Comparing possibilistic portfolios to probabilistic ones

Abstract

In this paper, we comparemean-variance portfolios based on the standard probabilistic representation of the stock returns to mean-variance portfolios built by using stock returns represented as possibilistic numbers.With reference to the latter, in this note we focus our attention on the definitions recently proposed in literature for modeling portfolio selection problems. In particular, first we investigate some theoretical properties of the possibilistic portfolios and compare them to the equivalent ones of the probabilistic portfolios, then, given the assets composing the Italian stock index FTSE MIB, we empirically compare the performances of the possibilistic portfolios to those of the probabilistic one. The results show that, generally, the probabilistic approach is more flexible than the possibilistic one in solving portfolio selection problems.