Portfolio selection with uncertainty measures consistent with additive shifts

Abstract

Assuming a non-satiable risk-averse investor, the standard approach to portfolio selection suggests discarding of all ineffi cient investment in terms of mean return and its standard deviation ratio within its fi rst step. However, in literature we can fi nd many alternative dispersion and risk measures that can help us to identify the most suitable investment opportunity. In this work two new dispersion measures, fulfi lling the condition that “more is better than less” are proposed. Moreover, their distinct characteristics are analysed and empirically compared. In particular, starting from the defi nition of dispersion measures, we discuss the property of consistency with respect to additive shifts and we examine two dispersion measures that satisfy this property. Finally, we empirically compare the proposed dispersion measures with the standard deviation and the conditional value at risk on the US stock market. Moreover, within the empirical example the so called “alarm” is incorporated in order to predict potential fails of the market.