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

For a bivariate data set the dependence structure cannot only be measured globally, for example with the Bravais–Pearson correlation coefficient, but the dependence structure can also be analysed 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 a chi-plot and which was introduced by Fisher and Switzer 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.