Testing the hypothesis that international equity market correlation increases in volatile times is a difficult exercise and misleading results have often been reported in the past because of a spurious relationship between correlation and volatility. This paper focuses on extreme correlation, that is to say the correlation between returns in either the negative or positive tail of the multivariate distribution. Using "extreme value theory" to model the multivariate distribution tails, we derive the distribution of extreme correlation for a wide class of return distributions. Using monthly data on the five largest stock markets from 1958 to 1996, we reject the null hypothesis of multivariate normality for the negative tail, but not for the positive tail. We also find that correlation is not related to market volatility per se but to the market trend. Correlation increases in bear markets, but not in bull markets.
First version: May 1996. This version: April 2000Keywords: international equity markets, volatility, correlation and extreme value theory.JEL classification numbers: G15, F3. 1 We would like to thank David Bates, Michael Brandt, Bernard Dumas, Paul Embrechts, Claudia Klüppelberg, Jérôme Legras, Jacques Olivier, Stefan Straetmans and the participants at the Bachelier seminar (Paris, October 1997), London School of Economics, INSEAD, Université de Genève, Université de Lausanne, the American Finance Association meetings (New York, January 1999), the French Finance Association meetings (Aix-en-Provence, June 1999), the workshop on "Extreme Value Theory and Financial Risk" at Münich University of Technology (Münich, November 1999) and the CCF Quants conference (Paris, November 1999) for their comments. Jonathan Tawn provided many useful suggestions. We also would like to thank René Stulz (the editor) and an anonymous referee whose comments and suggestions helped to greatly improve the quality of the paper. Longin benefited from the financial support of the CERESSEC research fund and the BSI GAMMA Foundation, and Solnik from the support of the Fondation HEC. International equity market correlation has been widely studied. Previous studies 4 suggest that correlation is larger when focusing on large absolute-value returns, and that this seems more important in bear markets. The conclusion that international correlation is much higher in periods of volatile markets (large absolute returns) has indeed become part of the accepted wisdom among practitioners and the financial press. However, one should exert great care in testing such a proposition. The usual approach is to condition the estimated correlation on the observed (or expost) realization of market returns. Unfortunately correlation is a complex function of returns and such tests can lead to wrong conclusions, unless the null hypothesis and its statistics are clearly specified. To illustrate our point, let us consider a simple example where the distribution of returns on two markets (say U.S. and U.K.) is multivariate normal with zero mean, unit ...
