Abstract
This paper presents three tests of contagion of the US subprime crisis to the European stock markets of the NYSE Euronext group. Copula models are used to analyse dependence structures between the US and the other stock markets in the sample, in the pre-crisis and in the subprime crisis periods. The first test assesses the existence of contagion on the relevant stock markets’ indices, the second checks the homogeneity of contagion intensities, and the third compares contagion in financial and in industrial sectors’ indices. Results suggest that contagion exists, and is equally felt, in most stock markets and that investors anticipated a spreading of the financial crisis to the indices of industrial sectors, long before such dissemination was observable in the real economy.
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Notes
NYSE Euronext is a US holding company, created in 2007 by the combination of NYSE Group, Inc. and Euronext N.V. It operates six stock exchanges in seven countries and eight derivatives exchanges. In Europe, NYSE Euronext comprises the stock exchanges of Paris, Amsterdam, Brussels and Lisbon.
Forbes and Rigobon (2001, p. 43) refer that analyses of financial contagion are of ‘critical importance in: portfolio investment strategy; justifying multilateral intervention; and understanding how shocks are propagated internationally’. From this perspective, assessing whether contagion exists and if contagion homogeneity varies across countries may also be of interest to justify distinct levels of intervention and attention on the part of the relevant authorities, following the subprime crisis.
A thorough survey of such theoretical and empirical literature is provided by Pericoli and Sbracia (2003).
See the development in Nelsen (2006).
The specific functional forms of these copulas may be found in Trivedi and Zimmer (2005).
Ravn and Uhlig (2002) suggested the use of the following equation to adjust the Hodrick–Prescott’s parameter (λ) to the frequency of the data: λ = s n*1,600, where s is related to the frequency of the data (s = 1/4 for annual data, s = 3 for monthly data, and s = 90 for daily data) and n is close to 4. Other authors have suggested alternative values for n. For instance, Backus and Kehoe (1992) used n = 2 and Correia et al. (1992) used n = 1. In our case (daily data), λ would be 104.976.000.000 if n = 4, 12.960.000 if n = 2, and 144.000 if n = 1. Since our objective was simply to get a good visual perception of the series’ trends, we used λ = 1.000.000. However, the choice of λ has no implications for the tests performed ahead.
On 17 August 2007, the Fed unexpectedly cut the reference interest rate in 50 b.p. which appears to have motivated a generalized increase in stock exchange indices. On 28 November 2008, the vice-chairman of the Fed made public comments which, according to the Reuters, generated expectations of future cuts of the reference rate. On 1 April 2008, the Financial Times reported that monetary policy actions to combat the financial crisis were discussed by central banks and governmental authorities at the Rome’s Financial Stability Forum.
The publication of quarterly reports by major financial institutions, revealing results above expectations, promoted increases in stock exchange indices (Reuters). Examples were Goldman and Sachs and Lehman Brothers, on 18 March 2008, Citigroup (though with news of negative results), on 18 April 2008, and JP Morgan Chase, on 16 April 2008.
Rank correlation coefficients from distinct copulas are directly comparable and may be used to assess dependence, just like the copulas’ global dependence parameters. Following Eq. 4, for the case of the Gumbel copula, the Kendall’s τ is expressed as a function of that copula’s global dependence parameter, \(\theta :\;\tau =1-\frac{1}{\theta };\theta \in \left[ {1,\infty } \right)\). For the Clayton copula, the relation between the τ and the θ is: \(\tau =\frac{\theta }{\theta +2};\theta \ge 0\). It is possible to convert each copula’s global dependence parameter into rank correlation measures, which allow direct comparisons of global dependence between variables. However, if the interest is not on global, but rather on local dependence, the copulas also allow such analysis. One possibility is to extract the asymptotic tail coefficients from each copula, using Eqs. 5 and 6, to compare asymptotic dependence between variables (this cannot be done using rank correlation coefficients). Flexibility is thus one additional advantage of using copulas in tests of financial contagion, or in other contexts where the understanding of the links between financial variables is important.
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Isabel Vieira gratefully acknowledges partial financial support from FCT, program POCTI.
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Horta, P., Mendes, C. & Vieira, I. Contagion effects of the subprime crisis in the European NYSE Euronext markets. Port Econ J 9, 115–140 (2010). https://doi.org/10.1007/s10258-010-0056-6
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DOI: https://doi.org/10.1007/s10258-010-0056-6