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Measuring Dependence in Financial Crisis A Copula Approach for Mexico and Brazil
Introduction
The 2008 financial crisis in the United States, along with its implications in the international financial markets, posed again as a main concern, particularly in risk management and asset allocation, if financial markets become more connected or interdependent during financial crises. Economists and financial markets analysts have been busy producing reseARCH on this matter, particularly in crisis periods such as the Mexican devaluation (Tequila crisis 1994-95), the Asian flu (1997) and the Russian default (1998). The reason behind this is that non-tranquil periods arise the interest to study in which extent financial markets are connected and, moreover, which type of connection is presented: whether contagion or dependence between them. The debate around the definition of true contagion is described by Calvo and Reinhart (1996), and later developed by Kaminsky and Reinhart (2000). They affirm that it is presented when common shocks and different channels of interconnection are either not present or have been controlled. As noted by Chan-Lau, Mathieson and Yao (2004), most of the reseARCH done in connection with this matter interprets contagion as the transmission mechanism in which an upward change in price co-movements is presented between financial markets. However, we need to note that this effect is neither a necessary nor sufficient condition to identify contagion, as it does not automatically imply a structural change in the data generating process (DGP).
Longin and Solnik (2001) emphasized the definition of contagion and conclude that the interactions noticed in the international correlations are stronger during high volatile periods. The common approach to these studies is to condition the estimation of the correlation to the observed returns of markets, and then conclude whether the relationship strengthens or not. However, this requires a method that carefully approaches the complex characteristics of the correlation function; if not, misleading conclusions might be reached, as established by Forbes and Rigobon (2002), especially when referring to a model based on the conditional correlation coefficient. That is, even if two markets show co-movement during stability periods, and it strengthens after the presence of a shock, it might not directly constitute a contagion effect. To show the latter, they apply an adjustment for heteroskedasticity and reversed the conclusion of an existing contagion effect. They noted that there is no universally accepted definition to true contagion due to a debate between two possibilities: whether it refers to modifications of cross-market relationships or not. Instead, they propose an interdependence focus in which market correlation suggests linkages between two economies rather than a significant increase in cross-market associations after a shock. Moreover, as noted by Costinot, Roncalli and Teiletche (2000), the dependence structure among financial markets, particularly on crisis periods, was better modeled through the utilization of copulas instead of a simple correlation analysis. It responds to the extreme dependence observed between international equity markets.
Roll (1992) suggests that the equity index behavior is affected by two factors: technical elements of the used method to construct and compose the index, and the role of the exchange rates involved. He also affirms that, when returns of indices are expressed in local currency, part of its volatility is induced by monetary phenomena such as changes in the inflation rates. Latin American crises are characterized by strong devaluation processes, as shown in those that took place in 1994 and 2001. This raises the need of an approach that includes this factor in its model when studying Latin American stock markets.
Taking into account the conclusions reached on this matter, we decided to work with a co-movement approach of the indices instead of using a contagion study; we also applied a non-simple correlation analysis: the copula approach. Copulas are very useful in understanding dependence at a deeper level, because they are invariant to strictly increasing transformations of random variables. Furthermore, they are built upon alternative measures rather than a simple correlation study, which allows us to develop a separate modeling of the dependence between random variables and their marginals. As pointed out by Chollete, Heinen and Valdesogo (2009), copulas are very helpful when dealing with financial information because they allow tail dependence. Another benefit is that the adaptation of Monte Carlo processes, in order to perform the simulations required by the technique, can be done relatively easy.
Canela and Pedreira (2012), Rodriguez (2007) and Okimoto (2008) did similar inquiries; however, they did not include the crisis of 2008. Our objective is to verify, in the case of Mexico and Brazil, the conclusions presented by the referred researches. During the Asian crisis Rodriguez employed daily returns on stock indices from Thailand, Malaysia, Indonesia, Korea and the Philippines; for the Mexican crisis he utilized those from Mexico, Argentina, Brazil and Chile. Okimoto focused on the US-UK stock indices. Both of the studies used regime-switching copulas in order to find evidence of changes in the dependence structure during the crisis periods. Canela and Pedreira also applied continuous two-dimensional copulas so as to study pairwise dependence structures of daily returns in Argentina, Brazil, Chile, Mexico, Peru and Venezuela. They concluded that cross-market dependence between Latin America stock markets present higher probability of extreme losses; therefore, we can expect that the dependence structure between them strengthens more in crisis periods than in tranquil ones.
It is known that, for financial appliances, the model construction has to acknowledge the need to treat stronger dependence between extreme losses, instead of that related to extreme gains. Since Latin American stock markets are characterized by this effect, we decided to use two simple Archimedean copulas, Clayton's and Gumbel's, because they capture the asymmetric tail dependence. As noted by Carol (2008), the Clayton copula captures lower tail dependence while the Gumbel copula captures upper tail dependence. We also decided to include the Normal or Gaussian copula --which is symmetric and exhibits tail independence--as a comparative estimation with the other two copulas.
When working with copulas that have different...
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