Before revision:  We also consider the so-called maximal and minimal tail dependence measures , defined as the maximum and minimum of the tail dependence measures among all tail generating measures for a given copula. It turns out that the minimal tail dependence measure coincides with the tail dependence coefficient, and the maximal tail dependencemeasure overestimates the degree of extreme co-movements.
After revision:  We also consider the so-called maximal and minimal tail dependence measures , defined as the maximum and minimum of the tail dependence measures . The infimum and supremum of TCMs over all generating measures are considered to investigate the issue of under- and overestimation of the degree of extreme co-movements. The infimum is shown to be attained by the classical tail dependence coefficient, and the maximal tail dependencemeasure overestimates the degree of extreme co-movements.