Extreme Correlation of International Equity Markets

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.

[1]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[2]  C. B. Tilanus,et al.  Applied Economic Forecasting , 1966 .

[3]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[4]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[5]  J. D. T. Oliveira,et al.  The Asymptotic Theory of Extreme Order Statistics , 1979 .

[6]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[7]  E. Kaplanis,et al.  Stability and forecasting of the comovement measures of international stock market returns , 1988 .

[8]  Richard Roll,et al.  The International Crash of October 1987 , 1988 .

[9]  Jonathan A. Tawn,et al.  Bivariate extreme value theory: Models and estimation , 1988 .

[10]  Dennis W. Jansen,et al.  On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective , 1989 .

[11]  Sidney I. Resnick,et al.  Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes , 1989 .

[12]  R. Reiss.  Approximate Distributions of Order Statistics , 1989 .

[13]  J. Angus.  The Asymptotic Theory of Extreme Order Statistics , 1990 .

[14]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[15]  F. Longin,et al.  Is the Correlation in International Equity Returns Constant: 1960-90? , 1995 .

[16]  Campbell R. Harvey,et al.  Forecasting International Equity Correlations , 1994 .

[17]  R. Engle,et al.  Do Bulls and Bears Move Across Borders? International Transmission of Stock Returns and Volatility , 1994 .

[18]  P. Phillips,et al.  Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets , 1994 .

[19]  F. Longin.  The Asymptotic Distribution of Extreme Stock Market Returns , 1996 .

[20]  Yann Le Fur,et al.  International Market Correlation and Volatility , 1996 .

[21]  A. Ledford,et al.  Statistics for near independence in multivariate extreme values , 1996 .

[22]  René M. Stulz,et al.  Why Do Markets Move Together? An Investigation of U.S.-Japan Stock Return Comovements , 1996 .

[23]  J. Teugels,et al.  Tail Index Estimation, Pareto Quantile Plots, and Regression Diagnostics , 1996 .

[24]  Bruno Gerard,et al.  International Asset Pricing and Portfolio Diversification with Time‐Varying Risk , 1997 .

[25]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[26]  Michael S. Gibson,et al.  Pitfalls in Tests for Changes in Correlations , 1997 .

[27]  F. Longin,et al.  From value at risk to stress testing : The extreme value approach Franc ß ois , 2000 .

[28]  S. Straetmans.  Extreme financial returns and their comovements , 1998 .

[29]  Raul Susmel,et al.  Volatility and Cross Correlation Across Major Stock Markets , 1998 .

[30]  R. Rigobón,et al.  No Contagion, Only Interdependence: Measuring Stock Market Co-Movements , 1999 .

[31]  R. Huisman,et al.  Tail-Index Estimates in Small Samples , 2001 .

[32]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[33]  P. Embrechts,et al.  Correlation and Dependency in Risk Management , 2002 .

[34]  R. Rigobón,et al.  No Contagion, Only Interdependence: Measuring Stock Market Comovements , 2002 .