ساختار وابستگی بین بازار سهام و بازار ارز خارج ؛ یک روش اتصال

This paper investigates the dependence structure between the equity market and the foreign exchange market by using copulas. In particular, several copulas with different dependence structure are compared and used to directly model the underlying dependence structure. We find that there exists significant symmetric upper and lower tail dependence between the two financial markets, and the dependence remains significant but weaker after the launch of the euro. Our findings have important implications for both global investment risk management and international asset pricing by taking into account joint tail risk.

Studying the co-movements across financial markets is an important issue for risk management and portfolio management. There is a great deal of research focusing on the co-movements of international equity markets. Chakrabarti and Roll (2002) find that the correlations increased from the pre-crisis to the crisis period in both Asian and European stock markets. They also find that the diversification potential was bigger in Asia than in Europe in the pre-crisis period, but this was reversed during the crisis. Other examples of research on the co-movements of equity markets can be found in Karolyi and Stulz, 1996, Longin and Solnik, 2001 and Forbes and Rigobon, 2002, while the methodology used is along the line of correlations and conditional correlations. Since the limitations of correlation-based models as identified in Embrechts et al. (2002), research has started to use copulas to directly model the dependence structure across financial markets. Works along this line include Mashal and Zeevi, 2002 and Hu, 2006 and Chollete et al. (2006), who report asymmetric extreme dependence between equity returns, i.e., the stock markets crash together but do not boom together. While the above literature focuses on the dependence structure and co-movements in equity markets via copulas, Patton (2006a) also employs copulas to model the asymmetric exchange rate dependence and finds that the mark and yen exchange rates are more correlated when they are depreciating against the US dollar than when they are appreciating. While there is extensive literature studying the co-movements between the international equity markets and some literature on modeling the dependence structure between the exchange rates via copulas, there is little literature on using copulas to study the co-movements across markets of different asset types, such as the equity and foreign exchange markets. In this paper, we consider both equities and foreign exchange rates in our study since the foreign exchange market is by volume one of the largest financial markets and currency is an important asset in international financial portfolios. In the literature, Giovannini and Jorion (1989) include exchange rates as assets in their portfolios. For global investors who wish to diversify portfolios internationally, the co-movements and dependence structure between equities and exchange rates would have important implications for their cross market risk management. There has been extensive research (both theoretical and empirical) on the relationship and co-movements between these two markets. Theoretical research includes the “flow-oriented” models of exchange rate (see Dornbusch and Fischer (1980)) and the “stock oriented” models of exchange rate (see Branson (1983) and Frankel (1983)). All these models argue that the stock market impacts the exchange rate and vice versa. Empirical studies of the interaction or causality relationship between the stock price and the exchange rate lead to mixed results (positive correlation, negative correlation, existence or nonexistence of causality, causality one way or the other). In this paper, we endeavor to investigate the dependence between the equity returns and the exchange rate returns, by using a relatively new technique: copulas. The methodology we use in this paper differs in a fundamental way from most of the methods used in the literature in analyzing dependence between the financial markets, which is also sometimes called co-movement. We will use dependence or co-movement interchangeably in this paper. The questions we intend to answer are: what is the dependence structure between these two assets? Is there any extreme value dependence1? Is the dependence symmetric or asymmetric? By answering these questions, we hope to better understand the co-movements of stock-currency markets and the risks associated with the dependence structure between markets. A copula is a function that connects the marginal distributions to restore the joint distribution. The advantage of using copulas in analyzing the co-movement concerned is multifold. First, copulas allow us to separately model the marginal behavior and the dependence structure. This property gives us more options in model specification and estimation. Second, the copula function can provide us not only the degree of the dependence but also the structure of the dependence. It allows for the tail dependence and asymmetric dependence. Linear correlation does not give the information about tail dependence and the symmetry property of the dependence. Third, unlike correlation, copulas do not require elliptically distributed random variables of the interest. As a result, they are especially useful when modeling the dependence between asset returns (especially from high frequency data). Finally, copulas are invariant to increasing and continuous transformations. This property is very useful as transformation is commonly used in economics and finance. For example, the copula does not change with returns or logarithm of returns. This is not true for the correlation, which is only invariant under liner transformations. To study the stock-foreign exchange dependence, we specify both the marginal models for the returns and a joint model for the dependence. We employ the AR-t-GARCH models for the marginal distributions of each stock index return and exchange rate return series. For the joint model, we choose three copulas with deferent dependence structure: the normal copula, which is symmetric but with zero tail dependence; the student-t copula, which retains the correlation dependence and also has symmetric nonzero tail dependence; and the SJC copula, which allows for asymmetric tail dependence and nests symmetry as a special case. We use AIC, BIC, and the ‘hit’ test in Patton (2006a) to check for the copula model specifications and goodness-of-fit tests. The financial markets considered are the G5 countries (US, UK, Germany, Japan, France) which include 5 stock markets and 4 exchange rates. We examine the dependence before and after the launch of the euro. We find that there exists significant positive tail dependence between the stock market and the foreign exchange market in each country for both the pre- and post-euro periods. Unlike the co-movements across international stock markets, the tail dependence is symmetric between the stock market and the foreign exchange market. This result is also different from tail dependence across foreign exchange markets or across equity-bond markets. For instance, Hartmann et al. (2003) find asymmetric extreme co-movements in currency markets in both industrial and emerging countries using an extreme value theory approach. As well, Cappiello et al. (2006) report asymmetric extreme dependence across equity-bond markets. One of our findings is that the equity-currency tail dependence is decreased after the launch of the euro, especially for the eurozone countries such as Germany. This may be explained by the fact that the uncertainty in the foreign exchange market is reduced after multiple currencies were replaced by a common currency, euro. The countries we examined are either in the eurozone (Germany and France) or have strong trade relationships with the eurozone (the United Kingdom and Japan). Moreover, the dependence of the German pair and the French pair is actually the dependence between the local stock market and the euro after the adoption of the euro. Our finding of significant tail dependence in the equity-currency pairs has important implications in risk management and asset pricing. First, left tail dependence indicates the potential of a simultaneous large loss in both the equity and foreign exchange markets. This joint downside risk has been well documented in the literature of equity market. It is formally discussed and measured in Chollete et al. (2006), where they find significant downside risk in G5 and Latin American stock markets. Equity-foreign exchange rate joint downside risk is important to global investors when investing in foreign stock markets. For example, an extreme market event involving a 20% loss in the London stock market would, under equity-foreign exchange tail dependence, imply the potential of a large depreciation, for instance 10%, in the exchange rate. Consequently, a US investor who invested in the London stock market would lose 28% in US dollars. Thus the existence of lower tail dependence implies a much higher downside risk in foreign stock market investment than the case of no tail dependence. This may also partially explain “investor home bias puzzle”. Second, tail dependence allows investors to measure the probability of simultaneous extreme losses. The likelihood of extreme joint losses suggests a higher than normal value-at-risk (VaR), which is an important factor for risk management. Ignoring the tail dependence would under estimate the VaR. Third, tail dependence is extremely important for safety-first agents investing globally. Susmel (2001) discussed the safety-first criterion and tail dependence in the context of investment in emerging stock markets. A safety-first investor minimizes the chances of a large loss, a loss that may drive her or her firm out of business. Equity-foreign exchange tail dependence measures the likelihood of large loss in foreign market investment. Thus a safety-first investor would especially care the size of tail dependence. Finally, this finding should also affect the pricing of assets. Discussed in Poon et al. (2004), tail dependence, which gives the probability of joint occurrence of the most extreme values, is a true measure for systematic risk in times of financial crisis. Global investors should be compensated for exposure to such systematic joint risk in stock-foreign exchange markets during market extremes. In the literature, this type of joint extreme risk has not been considered in the asset pricing model. We hope that this work will also improve our understanding of risks associated with the extreme events and our results will lead to the possible revision of the asset pricing models by picking up the tail dependence. The remainder of the paper is structured as follows. Section 2 provides a brief review of copula concepts. Section 3 specifies the models and the estimation. In Section 4, we describe the data and discuss the results. Section 5 concludes.

In this paper, we examine the extreme co-movements between the stock and the exchange rate markets by directly modeling their dependence structure via the use of the copulas. The symmetric tail dependence is found to be significant in all the stock-currency return pairs analyzed in this study for both pre- and post-euro periods. This finding is very important for global investors in their risk management during extreme market events. The finding also implies that the Gaussian dependence hypothesis that underlies most modern financial applications may be inadequate. Picking up the tail dependence could lead to a more realistic assessment of the linkage between financial markets and possibly more accurate risk management and pricing models.