Volatility and correlation in international stock markets and the role of exchange rate fluctuations

Int. Fin. Markets, Inst. and Money 17 (2007) 25–41

Volatility and correlation in international stock markets and the role of exchange rate fluctuations Kyung-Chun Mun ∗ Division of Business and Accountancy, Truman State University, Kirksville, MO 63501, USA Received 21 April 2005; accepted 9 August 2005 Available online 5 October 2005

Abstract This paper develops a direct, explicit model for the role of exchange rate fluctuations in international stock markets and examines how and to what extent volatility and correlations in equity markets are influenced by exchange rate fluctuations. Evidence presented in this paper indicates that a higher foreign exchange rate variability mostly increases local stock market volatility but decreases volatility for the US stock market. The extent to which stock market volatility is influenced by foreign exchange variability is greater for local markets than for the US market, due to the fact that exchange rate changes are more strongly correlated with local equity market returns than the US market returns. We find that a higher exchange rate fluctuation marginally decreases the US/local equity market correlation. While exchange rate fluctuations held a relatively large fraction of the variation in local stock market returns, there was no significant influence on the US/local equity market correlation. © 2005 Elsevier B.V. All rights reserved. JEL classification: F30 Keywords: Exchange rate fluctuations; Conditional volatility; Conditional correlation

1. Introduction The return from a foreign asset investment is comprised of the return on the foreign asset and the exchange rate fluctuation due to the fact that investing in foreign stock markets entails exposure to exchange rate risk. It is, thus, theoretically apparent that the US dollar return of a foreign stock investment is automatically influenced by exchange rate movements because ∗

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the conversion process of local-currency returns into US dollar values has already introduced a direct link between exchange rates and the US dollar returns. Yet, empirical findings provide conflicting results for the linkage between exchange rate movements and stock market returns. Some researchers claim that exchange rate movements provide little or no explanation for US investors in making investment decisions (see Jorion, 1990, 1991; Amihud, 1993; Bartov and Bodnar, 1994; Bernard and Galati, 2000; and Griffin and Stulz, 2001), while others argue that stock returns in US dollars are significantly affected by exchange rate fluctuations (Roll, 1992; Ferson and Harvey, 1993; Dumas and Solnik, 1995; Chow et al., 1997; Choi et al., 1998; De Santis and Gerard, 1998; Doukas et al., 1999; and Patro et al., 2002). Although models and empirical methodologies vary widely, these studies explain the linkage between stock and foreign exchange markets using first moments in their analysis and thus ignore an important role of second moments in the linkage. A good understanding of the role of second moments in international stock and foreign exchange markets is important for international investors because any change in variances and cross-market correlations in international stock markets due to exchange rate movements makes it more difficult for them to select an optimal investment strategy. Few studies focus on the linkage between stock and foreign exchange markets using second moments. Bartov et al. (1996) examine the relationship between exchange rate variability and stock return volatility for US multinational firms and find that there is a significant positive linkage between the two volatilities. Karolyi and Stulz (1996) examine the impact of a foreign exchange shock on the volatility and US/Japanese stock market correlation and find that a foreign exchange shock has a significantly positive impact on the volatility and US/Japanese market correlation. Bodart and Reding (1999) examine the impact of German exchange rate fluctuations on the stock market volatility and the correlation between the German stock market and a selected group of European markets (France, Belgium, UK, Sweden, and Italy). They find that there is no strong evidence that a higher exchange rate variability increases stock market volatility. They also find that sample markets’ correlation with the German market declined when exchange rates were volatile, suggesting that a higher exchange rate variability for the German mark implied a lower cross-market correlation. While these studies examine the effect of exchange rate fluctuations on international stock market fundamentals, they fail to quantitatively measure the extent to which the stock market fundamentals can be accounted for by exchange rate fluctuations. This paper presents a direct, explicit model for the role of exchange rate fluctuations in international stock market fundamentals and examines how and to what extent the equity market volatility and cross-market correlations are influenced by exchange rate fluctuations. In our model, the market volatility as well as the cross-market correlation is decomposed into fractions that are attributable to local market returns and exchange rate fluctuations, so that the role of exchange rate fluctuations can be explicitly identified relative to local stock market returns. To achieve the objective, the extent to which international stock market fundamentals are attributable to exchange rate fluctuations is quantitatively measured and tested for eight mature markets in relation to the US market (UK, France, Germany, Italy, Australia, Hong Kong, Japan, and Singapore). We find that a higher exchange rate variability mostly increases local equity market volatility but decreases the US stock market volatility. Local stock markets are influenced to a larger extent by the exchange rate variability than the US market, due to the fact that exchange rate changes are more strongly correlated with local equity market returns than the US market returns. We also find that the exchange rate fluctuation has a marginally negative impact on the US/local equity market correlation. The rest of the paper is organized as follows. Section 2 models the proportion of the stock market volatility/cross-market correlations that can be attributable to exchange rate fluctuations.

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Section 3 provides a description of the data and fundamental statistics including the conditional volatility and cross-market correlations. Section 4 presents empirical results based on our model and the forecast error variance decomposition. Section 5 presents statistical tests for the role of exchange rate fluctuations. Conclusions are provided in Section 6. 2. The model The US dollar returns are widely used in studies on international stock markets because they are more useful from the foreign investor’s perspective and can provide consistence in making comparisons of inter-country equity returns (see, for example, Roll, 1992; Dumas and Solnik, 1995; Harvey, 1995; Karolyi and Stulz, 1996; De Santis and Gerard, 1998; Ng, 2000; and Forbes and Rigobon, 2002 among others). In line with Roll (1992), we first describe the US dollar return in the currency j stock market, RUSD jt , as the following: = ln Pjt Sjt − ln Pjt−1 Sjt−1 = (ln Pjt − ln Pjt−1 ) + (ln Sjt − ln Sjt−1 ) RUSD jt = RLCD + Zjt jt

(1)

where RLCD ≡ ln Pjt −ln Pjt−1 = the local-currency denominated (LCD) index return in the curjt rency j equity market at time t; Pjt = the price index in the currency j equity market at time t; Zjt ≡ ln Sjt −ln Sjt−1 = the appreciation rate of local currency j at time t relative to the US dollar. Zjt is also the exchange rate fluctuation (change) for currency j; Sjt = the exchange rate for currency j (US dollars per unit of local currency) at time t. Eq. (1) represents that the US dollar return on a local market index is comprised of the localcurrency equity return and the exchange rate fluctuation. The proportion of the US dollar local market volatility that can be attributable to exchange rate fluctuations, ψ, can be directly measured as: ψ =1−

Var(RLCD jt ) Var(RUSD jt )

=

Var(Zjt ) + 2Cov(RLCD jt , Zit ) Var(RUSD jt )

(2)

LCD LCD since Var(RUSD jt ) = Var(Rjt ) + Var(Zjt ) + 2Cov(Rjt , Zjt ). Eq. (2) indicates that the proportion of local equity market volatility that can be explained by exchange rate fluctuations is determined by the volatility in foreign exchange markets and the covariance risk between local-currency equity returns and exchange rate changes. The important feature of this representation is that it is not necessarily the case that a higher exchange rate volatility implies a higher local market volatility, due to the covariance term that can be negative. We now examine the correlation coefficient between the US dollar local return, RUSD jt , and the US market return, Rt . The correlation coefficient is written as:

ρ(RUSD jt , Rt ) = 

Cov(RLCD Cov(RUSD jt , Rt ) jt , Rt ) + Cov(Zjt , Rt )  = √ √ Var(RUSD Var(RUSD jt ) Var(Rt ) jt ) Var(Rt )

Breaking up the right hand side of Eq. (3) into two parts and manipulating, we obtain:     Var(RLCD Var(Zjt ) jt ) USD LCD  + ρ(Zjt , Rt ) ρ(Rjt , Rt ) = ρ(Rjt , Rt ) USD Var(Rjt ) Var(RUSD jt )

(3)

(4)

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The proportion of the correlation coefficient between the US and local market returns that can be attributable to exchange rate fluctuations, Φ, can be measured as:  ρ(Zjt Rt ) Var(Zjt ) (5) Φ= USD ρ(Rjt , Rt ) Var(RUSD jt ) Due to the empirical evidence that ρ(RUSD jt , Rt ) > 0 for all of the sample countries, the values of Φ are essentially determined by the correlation of US equity market returns with local currency values and the  volatility ratio of the foreign exchange market relative to the local equity market,  Var(Zjt )/ Var(RUSD jt ). 3. Data and methodology 3.1. Data The data set we analyze is the weekly series for the period from 8 January 1990 to 5 September 2003, providing a sample size of 714 observations. Weekly data are used to avoid the problems of non-synchronous trading between the US and other sample countries. The data consist of closing exchange rates and stock market indices of eight countries: UK, France, Germany, Italy, Australia, Hong Kong, Japan, and Singapore. These countries are sampled because stock markets in these countries represent the major segments of international stock markets. The stock market indices used are the S&P 500 Index, the FTSE 100 of the UK, the Paris CAC of France, the DAX of Germany, the Milan Stock Exchange MIB of Italy, the ASX All Index of Australia, the Hang Seng Index of Hong Kong, the Tokyo Stock Exchange Price Index (TOPIX), and the Stock Exchange of Singapore All Share Index. All these stock market indices are value-weighted indices and collected from the Global Financial Data (GFD) base. Weekly index returns are computed as the logarithmic difference of weekly stock indexes. Exchange rates are expressed as US dollar per unit of local currency and the logs of the nominal rates, which are also collected from the GFD database. To visually observe the dynamics of sample data, time series movements of local stock market indexes and exchange rates are plotted in Fig. 1. The values for the first week of January of 1990 are set to 100 as the base point. The solid dark line represents local market indexes and the lighter line represents exchange rates. Fig. 1 shows that the stock market indexes of European countries (UK, France, Germany, and Italy) moved by and large in the same direction and trended upward from March 1995 until the bull market reached its apex in the first half of 2000 due largely to the exuberance in the technology-sector stocks. In the wake of the Asian financial crisis that began in Thailand in the summer of 1997, Hong Kong and Singapore concomitantly experienced a dramatic decline in equity values. All the sample countries suffered an extreme bear market during August of 2002 when the US stock market rapidly fell due to the declining confidence by investors coupled with financial scandals that have involved accounting irregularities by some major companies. Table 1 reports the means, standard deviations, and correlations with the US market for weekly local market returns. Mean equity market returns are positive although statistically insignificant for all the sample countries with the exception of Japan for which mean returns are insignificantly negative. Table 1 also reveals that the local equity return is strongly positively correlated with local currency values (except for Hong Kong), indicating that the local equity return increases as the

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Fig. 1. Market indices & FX rates.

29

30

UK

France

Germany

Italy

Australia

Hong Kong

Japan

Equity market Mean (%) S.D.

0.0858 (0.76) 0.0300

0.0718 (0.61) 0.0314

0.0879 (0.69) 0.0338

0.0296 (0.23) 0.0338

0.1170 (1.47) 0.0212

0.1934 (1.26) 0.0411

−0.1127 (−0.80) 0.0144 (0.11) 0.0375 0.0345

FX market Mean (%) S.D.

0.0061 (0.12) 0.0138

−0.0052 (−0.09) −0.0076 (−0.14) −0.0467 (−0.84) 0.0268 (0.54) 0.0146 0.0151 0.0149 0.0133

0.0002 (0.10) 0.0006

0.0295 (0.48) 0.0164

0.5645 [0.000]

0.5824 [0.000]

0.5706 [0.000]

0.4036 [0.000]

0.3303 [0.000]

0.4457 [0.000] 0.2305 [0.000]

0.3798 [0.000]

0.6117 [0.000]

0.2097 [0.000]

0.2734 [0.000]

0.3310 [0.000]

0.4778 [0.000]

0.0259 [0.246] 0.5533 [0.000]

0.5061 [0.000]

−0.1321 [0.000]

−0.1052 [0.000]

−0.1525 [0.000] 0.0145 [0.352] −0.0333 [0.179]

Return correlation US and local equity market Local equity and FX market US equity and FX market

−0.105 [0.003] −0.1463 [0.000]

Numbers in parentheses are t-statistics and numbers in brackets are p-values.

Singapore

0.0106 (0.36) 0.0078

−0.0435 [0.126]

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Table 1 Summary statistics

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local currency appreciates and vice versa. In contrast, the US equity return is weakly negatively correlated with local currency values. 3.2. Methodology In this section, dynamic movements of the stock market volatility and cross-market correlations are examined within an exponential GARCH (EGARCH) framework. The conditional volatility of an individual sample market is obtained from the time path of standard deviation of residuals for which individual market returns are regressed on constants within an EGARCH framework developed by Nelson (1991).1 The model has an error process that is conditionally heteroskedastic with time-varying variance given by: 2 ln(σt2 ) = a0 + a1 (|λt−1 | − E|λt−1 | + a2 λt−1 ) + a3 ln(σt−1 )

(6)

where σt2 is the conditional variance of residual; λt is the standardized residual; a0 , a1 , a2 , and a3 are parameters. Similarly, the conditional correlation of an individual market return with the US return is obtained from the time path of conditional covariance matrix of residuals by estimating the following format of a bivariate EGARCH model: 2  2 2 ln(σj,t−1 ) = ci + ci,j fj (λj,t−1 ) + di ln(σi,t−1 ) for ri,t = αi + εi,t for i = 1, 2; j=1

i, j = 1, 2;

fj (λj,t−1 ) = |λj,t−1 | − E|λj,t−1 | + δj λj,t−1

σij,t = ρij,t σi,t σj,t

for 1, 2 and i = j.

for j = 1, 2; (7)

where ri,t , = the return at time t for market i (i = 1, 2 where 1 = the local market and 2 = the US market); αi = the conditional mean return for market i; and λi,t = εi,t /σ i,t . Time series dynamics of conditional volatility in equity and foreign exchange returns are plotted in Fig. 2 by country. The solid dark line represents the volatility for equity returns and the lighter line represents the exchange rate volatility. In Fig. 2, one can discern certain important events feeding through into the exchange rate volatility sequences. There was, for instance, a sharp increase in the exchange rate volatility for the UK pound and the Italian lira during the currency crisis of September 1992 when Italy and the UK pulled out of the exchange rate mechanism (ERM) as the Bundesbank forced up German interest rates. The 1997–1998 Asian currency crisis was another incident that provided a drastic increase in the exchange rate volatility for countries like Australia, Japan, and Singapore. Fig. 3 exhibits the conditional correlation of an individual local market return with the US market return by country. The correlation coefficient of an individual equity market return with the US market return is clearly time varying, with a fair amount of switching between positive and negative. Equity returns between the US and local markets are positively correlated most of the time, and the correlation coefficient for most of the sample countries appears to have reached its apex during August of 2002 when the equity markets were extremely bearish. This situation implies worsening investment conditions for internationally diversified investors because the generally increased volatility and market correlations lead to an erosion of the expected gains from international diversification. 1 It is widely known that negative stock returns are followed by higher volatility than positive returns of an equal sample size, the so-called asymmetric effect of stock returns (see, for example, Black, 1976; Nelson, 1991; and Koutmos and Booth, 1995). The asymmetric effect of innovation on volatility can be effectively captured by the EGARCH model.

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Fig. 2. Conditional volatility.

4. Empirical results 4.1. The direct model In this section, we directly examine the role of exchange rate fluctuations in international equity market fundamentals using both unconditional and conditional values for ψ

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Fig. 3. Conditional correlations.

and Φ. Unconditional values for ψ and Φ are obtained by substituting appropriate unconditional moments into Eqs. (2) and (5). Conditional values for ψ and Φ are obtained from the time path of residual variances and covariances for which the variables in Eqs. (2) and (5) are regressed on constants within a multivariate EGARCH process similar to Eqs. (6) and (7).

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Table 2 Volatility and correlation attributable to exchange rate fluctuations Country

UK France Germany Italy Australia Hong Kong Japan Singapore

Volatility attributable to exchange rate fluctuations (ψ)

International correlations attributable to exchange rate fluctuations (Φ)

Unconditional (%)

Unconditional (%)

Conditional (%)

−8.58 −1.73 −0.32 −1.48 −18.89 −0.049 −1.32 −0.36

−7.99 (−10.39)** −0.69 (−1.04) −0.73 (−0.80) −0.54 (−0.55) −15.51 (−15.73)** −0.173 (−0.80) −1.04 (−1.10) −0.64 (−0.95)

19.44 −1.10 0.16 5.00 10.92 0.028 15.91 9.30

Conditional (%) (37.91)**

18.85 −0.62 (−1.36) 0.24 (0.88) 4.98 (17.81)** 11.18 (31.00)** 0.043 (0.72) 16.38 (62.69)** 3.65 (14.59)**

Numbers in parentheses are t-statistics. * Statistical significance at the 5% level. ** Statistical significance at the 1% level.

Table 2 reports the volatility and correlation coefficient accounted for by exchange rate fluctuations for both unconditional and conditional data. Conditional values of ψ are mostly significant and positive, suggesting that a higher exchange rate volatility implies a higher local equity market volatility. Exceptions are Germany, France, and Hong Kong for which conditional values of ψ are insignificant, indicating that there is no measurable influence of exchange rate fluctuations on the local stock market volatility. Overall, conditional data support unconditional data with strong statistical significance for most of the sample countries. Table 2 also shows that a higher exchange rate fluctuation has a marginally negative impact on the US/local equity market correlation. A possible explanation for this result would be that a downward movement of local stock markets, for instance, will trigger international investors to seek better returns in the US stock markets, causing outflow of funds from local markets, thus depreciating the local currency (or appreciating the US dollar). This implies that depreciating local currencies are associated with rising US stock markets, suggesting a negative impact of exchange rate fluctuations on the US/local equity market correlation. To visually observe the dynamics of ψ and Φ, we plot time series movements of conditional volatility and correlation coefficients that can be attributable to exchange rate fluctuations in Figs. 4 and 5, respectively. Fig. 4 reveals that the values of ψ are in most cases positive although they often switch between positive and negative, implying that the exchange rate fluctuation can make international investors more often worse off than better off by adding an additional source of risk into their portfolio, namely exchange rate risk. On the other hand, it appears that countries like France, Germany, and Hong Kong do not exhibit strong evidence of the positive influence of exchange rate fluctuations. The plots in Fig. 5 reveal that the values of Φ are time-varying similar to those of ψ. This is not wholly unexpected, given that the correlation could be driven by both local market return factors and exchange rate fluctuations whose influence changes over time. 4.2. Forecast error variance decomposition While the previous section of this paper is primarily focused on the direct and explicit measurement of the role of exchange rate fluctuations, it would be important to gain an indication of the extent to which exchange rate fluctuations are important in explaining the time series behavior of volatility and cross-market correlations. The relative importance of the exchange rate

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Fig. 4. Volatility attributable to FX fluctuations.

fluctuation is often estimated using the vector autoregression (VAR)-based forecast error variance decomposition (see, for example, Campbell and Ammer, 1993; Tse et al., 1996; and Kim, 2002 among others). We thus consider a VAR system of two variables, denoted by the column vector USD   xt = [Zjt , RUSD jt ] or [Zjt , ρ(Rjt , Rt )] . The VAR system is specified in the following form: xt = A0 + A1 xt−1 + A2 xt−2 + . . . + Ap xt−p + et

(8)

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Fig. 5. Correlations attributable to FX fluctuations.

where A0 = the (2 × 1) vector of constants; Ai = the (2 × 2) matrices of coefficients (i = 1, 2, . . ., p); and et = the error vector. One lag is chosen in the estimation as this is the lag length that minimizes the Schwartz Baysian criterion (SBC). A Choleski decomposition is used to orthogonalize the underlying errors using the ordering as defined above. Placed first in the ordering, the exchange rate change is implicitly assumed to be exogenous in the VAR.

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Table 3 Forecast error variance decomposition for local market returns and international correlations Country

Horizon (weeks)

Local equity market returns

International correlations

S.E.

Own shock (%)

FX shock (%)

S.E.

Own shock (%)

FX shock (%)

UK

1 2 4 8

0.0299 0.0300 0.0300 0.0300

61.545 61.644 61.648 61.648

38.455a 38.356a 38.352a 38.352a

0.0083 0.0117 0.0144 0.0164

96.717 96.771 96.797 96.809

3.283a 3.229a 3.203a 3.191a

France

1 2 4 8

0.0311 0.0314 0.0314 0.0314

95.705 95.785 95.786 95.786

4.295 4.215 4.214 4.214

0.0464 0.0646 0.0884 0.1172

98.907 98.704 98.616 98.573

1.093 1.296 1.384 1.427

Germany

1 2 4 8

0.0336 0.0338 0.0338 0.0338

96.819 96.768 96.767 96.767

3.181 3.232 3.233 3.233

0.0085 0.0118 0.0159 0.0206

98.482 98.685 98.736 98.761

1.518 1.315 1.264 1.239

Italy

1 2 4 8

0.0337 0.0338 0.0338 0.0338

89.065 88.523 88.523 88.523

10.935a 11.477a 11.477a 11.477a

0.0075 0.0102 0.0133 0.0162

99.194 99.196 99.197 99.198

0.806 0.804 0.803 0.802

Australia

1 2 4 8

0.0211 0.0211 0.0211 0.0211

77.166 77.251 77.252 77.252

22.834a 22.749a 22.748a 22.748a

0.0089 0.0102 0.0106 0.0106

95.995 95.851 95.606 95.586

4.005a 4.149a 4.394a 4.414a

Hong Kong

1 2 4 8

0.0408 0.0411 0.0411 0.0411

99.912 99.727 99.714 99.714

0.088 0.273 0.286 0.286

0.0059 0.0081 0.0110 0.0143

99.908 99.944 99.959 99.966

0.092 0.056 0.041 0.034

Japan

1 2 4 8

0.0372 0.0375 0.0375 0.0375

69.866 70.024 70.026 70.026

30.134a 29.976a 29.974a 29.974a

0.0104 0.0115 0.0118 0.0118

99.884 99.814 99.801 99.800

0.116 0.186 0.199 0.200

Singapore

1 2 4 8

0.0344 0.0345 0.0345 0.0345

74.541 74.667 74.667 74.667

25.459a 25.333a 25.333a 25.333a

0.0059 0.0081 0.0110 0.0141

99.553 99.711 99.780 99.814

0.447 0.289 0.220 0.186

a

Indicates statistical significance at the 1% level.

Table 3 presents the decomposition of k-step ahead forecast error variances (k = 1, 2, 4, and 8) of the local market return as well as its correlation with the US market return into fractions that are attributable to its own innovations and to innovations in exchange rate changes. The column for local market returns reveals that an exchange rate innovation accounted for a relatively large portion of variations in the local market return although the extent varied across countries. For example, at an 1-step horizon, the proportion of forecast error variance in the local market return that can be explained by exchange rate fluctuations is 38.5% for the UK, 30.1% for Japan, 25.5% for Singapore, and 22.83% for Australia, all of which are statistically significant.

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This suggests that exchange rate fluctuations are important in explaining the local equity market volatility. Contrary results are presented for the variance decomposition of the correlation of local market returns with US market returns. For example, innovations in exchange rate changes account for only 4.01% of the forecast error variances of Australia’s correlation with the US market at an 1-step horizon, 3.28% for the UK, 1.5% for Germany, and 1.1% for France. These values are significant only for the UK and Australia but are insignificant for the rest of the sample countries, suggesting that cross-market correlations cannot be explained by the exchange rate fluctuation to a meaningful extent (except for the UK and Australia). 5. Statistical tests for the effect of exchange rate fluctuations Testing for the effect of exchange rate fluctuations on the volatility and cross-market correlations is conducted using Eq. (7) with the following variance-covariance dynamics: fj (λj,t−1 ) = |λj,t−1 | − E|λj,t−1 | + δj λj,t−1 + dj |Zt−1 |, fi (λi,t−1 ) = |λi,t−1 | − E|λi,t−1 | + δi λi,t−1 + di |Zt−1 |, σij,t = [ρit,t + dij |Zt−1 |](σi,t σj,t )

(9)

where pij,t is the correlation coefficient between the local and US market returns (i = the local market and j = the US market); |Zt−1 | is the exchange rate fluctuation. Table 4 provides for the parameter estimates for the variance-covariance process with t-statistics and the test results for the hypothesis that exchange rate variability has no impact on the volatility and/or cross-market correlations. The t-statistics for the coefficient di are significantly positive at the 5% level for most of the sample countries, suggesting that a higher exchange rate variability increases local equity market volatility. On the other hand, the coefficient dj is significantly negative for most of the sample countries, implying that a higher exchange rate variability decreases the US equity market volatility. This result provides a strong evidence for the role of exchange rate fluctuations in the US equity market volatility. Interestingly, the values of the coefficient di are all greater in an absolute value than those of the coefficient dj , indicating that the exchange rate variability affects the local equity market volatility to a greater extent than the US market volatility. This can be attributed to the fact that exchange rate changes are more strongly correlated with the local equity market than the US market (see Table 1). Table 4 also provides for the parameter estimates with t-statistics for the effect of the exchange rate variability on the cross-market correlation of equity returns. The values of the coefficient dij in Eq. (9) are all negative, indicating that a higher exchange rate variability decreases the cross-market correlation between the US and local markets. Test results for the hypothesis that the exchange rate variability has no impact on the volatility and/or cross-market correlations are provided in the last two columns of Table 4. The hypothesis of no impact of exchange rate variability on the market volatility, i.e., di = dj = 0, is strongly rejected for all the sample countries: the computed χ2 statistics with two degrees of freedom ranges from 9.50 (for Hong Kong) to 25.86 (for Germany). The null hypothesis that the exchange rate variability has no impact on the volatility and US/local market correlations, i.e., di = dj = dij = 0, is also strongly rejected for all sample countries. This rejection is ascribable mostly to the high χ2 values from the previous hypothesis (di = dj = 0).

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Table 4 Effect of FX fluctuations on stock market volatility and correlations with US market Country

di

dj

dij

H0 : di = dij = 0; χ2 (2)

H0 : di = dj = dij = 0; χ2 (3)

UK France Germany Italy Australia Hong Kong Japan Singapore

0.0450 (8.27)** −0.0018 (1.63) 0.0019 (0.22) 0.0153 (3.29)** 0.0203 (5.57** 0.0074 (1.35) 0.0543 (7.31)** 0.0549 (6.86)**

−0.0006 (−1.96)* −0.0017 (−21.0)** −0.0015 (−23.6)** −0.0007 (−2.77)** −0.0020 (−2.87)** 0.0012 (1.32) −0.0004 (−1.07) −0.0015 (−1.59)

−0.0869 (−3.00)** −0.0266 (−1.53) −0.0276 (−1.73) −0.0193 (−1.45) −0.0624 (−2.66)** −0.0037 (−0.74) −0.0131 (−0.31) −0.0083 (−0.23)

19.11** 15.24** 25.86** 18.52** 24 99** 9.50** 17.68** 20.71**

36.63** 21.19** 30.98** 19.36** 34.31** 14.52** 29.93** 26.31**

Numbers in parentheses are t-statistics. The following variance-covariance dynamics is estimated using Eq. (7) to test the effect of FX fluctuations on the local equity market volatility and correlations with the US market: fj (λj,t−1 )=|λj,t−1 | − E|λj,t−1 | + δj λj,t−1 + dj |Zt−1 |,

fi (λi,t−1 )=|λi,t−1 | − E|λi,t−1 | + δi λi,t−1 + di |Zt−1 |,

σij,t = [ρij,t + dij |Zt−1 |](σi,t σj,t ) where |Zt−1 | is the exchange rate fluctuation. The estimation of coefficients di (dj ) should capture the effect of exchange rate fluctuations on the conditional variance of the local (US) market returns. The estimation of coefficient dij should capture the effect of exchange rate fluctuations on conditional correlations. The hypothesis that a higher FX volatility implies a higher local (US) stock market volatility will be accepted if the coefficient di (dj ) is statistically significantly positive. Similarly, the hypothesis that a higher FX volatility implies a higher correlation will be accepted if the coefficient, dij , is statistically significantly positive. * Statistical significance at the 5% level. ** Statistical significance at the 1% level.

6. Conclusions In this paper we investigate how and to what extent international stock market volatility and cross-market correlations are influenced by exchange rate fluctuations. To achieve our objective, we develop a model that quantitatively captures the role of exchange rate fluctuations in international stock market fundamentals in a direct and explicit fashion. The sample countries are the UK, France, Germany, Italy, Australia, Hong Kong, Japan, and Singapore. Empirical results based on our model indicate that a higher exchange rate variability mostly increases local equity market volatility. This can be attributable to a positive correlation in returns between the local equity and foreign exchange market. In contrast, the exchange rate fluctuation has a marginally negative impact on the US/local equity market correlation. A possible explanation would be that an upward movement of local stock markets, for instance, would trigger international investors to invest in local stock markets rather than in the US market, causing outflow of funds from the US market, thus depreciating the US dollar (or appreciating the local currency). This implies that appreciating local currencies is associated with falling US stock markets, suggesting a negative impact of exchange rate fluctuations on the US/local equity market correlation. Results from the forecast error variance decomposition indicate that exchange rate fluctuations held a relatively large fraction of the variation in local stock market returns, while only a small fraction of the variation in US/local market correlations was accounted for by exchange rate fluctuations. The extent to which the exchange rate variability affects equity market volatility is greater for local markets than for the US market, due to the fact that exchange rate changes are

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