On the use of dispersion measures consistent with additive shifts

In financial literature we can find many alternative dispersion and risk measures that can help us to identify a proper investments. However, only few di s- persion measures are consistent with additive shifts. In this work we propose to study the class of dispersion measures that consider that "more is better than less" and we analyze and empirically compare their different characteristics. In particular, we discuss the property of consistency with respect to additive shifts and we exa m- ine a class of dispersion measures that satisfy this property. Finally, we examine the use of some of these dispersion measures in financial problems with particular atte n- tion to the portfolio selection problem.