تعقیب سنگین و بحران ارز

In affine models of foreign exchange rate returns, the nature of cross sectional interdependence in crisis periods hinges on the tail properties of the fundamentals' distribution. If the fundamentals exhibit thin tails like the normal distribution, the dependence vanishes asymptotically; while the dependence remains in the case of heavy tailed fundamentals as in case of the Student-t distribution. The linearity of the monetary model and heavy tail distributed fundamentals are sufficient conditions for fundamentals-based repeated joint currency crises. An estimator for the extreme exchange rate interdependencies is obtained and applied to Western, Asian and Latin American currency block data.

In the year 1963 Mandelbrot published two remarkable papers (Mandelbrot, 1963a and Mandelbrot, 1963b) in which he noted the two important features of speculative price data which gave financial econometricians enough to work on for the subsequent thirty years. The first feature is the Pareto nature of the tails of the distributions of financial returns. Heavy tails in itself were not new to economists, as Pareto himself had discovered this feature in high income data. But for financial economists, who had just discovered the niceties of Brownian motion and were on their way to option pricing, this was novel. In the end it carried the unfortunate message that markets are more likely to be incomplete than otherwise. The positive side of incompleteness is, though, that it gives sufficient motives for active hedging and risk management. The importance of this discovery only came to be fully recognized some thirty years later when banks started to calculate the Value-at-Risk (VaR) measure and had to come to terms with the non-normality of the distribution of financial asset returns. Due to the Pareto nature, the tail probabilities are self scaling, see Feller (1971, VIII.8). This intriguing mathematical phenomenon is very helpful for practical VaR calculations. Upon assuming that the self scaling property applied to the entire distribution, Mandelbrot concluded the distribution of asset returns had to be an infinite variance sum stable distribution. The second empirical observation reported by Mandelbrot and attributed to Houthakker was the clustering of volatility feature. This data feature lay dormant until Engle's ARCH model (1982) gave a succinct representation which preserved the martingale property of asset prices. The ARCH model nicely implies that even though the innovations are normal, the stationary solution exhibits a Pareto type tail, consistent with the first data feature; see De Haan et al. (1989). The 1963 articles also ask the question about the economic mechanism that could be responsible for the noted data features. As of today little work has been devoted to this question, although some early work on income distribution, notably Chapernowne (1953) and some other more recent work, do provide some insight for the marginal distributions to be fat tailed, see e.g. Gabaix et al. (2003). In this article we like to extend the original work of Mandelbrot and subsequent developments by discussing the economics and econometrics of extremes in a multivariate setting. Thirty years later we know a lot more about the univariate issues concerning the heavy tail and summability features. For example, we now realize it suffices to assume the scaling only holds in the tail area. This has the benefit that one does not need to make the infinite variance assumption. But the multivariate issues are wide open for research. The aim of the paper is to show in which direction research is currently evolving. For this purpose we analyze the multivariate dependency structure in affine models of foreign exchange rate returns. We clarify the cross sectional return dependency during crises by combining the univariate data feature discovered by Mandelbrot with Frenkel's monetary model of the exchange rate. In doing so we do not explain the Pareto tail nature of the univariate series, which we take as given, but we offer an economic explanation for the observed strong crisis spillovers. While fat tails and tail dependence of forex returns have by now been extensively documented in the empirical literature, how the marginal tail thickness relates theoretically to the bivariate and multivariate tail dependence of returns in standard foreign exchange rate models has not been dealt with before. The multivariate questions are certainly new and could hardly have been addressed at the time Mandelbrot was writing his fascinating articles. There is a long standing discussion about the origins of financial crises. One view holds that such crises are the expression of an occasional inherent malfunctioning of financial institutions or markets (sunspots). Another view rather sees crises as caused by bad outcomes in underlying economic variables (fundamentals). Representative of the first view is the literature modelling univariate crises as self-fulfilling events in the presence of multiple equilibria. For example, Diamond and Dybvig (1983) show that bank depositor runs can occur as a self-fulfilling prophecy, which would imply that they happen more or less randomly. Obstfeld (1986) argues that currency crises can occur as a consequence of multiple equilibria. This is in contrast with the literature which links crises to unfavorable macroeconomic conditions, sometimes caused by bad economic policies. For example, Gorton (1988) argues that most episodes of banking instability in US history were related to business cycle downturns. Krugman (1979) shows how unsustainable large budget deficits can lead to currency attacks. According to Gencay and Selcuk (2006) domestic financial repression may also be an important trigger of emerging currency crashes.1Masson (1999) nests most of the previously mentioned channels in a model of contagious currency crises. In the present paper we do not take a position on the two views of self-fulfilling and fundamentals-based exchange rate crises. Rather, we concentrate on the significance of a crisis. In particular we give sufficient conditions for the repeated occurrence of widespread crises. We use joint currency crashes as an application to illustrate our point, but the argument is more general. It applies to any group of assets whose values are linearly driven by underlying economic variables, or risk factors. Two basic conditions are sufficient for the frequent occurrence of systemic (widespread) market crises. First, the univariate distributions describing the behavior of economic variables (or ‘fundamentals’) underlying the exchange rates need to exhibit heavy tails. Loosely speaking, the heavy tail feature means that the probability of univariate currency collapses is approximately Pareto distributed. Mandelbrot's hypothesis of non-normal stable distributions and Student-t distributions exhibit an expansion of their tails in which the first term is a power function like Pareto's distribution. This implies that the probability of a currency crisis is much higher than one would expect if the underlying fundamentals were normally distributed (with the same mean and variance). Second, the (logarithm of) nominal bilateral exchange rates, expressed against the same base currency, are linear expressions of the domestic and the base currency fundamentals. The standard monetary model of the foreign exchange rate provides such an affine framework. The two conditions are shown to imply that joint currency crises will occur frequently and with vehemence. The surprising element of this result is that the degree of cross-sectional dependence between exchange rate returns during crisis periods (so called asymptotic dependence) is related to the univariate characteristics of the tails of the fundamentals' distributions. 2 One may therefore classify currency linkages during times of market stress into a weak and a strong type, depending on whether the conditional crash probability vanishes or remains asymptotically. Correspondingly, the international monetary and financial system may be characterized as being relatively stable in the former case, while it is more fragile in the latter case. Our two conditions, univariate heavy tails and linearity, are sufficient for a more fragile system. We emphasize that in general the dependency structure of a multivariate distribution and the shape of the univariate distributions are two unrelated concepts. But here the affine economic structure induces that the characteristics of the marginals affect the multivariate dependency structure in a specific way. The same also applies to other asset classes. For example, bank equity returns are asymptotically dependent, if banks hold correlated linear portfolios of partly common, heavy-tail distributed assets, see De Vries (2005).3 In the empirical application of the paper, we assess the strength of the asymptotic dependence for panels of industrial (developed) and emerging market currencies by using a simple count based estimator for the extreme interdependencies.4 The linkage estimates are suggestive of considerable asymptotic dependence. The amount of extreme dependency that we find varies, however, with the choice of the numeraire currency. We argue that this heterogeneity stems from the scale magnitudes of the fundamental variables which drive the base currency. We see two policy implications. One is that risk management has to take into account that the likelihood of multiple currency crises is much higher than under the usual multivariate normal distribution assumption. The second implication is that macro policies instead of micro market quirks are the main drivers of the larger exchange rate swings. This implies that prudent (monetary) policy should exhibit moderation instead of overshooting and feeding onto the market uncertainties. The remainder of this paper proceeds as follows. In Section 2 we introduce the canonical affine exchange rate model in which we study the relationship between marginal tail thickness and bivariate tail dependence. A discussion and comparison of different measures to characterize currency linkages during periods of market stress is provided in Section 3. The central result of the paper on the relationship between the exchange rates' marginal tail properties and the degree of tail dependence is in Section 4. The two cases of thin tailed and fat tailed marginals are treated in two separate subsections. Section 5 discusses estimators and presents empirical evidence. Section 6 concludes. The Appendix contains a number of insightful figures.

It is by now well known that financial returns exhibit heavy tails and thus are non-normally distributed. This implies that extreme market conditions tend to occur more frequently than expected on the basis of the normal distribution, which is used so often in standard asset pricing approaches. From the point of view of international financial stability and portfolio diversification, the strength of asset linkages during crisis periods matters even more, as these determine the stability of the system as a whole. This paper has shown how Mandelbrot's innovative work on the univariate properties of the speculative price series inspired us to investigate the multivariate properties of currency systems and their stability. We show that in affine models of the (international) financial system the fragility of the system or its systemic stability hinges critically on the type of marginal distribution that applies to the country fundamentals. More specifically, we demonstrate that in linear models of forex returns, the nature of interdependency between different exchange rate returns in times of crisis is fundamentally related to the univariate properties of the distribution of the risk factors. Suppose that the logarithmic exchange rate returns are a linear function of the domestic and foreign fundamentals. This implies that different exchange rate returns against the same base currency are correlated because they share common fundamentals. Nevertheless, if one currency return crashes, the probability that the other currency breaks down as well vanishes asymptotically if the forex fundamentals exhibit thin tails, as is the case for the normal distribution. Alternatively, if the marginal distributions exhibit heavier tails than the normal, e.g. are Student-t distributed, the probability that the other currency breaks down as well remains strictly positive even in the limit. We therefore speak of, respectively, weak and strong crisis linkages between different currencies. Correspondingly, the international monetary and financial system may be characterized as relatively robust in the former case, where destabilizing phenomena like contagion do not occur systematically, while it is relatively fragile in the latter case. Our theoretical derivation has direct relevance for economic policy. By pursuing policies with a ‘steady hand’ instead of orchestrating drastic changes in variables like money supply, interest rates or public expenditure, public authorities can diminish the scope for fat tails in the fundamentals. In specific circumstances of large market-driven fluctuations, strong counteracting measures may be advisable. In the light of our argument, policy institutions may in this way contribute to the stability of the international exchange rate system. Empirically we uncovered important differences between Western and non-Western currencies. The former reveal a higher joint connection to the dollar than the other currencies. This may be considered evidence for decoupling. However, this being said, we also find evidence for a stronger interdependency among the non-Western currency blocs than for the Western currencies.