turkey UK

[-0.008, 0.128] [0.044, 0.183] [0.197, 0.319] [0.240, 0.358] [0.074, 0.217] [0.134, 0.268] [0.155, 0.281] [0.200, 0.322] [-0.113, 0.035] [-0.143, 0.008] [-0.248, -0.093] [-0.260, -0.100] [0.044, 0.167] [0.064, 0.186] [0.263, 0.382] [0.306, 0.416] [0.182, 0.302] [0.199, 0.320] [-0.412, -0.315] [-0.504, -0.421] [0.192, 0.306] [0.244, 0.355] [-0.116, 0.008] [-0.094, 0.022] [-0.024, 0.123] [0.013, 0.156] [0.176, 0.305] [0.198, 0.326] [0.090, 0.228] [0.093, 0.230] [0.099, 0.226] [0.151, 0.281] [-0.202, -0.064] [-0.162, 0.004] [-0.353, -0.228] [-0.336, -0.212] [0.229, 0.331] [0.266, 0.403] [0.333, 0.455] [0.365, 0.484] [-0.295, -0.173] [-0.182, -0.051]

Full

Pre-crisis

Lower tail Crisis

Post-crisis

Full

Pre-crisis

Upper tail Crisis

Post-crisis

[0, 0.007] [0.075, 0.230] [0, 0.091] [0, 0.141] [0, 0.001] [0.039, 0.153] [0.005, 0.113] [0.098, 0.224] [0] [0, 0.012] [0, 0.034] [0.005, 0.081] [0.067, 0.203] [0.111, 0.263] [0] [0] [0.117, 0.265] [0.196, 0.335] [0, 0.008] [0.004, 0.016] [0, 0.039] [0, 0.139] [0, 0.014] [0, 0.012] [0, 0.022] [0.008, 0.138] [0] [0.157, 0.304] [0.001, 0.161] [0.059, 0.229] [0, 0.112] [0.049, 0.197] [0, 0.006] [0.021, 0.097] [0, 0.000] [0] [0] [0, 0.124] [0.111, 0.236] [0.100, 0.271] [0] [0, 0.027]

[0, 0.030] [0, 0.230] [0, 0.050] [0, 0.114] [0] [0, 0.211] [0, 0.108] [0.027, 0.263] [0, 0.165] [0, 0.188] [0] [0] [0.014, 0.280] [0.053, 0.320] [0.053, 0.334] [0.164, 0.431] [0.139, 0.378] [0.196, 0.436] [0, 0.121] [0, 0.191] [0] [0.044, 0.286] [0] [0] [0] [0, 0.001] [0] [0.166, 0.422] [0, 0.118] [0, 0.274] [0, 0.054] [0, 0.117] [0] [0, 0.104] [0] [0] [0] [0] [0.097, 0.386] [0.024, 0.369] [0] [0]

[0] [0.202, 0.419] [0] [0, 0.312] [0, 0.001] [0, 0.126] [0, 0.018] [0, 0.170] [0] [0] [0] [0] [0, 0.213] [0.009, 0.185] [0] [0] [0, 0.212] [0, 0.303] [0] [0, 0.006] [0] [0] [0, 0.034] [0, 0.138] [0] [0] [0.037, 0.262] [0.099, 0.331] [0] [0] [0.049, 0.264] [0.073, 0.351] [0, 0.086] [0.042, 0.254] [0] [0] [0] [0] [0] [0] [0, 0.000] [0.005, 0.186]

[0] [0] [0, 0.274] [0.105, 0.397] [0] [0] [0] [0] [0] [0] [0, 0.043] [0, 0.027] [0, 0.156] [0, 0.209] [0] [0] [0.021, 0.268] [0.064, 0.336] [0] [0] [0] [0] [0] [0] [0] [0] [0] [0] [0] [0, 0.068] [0] [0] [0] [0, 0.086] [0] [0] [0] [0, 0.348] [0.175, 0.356] [0.162, 0.402] [0] [0]

[0.011, 0.151] [0.067, 0.220] [0, 0.091] [0, 0.141] [0] [0] [0] [0] [0, 0.073] [0] [0, 0.034] [0.005, 0.081] [0] [0, 0.192] [0] [0] [0.131, 0.285] [0.174, 0.324] [0, 0.008] [0.004, 0.016] [0, 0.039] [0, 0.139] [0, 0.014] [0] [0] [0.019, 0.171] [0] [0.011, 0.181] [0.021, 0.165] [0.106, 0.255] [0, 0.112] [0.049, 0.197] [0, 0.006] [0.021, 0.097] [0, 0.000] [0] [0] [0, 0.124] [0.111, 0.236] [0.100, 0.271] [0] [0, 0.027]

[0] [0] [0, 0.050] [0, 0.114] [0] [0] [0] [0] [0, 0.165] [0, 0.188] [0] [0] [0] [0] [0] [0] [0] [0, 0.245] [0, 0.121] [0, 0.191] [0] [0] [0] [0] [0] [0] [0] [0] [0, 0.118] [0, 0.202] [0, 0.054] [0, 0.117] [0] [0, 0.104] [0] [0] [0] [0] [0.097, 0.386] [0.024, 0.369] [0] [0]

[0] [0.142, 0.390] [0] [0, 0.312] [0] [0, 0.126] [0] [0] [0] [0] [0] [0] [0, 0.213] [0.009, 0.185] [0] [0] [0, 0.212] [0, 0.303] [0] [0, 0.006] [0] [0] [0, 0.034] [0] [0] [0] [0] [0.022, 0.290] [0] [0] [0] [0.073, 0.351] [0] [0.117, 0.345] [0] [0] [0] [0] [0] [0] [0] [0]

[0, 0.173] [0] [0.178, 0.437] [0.177, 0.447] [0] [0] [0] [0] [0] [0] [0, 0.043] [0, 0.027] [0] [0] [0] [0] [0.129, 0.391] [0.118, 0.392] [0] [0] [0] [0] [0] [0] [0, 0.166] [0.020, 0.208] [0] [0] [0] [0.088, 0.349] [0.134, 0.291] [0.200, 0.355] [0] [0, 0.086] [0] [0] [0] [0, 0.348] [0.175, 0.356] [0.162, 0.402] [0] [0]

M

[0.088, 0.196] [0.255, 0.353] [0.224, 0.325] [0.357, 0.470] [-0.013, 0.079] [0.080, 0.216] [0.006, 0.105] [0.077, 0.167] [0.009, 0.137] [0.095, 0.213] [0.033, 0.152] [0.158, 0.264] [0.131, 0.278] [0.245, 0.367] [0.290, 0.380] [0.384, 0.458] [0.237, 0.366] [0.297, 0.418] [-0.261, -0.162] [-0.360, -0.236] [0.289, 0.381] [0.393, 0.466] [-0.112, 0.019] [0.075, 0.153] [0.145, 0.258] [0.277, 0.375] [0.103, 0.206] [0.177, 0.283] [0.155, 0.264] [0.281, 0.368] [0.108, 0.207] [0.265, 0.388] [0.033, 0.139] [0.180, 0.283] [-0.169, -0.055] [-0.100, -0.005] [0.222, 0.326] [0.304, 0.394] [0.259, 0.361] [0.385, 0.465] [-0.025, 0.065] [0.084, 0.174]

ed

Colombia

[-0.011, 0.128] [0.063, 0.195] [0.109, 0.279] [0.241, 0.395] [-0.095, 0.041] [0.074, 0.186] [0.033, 0.149] [0.098, 0.207] [-0.061, 0.096] [-0.024, 0.132] [-0.283, -0.188] [-0.144, -0.018] [0.092, 0.214] [0.111, 0.231] [0.110, 0.238] [0.158, 0.286] [0.148, 0.260] [0.205, 0.315] [-0.129, 0.041] [-0.090, 0.087] [0.029, 0.162] [0.106, 0.217] [-0.147, 0.000] [-0.116, 0.030] [-0.102, 0.012] [-0.017, 0.089] [0.099, 0.231] [0.159, 0.282] [0.023, 0.184] [0.104, 0.237] [-0.156, -0.003] [-0.093, 0.061] [-0.205, -0.081] [-0.118, 0.035] [-0.313, -0.182] [-0.219, -0.090] [0.190, 0.296] [0.227, 0.331] [0.244, 0.392] [0.298, 0.439] [-0.289, -0.172] [-0.146, -0.012]

Post-crisis

pt

Chile

[0.043, 0.117] [0.167, 0.235] [0.211, 0.294] [0.315, 0.390] [0.006, 0.066] [0.100, 0.157] [0.078, 0.141] [0.131, 0.188] [-0.006, 0.053] [0.023, 0.087] [-0.152, -0.065] [-0.046, 0.039] [0.116, 0.179] [0.164, 0.234] [0.253, 0.315] [0.321, 0.377] [0.206, 0.272] [0.250, 0.312] [-0.271, -0.186] [-0.317, -0.235] [0.192, 0.278] [0.267, 0.346] [-0.081, 0.002] [0.032, 0.082] [0.030, 0.096] [0.115, 0.183] [0.157, 0.227] [0.184, 0.252] [0.114, 0.190] [0.176, 0.246] [0.036, 0.121] [0.138, 0.222] [-0.083, -0.001] [0.023, 0.110] [-0.248, -0.170] [-0.177, -0.107] [0.245, 0.304] [0.287, 0.364] [0.296, 0.370] [0.371, 0.441] [-0.191, -0.117] [-0.046, 0.037]

ce

Brazil

Pre-crisis

Ac

Australia

Kendall’s τ Crisis

Full

an

Table 11: 90-percent confidence intervals for dependence measures from a vine and a non-vine copula

Notes: The table reports 90-percent confidence intervals for dependence measures from a vine (presented in the first row) and from a non-vine copula (presented in the second row). The dependence measures are Kendall’s τ and the lower and upper tail dependence between domestic stock and currency returns. Confidence intervals for tail dependence are restricted to [0, 1]. When there is no tail dependence, its confidence interval is denoted as [0]. The set of two confidence intervals in bold means that they do not overlap each other.

Page 47 of 54

Table 12: Estimation results for dynamic vine copulas US stock – Local stock (Vine, first tree) Copula Parameter

US stock – Local currency (Vine, first tree) Copula Parameter

Local stock – Local currency (Vine, second tree) Copula Parameter

Local stock – Local currency (Non-vine) Copula Parameter

Australia

Student-t

1.398 (0.749) * -1.768 (2.043) 0.195 (0.136) 16.106 (7.958) **

Student-t

0.018 1.787 0.087 6.561

Clayton

-3.713 (1.469) ** -6.901 (35.538) 5.680 (8.695)

BB7

Brazil

Student-t

0.058 1.857 0.078 8.007

Clayton

0.910 (0.883) -5.810 (2.891) ** -3.823 (1.968) *

Student-t

0.382 (0.812) 0.224 (3.765) 0.098 (0.188) 10.857 (4.171) ***

Student-t

Chile

BB7

Student-t

0.794 (0.220) *** -2.083 (1.104) * 0.307 (0.144) ** 12.212 (6.608) *

90◦ rotated Gumbel

8.207 (4.026) ** -4.251 (3.131) -50.139 (20.224) **

Clayton

Colombia

Clayton

-0.731 (1.392) 2.986 (1.586) * -4.665 (4.153) 1.041 (3.042) -6.635 (12.106) -7.252 (7.005) -0.054 (3.575) -1.393 (10.635) -3.948 (5.466)

Gaussian

0.019 (0.209) 1.852 (1.136) 0.064 (0.224)

Clayton

-2.571 (2.098) 7.553 (9.661) -1.343 (4.307)

Clayton

-2.128 (1.552) 5.212 (4.970) -1.353 (2.921)

Czech Rep.

Gaussian

0.056 (0.252) 1.747 (1.104) 0.061 (0.162)

Student-t

0.193 (0.061) *** -1.990 (0.604) *** 0.917 (0.166) *** 16.614 (17.057)

0.005 (0.103) 1.828 (3.469) 0.014 (0.178)

Student-t

0.011 (0.065) 1.658 (1.104) 0.089 (0.212) 18.025 (16.721)

Euro area

Student-t

0.048 2.105 0.045 7.120

Student-t

0.238 (0.066) *** -1.995 (0.730) *** 0.799 (0.182) *** 23.810 (28.722)

Student-t

-0.002 (0.060) 1.951 (0.531) *** 0.028 (0.103) 8.693 (5.146) *

Student-t

-0.001 (0.049) 1.952 (0.443) *** 0.031 (0.106) 9.895 (5.033) **

Hungary

Gaussian

0.002 (0.166) 1.973 (0.674) *** 0.061 (0.149)

0.431 (0.109) *** -2.008 (0.828) ** 0.656 (0.147) *** 11.722 (6.814) *

BB7

-3.081 (2.584) -1.317 (52.331) 3.742 (15.666) 2.135 (11.338) -7.452 (37.635) -16.074 (34.285) 0.787 (1.129) -0.897 (4.198) 0.141 (0.217)

Student-t

0.009 (0.147) 1.937 (0.723) *** 0.038 (0.112) 12.412 (5.837) **

Gaussian

-0.007 (0.202) 2.029 (0.624) *** 0.068 (0.140)

te Student-t

ip t

-1.153 (2.209) 3.602 (2.592) -3.888 (6.635) 3.194 (3.597) -3.787 (6.975) -18.396 (12.244) 0.567 (1.017) 0.231 (3.215) 0.141 (0.214) 11.754 (4.171) ***

cr

us

an

M

Gaussian

d

(0.660) (1.249) * (0.069) (1.231) ***

Ac ce p

India

(0.425) (1.187) (0.116) (2.092) ***

(0.117) (0.596) *** (0.097) (1.830) ***

1.581 (1.867) -6.378 (5.595) -9.479 (4.409) **

Student-t

0.972 (0.653) -1.301 (2.222) 0.180 (0.152) 11.368 (5.100) **

Student-t

0.527 (0.820) -0.604 (4.041) 0.199 (0.311) 15.575 (12.358)

Gaussian

Indonesia

Clayton

-1.621 (3.074) 1.995 (13.550) -1.095 (3.362)

Student-t

0.435 (0.339) -1.025 (2.303) 0.293 (0.231) 13.943 (9.679)

Student-t

0.521 (0.407) -0.408 (1.846) 0.274 (0.204) 15.163 (10.671)

Student-t

0.620 (0.497) -0.501 (1.985) 0.274 (0.200) 9.819 (4.212) **

Japan

Gaussian

1.202 (0.882) -1.450 (2.553) 0.291 (0.214)

Student-t

-0.002 (0.072) 1.954 (0.445) *** 0.040 (0.139) 12.053 (6.624) *

Student-t

-0.560 (0.637) -0.713 (3.057) 0.183 (0.192) 6.141 (1.969) ***

90◦ rotated Gumbel

1.529 (0.811) * -1.032 (1.248) -9.493 (2.061) ***

BB7

5.755 (1.104) *** -4.339 (1.164) *** -20.353 (3.867) *** 1.090 (7.060) -2.769 (18.401) -11.904 (22.375)

Student-t

0.333 0.106 0.172 8.187

Gaussian

0.608 (0.198) *** -1.685 (1.186) 0.764 (0.274) ***

Gaussian

0.810 (0.128) *** -2.054 (0.575) *** 1.005 (0.171) ***

Korea

(0.608) (3.419) (0.292) (3.227) **

Page 48 of 54

(Continued) US stock – Local stock (Vine, first tree) Copula Parameter

US stock – Local currency (Vine, first tree) Copula Parameter

Local stock – Local currency (Vine, second tree) Copula Parameter

Local stock – Local currency (Non-vine) Copula Parameter

New Zealand

Student-t

0.440 (0.288) -0.889 (1.872) 0.374 (0.250) 8.167 (2.819) ***

Student-t

0.021 1.718 0.086 6.774

(0.110) (0.731) ** (0.112) (2.424) ***

Student-t

-0.018 (0.083) 1.729 (1.286) -0.053 (0.153) 15.170 (14.030)

Student-t

Norway

Student-t

0.102 (0.353) 1.704 (0.988) * 0.121 (0.142) 10.926 (3.582) ***

Student-t

0.003 1.944 0.030 8.451

(0.096) (0.668) *** (0.107) (4.008) **

Gaussian

0.002 (0.074) 1.970 (0.767) ** 0.018 (0.169)

Gaussian

Philippines

Clayton

0.723 (1.553) -5.174 (4.935) -3.786 (2.421)

Clayton

-2.606 (2.003) 6.578 (8.783) -0.430 (3.396)

Poland

Gaussian

0.017 (0.286) 1.942 (0.924) ** 0.072 (0.163)

Gaussian

0.418 (0.080) *** -2.001 (0.607) *** 1.076 (0.193) ***

South Africa

Gaussian

0.336 (0.490) 0.812 (1.711) 0.235 (0.274)

Student-t

0.004 1.986 0.027 6.568

Sweden

Student-t

1.769 (0.507) *** -1.685 (1.084) 0.208 (0.066) *** 6.573 (1.155) ***

Student-t

Switzerland

Student-t

1.987 (0.450) *** -2.058 (0.928) ** 0.200 (0.097) ** 13.681 (4.545) ***

Student-t

0.573 (1.019) -0.579 (4.663) -0.172 (0.325)

ip t 0.048 (0.291) 1.785 (1.314) 0.043 (0.181)

-3.026 (1.623) * 8.792 (10.747) -0.071 (1.834)

Student-t

0.031 (0.166) 1.814 (0.884) ** 0.066 (0.153) 14.160 (9.040)

Student-t

0.002 2.000 0.004 8.720

Student-t

0.093 1.246 0.193 8.151

(0.121) (0.812) (0.160) (3.458) **

0.006 (0.100) 1.929 (0.726) *** 0.033 (0.105) 10.572 (5.320) **

90◦ rotated Clayton

4.736 (4.159) -3.484 (5.765) -28.252 (15.701) *

Student-t

0.001 1.959 0.025 9.015

(0.054) (0.486) *** (0.084) (3.261) ***

0.092 (0.051) * -1.978 (0.849) ** 0.617 (0.164) *** 12.527 (11.253)

90◦ rotated BB7

0.285 (5.512) 1.956 (9.070) -10.895 (18.330) -0.377 (5.706) -0.522 (16.921) -3.274 (9.291) 0.007 (0.268) 2.008 (0.980) ** 0.018 (0.153)

90◦ rotated Gumbel

0.876 (1.122) -0.401 (2.124) -9.402 (3.047) ***

Student-t

0.120 (0.223) 1.287 (0.981) 0.275 (0.259) 15.064 (9.750)

an

Gaussian

us

cr

0.004 (0.082) 1.970 (0.516) *** 0.033 (0.164)

Gaussian

Gumbel

M

d

(0.120) (0.557) *** (0.100) (2.277) ***

te

Ac ce p

0.038 (0.139) -0.704 (9.164) 0.061 (0.201) 7.174 (2.948) **

(0.090) (0.737) *** (0.109) (5.235) *

Taiwan

Gaussian

0.612 (0.696) -0.361 (2.669) 0.312 (0.312)

Student-t

0.015 (0.098) 1.827 (0.715) ** 0.075 (0.176) 11.447 (6.904) *

Gaussian

Turkey

Student-t

0.936 (0.199) *** -2.088 (0.848) ** 0.470 (0.159) *** 24.966 (22.443)

Student-t

0.015 (0.183) 1.896 (0.784) ** 0.067 (0.144) 11.829 (6.068) *

Student-t

1.102 (1.259) -1.393 (3.925) 0.123 (0.143) 8.450 (2.202) ***

Student-t

1.423 (0.577) ** -1.902 (1.610) 0.352 (0.155) ** 9.477 (2.947) ***

UK

Student-t

0.052 (0.748) 2.072 (1.461) 0.058 (0.091) 10.105 (2.367) ***

Gaussian

0.421 (0.117) *** -2.008 (1.014) ** 0.716 (0.223) ***

90◦ rotated BB7

4.181 (2.035) ** -20.232 (22.095) -24.299 (10.571) ** -2.255 (5.824) 5.277 (22.283) -0.913 (9.441)

Student-t

-0.022 (0.054) -0.139 (2.287) 0.310 (0.341) 11.403 (9.366)

Notes: The table reports estimation results for the dynamic vine copula model. “Parameter” reports estimated coefficients in the dynamic equations (11)–(13): (ω0 , ω1 , ω2 )0 for Gaussian, Clayton, and Gumbel; (ω0 , ω1 , ω2 , ν)0 for Student’s t; and (ω0L , ω1L , ω2L , ω0U , ω1U , ω2U )0 for BB7. Standard errors are reported in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

Page 49 of 54

Table 13: Tests for stronger correlation in volatile times

Euro area Hungary India Indonesia Japan Korea New Zealand Norway

Ac ce p

Philippines

-0.136 *** (0.003) -0.118 *** (0.001) -0.148 *** (0.003) -0.062 *** (0.001) -0.031 *** (0.002) -0.090 *** (0.003) -0.069 *** (0.003) -0.070 *** (0.002) -0.040 *** (0.001) 0.039 *** (0.004) -0.070 *** (0.002) -0.070 *** (0.002) -0.078 *** (0.002) -0.048 *** (0.002) -0.116 *** (0.003) -0.088 *** (0.004) -0.108 *** (0.005) -0.050 *** (0.002) -0.055 *** (0.003) -0.078 *** (0.001) -0.146 *** (0.003) -0.078 *** (0.001)

Poland

South Africa Sweden

Switzerland Taiwan Turkey UK All

ip t

-0.026 *** (0.003) -0.011 *** (0.001) -0.006 ** (0.003) -0.003 *** (0.001) -0.033 *** (0.002) -0.014 *** (0.002) -0.026 *** (0.003) -0.024 *** (0.002) -0.010 *** (0.001) 0.001 (0.003) -0.025 *** (0.002) -0.012 *** (0.002) -0.010 *** (0.002) -0.003 * (0.001) -0.031 *** (0.002) -0.035 *** (0.003) -0.036 *** (0.004) -0.010 *** (0.002) -0.022 *** (0.003) -0.014 *** (0.001) -0.024 *** (0.002) -0.018 *** (0.001)

cr

0.059 *** (0.004) 0.005 *** (0.001) 0.012 *** (0.002) 0.017 *** (0.002) 0.037 *** (0.004) 0.026 *** (0.003) 0.036 *** (0.003) 0.010 *** (0.001) 0.013 *** (0.001) -0.052 *** (0.004) 0.022 *** (0.001) 0.058 *** (0.003) 0.028 *** (0.003) 0.004 *** (0.001) 0.041 *** (0.004) 0.040 *** (0.003) 0.027 *** (0.003) 0.007 ** (0.003) 0.034 *** (0.003) 0.038 *** (0.002) 0.020 *** (0.002) 0.023 *** (0.001)

us

Czech Rep.

0.229 *** (0.004) 0.215 *** (0.002) 0.223 *** (0.002) 0.213 *** (0.002) 0.090 *** (0.005) 0.095 *** (0.004) 0.160 *** (0.004) 0.230 *** (0.001) 0.174 *** (0.001) -0.145 *** (0.005) 0.212 *** (0.002) 0.171 *** (0.004) 0.150 *** (0.003) 0.152 *** (0.001) 0.179 *** (0.005) 0.239 *** (0.004) 0.153 *** (0.003) 0.023 *** (0.003) 0.169 *** (0.004) 0.274 *** (0.003) 0.141 *** (0.003) 0.159 *** (0.001)

0.009 *** (0.001) 0.030 *** (0.002) 0.008 *** (0.003) 0.009 *** (0.001) 0.021 *** (0.001) 0.015 *** (0.001) 0.036 *** (0.003) 0.011 *** (0.001) 0.003 *** (0.000) 0.011 *** (0.001) 0.019 *** (0.003) 0.033 *** (0.002) 0.028 *** (0.002) 0.002 * (0.001) 0.022 *** (0.002) 0.019 *** (0.002) 0.016 *** (0.001) 0.008 *** (0.001) 0.018 *** (0.001) 0.020 *** (0.002) 0.016 *** (0.001) 0.017 *** (0.001)

an

Colombia

0.393 *** (0.001) 0.417 *** (0.002) 0.269 *** (0.003) 0.200 *** (0.001) 0.261 *** (0.001) 0.565 *** (0.002) 0.285 *** (0.003) 0.319 *** (0.001) 0.173 *** (0.000) 0.384 *** (0.001) 0.306 *** (0.004) 0.202 *** (0.002) 0.428 *** (0.002) 0.209 *** (0.001) 0.346 *** (0.002) 0.358 *** (0.002) 0.509 *** (0.001) 0.506 *** (0.001) 0.312 *** (0.001) 0.276 *** (0.002) 0.554 *** (0.002) 0.346 *** (0.001)

M

Chile

Local stock – Local currency Eq. (15) c b

d

Brazil

US stock – Local currency Eq. (14) c b

te

Australia

US stock – Local stock Eq. (14) c b

Notes: The table reports estimation results for Eqs.(14) and (15). The last row shows the results estimated by pooling data across economies. Standard errors are reported in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

Page 50 of 54

ip t

10

9

cr

8

us

7

6

an

5

4

M

3

1

05

07

09

11

13

15

17

Ac ce p

0 03

te

d

2

Figure 1: US stock market volatility. The figure presents a time-series plot of conditional standard deviation of the US stock returns, σ ˆ1t , which is computed from the marginal model of the US stock returns.

Page 51 of 54

Australia

Brazil

1

0.5

0.5

0.5

0

0

0

-0.5

-0.5

-0.5

-1

-1

-1

1

0

0 -0.5

-1

-1 03 05 07 09 11 13 15 17

Hungary

0

-0.5 -1

India

1

0.5

0.5

0

0

-0.5

-0.5

-1

-1

1

0.5

03 05 07 09 11 13 15 17

03 05 07 09 11 13 15 17

Japan

03 05 07 09 11 13 15 17

1 0

-0.5 -1

03 05 07 09 11 13 15 17 1

Korea

03 05 07 09 11 13 15 17 1 0.5

0

0

-0.5

-0.5

-1

-1

te

d

0.5

0 -1

03 05 07 09 11 13 15 17

03 05 07 09 11 13 15 17

Philippines

-0.5

-0.5

-0.5

-1

-1

-1

1 0.5 0 -0.5 -1

1

1 0.5 0

South Africa

0.5

0

0

-0.5

-0.5

-1

-1

1

03 05 07 09 11 13 15 17

1

Sweden

1 0.5

0

0

03 05 07 09 11 13 15 17 1

Turkey

1

0.5

0

0

0

-0.5

-0.5

-0.5

-1

-1

-1 03 05 07 09 11 13 15 17

Switzerland

03 05 07 09 11 13 15 17

0.5

03 05 07 09 11 13 15 17

Poland

03 05 07 09 11 13 15 17

0.5

03 05 07 09 11 13 15 17

Taiwan

1

0.5

03 05 07 09 11 13 15 17

New Zealand

03 05 07 09 11 13 15 17

Ac ce p

Norway

Indonesia

0.5

0.5 -0.5

Euro area

us

0.5

-0.5

1

1

an

0.5

03 05 07 09 11 13 15 17

Czech Republic

M

1

Colombia

03 05 07 09 11 13 15 17

cr

03 05 07 09 11 13 15 17

Chile

1

ip t

1

UK

0.5

03 05 07 09 11 13 15 17

Figure 2: Dynamic Kendall’s τ correlations between the US and local economies’ stock returns. Page 52 of 54

Australia

Brazil

1

0.5

0.5

0.5

0

0

0

-0.5

-0.5

-0.5

-1

-1

-1

1

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0 -0.5

-1

-1 03 05 07 09 11 13 15 17

Hungary

0

-0.5 -1

India

1

0.5

0.5

0

0

-0.5

-0.5

-1

-1

1

0.5

03 05 07 09 11 13 15 17

03 05 07 09 11 13 15 17

Japan

03 05 07 09 11 13 15 17

1 0

-0.5 -1

03 05 07 09 11 13 15 17 1

Korea

03 05 07 09 11 13 15 17 1 0.5

0

0

-0.5

-0.5

-1

-1

te

d

0.5

0 -1

03 05 07 09 11 13 15 17

03 05 07 09 11 13 15 17

Philippines

-0.5

-0.5

-0.5

-1

-1

-1

1 0.5 0 -0.5 -1

1

1 0.5 0

South Africa

0.5

0

0

-0.5

-0.5

-1

-1

1

03 05 07 09 11 13 15 17

1

Sweden

1 0.5

0

0

03 05 07 09 11 13 15 17 1

Turkey

1

0.5

0

0

0

-0.5

-0.5

-0.5

-1

-1

-1 03 05 07 09 11 13 15 17

Switzerland

03 05 07 09 11 13 15 17

0.5

03 05 07 09 11 13 15 17

Poland

03 05 07 09 11 13 15 17

0.5

03 05 07 09 11 13 15 17

Taiwan

1

0.5

03 05 07 09 11 13 15 17

New Zealand

03 05 07 09 11 13 15 17

Ac ce p

Norway

Indonesia

0.5

0.5 -0.5

Euro area

us

0.5

-0.5

1

1

an

0.5

03 05 07 09 11 13 15 17

Czech Republic

M

1

Colombia

03 05 07 09 11 13 15 17

cr

03 05 07 09 11 13 15 17

Chile

1

ip t

1

UK

0.5

03 05 07 09 11 13 15 17

Figure 3: Dynamic Kendall’s τ correlations between the US stock and local economies’ currency returns. Page 53 of 54

Australia

Brazil

1

0.5

0.5

0.5

0

0

0

-0.5

-0.5

-0.5

-1

-1

-1

1

0

0 -0.5

-1

-1 03 05 07 09 11 13 15 17

Hungary

0

-0.5 -1

India

1

0.5

0.5

0

0

-0.5

-0.5

-1

-1

1

0.5

03 05 07 09 11 13 15 17

03 05 07 09 11 13 15 17

Japan

03 05 07 09 11 13 15 17

1 0

-0.5 -1

03 05 07 09 11 13 15 17 1

Korea

03 05 07 09 11 13 15 17 1 0.5

0

0

-0.5

-0.5

-1

-1

te

d

0.5

0 -1

03 05 07 09 11 13 15 17

03 05 07 09 11 13 15 17

Philippines

-0.5

-0.5

-0.5

-1

-1

-1

1 0.5 0 -0.5 -1

1

1 0.5 0

South Africa

0.5

0

0

-0.5

-0.5

-1

-1

1

03 05 07 09 11 13 15 17

1

Sweden

1 0.5

0

0

03 05 07 09 11 13 15 17 1

Turkey

1

0.5

0

0

0

-0.5

-0.5

-0.5

-1

-1

-1 03 05 07 09 11 13 15 17

Switzerland

03 05 07 09 11 13 15 17

0.5

03 05 07 09 11 13 15 17

Poland

03 05 07 09 11 13 15 17

0.5

03 05 07 09 11 13 15 17

Taiwan

1

0.5

03 05 07 09 11 13 15 17

New Zealand

03 05 07 09 11 13 15 17

Ac ce p

Norway

Indonesia

0.5

0.5 -0.5

Euro area

us

0.5

-0.5

1

1

an

0.5

03 05 07 09 11 13 15 17

Czech Republic

M

1

Colombia

03 05 07 09 11 13 15 17

cr

03 05 07 09 11 13 15 17

Chile

1

ip t

1

UK

0.5

03 05 07 09 11 13 15 17

Figure 4: Dynamic Kendall’s τ correlations between stock and currency returns in local economies. The blue and the red lines represent the dynamic correlation estimated from a vine and a non-vine copula, respectively. Page 54 of 54