A simple graphical method to explore tail-dependence in stock-return pairs

Abstract

For a bivariate data set the dependence structure can not only be measured globally, for example with the Bravais-Pearson correlation coefficient, but the dependence structure can also be analyzed locally. In this article the exploration of dependencies in the tails of the bivariate distribution is discussed. For this a graphical method which is called chi-plot and which was introduced by Fisher and Switzer (1985, 2001) is used. Examples with simulated data sets illustrate that the chi-plot is suitable for the exploration of dependencies. This graphical method is then used to examine stock-return pairs. The kind of tail-dependence between returns has consequences, for example, for the calculation of the Value at Risk and should be modelled carefully. The application of the chi-plot to various daily stock-return pairs shows that different dependence structures can be found. This graph can therefore be an interesting aid for the modelling of returns.