Possibilistic mean–variance portfolios versus probabilistic ones: the winner is...

In this paper, we compare the mean–variance portfolio modeling based on the possibilistic representation of the future stock returns to the one based on the classical probabilistic modelization of the same returns. There exist several different definitions of possibilistic mean, possibilistic variance and possibilistic covariance. In this paper, we consider definitions recently proposed in the literature for modeling portfolio selection problems: the possibilistic mean and variance à la Carlsson–Fullér–Majlender, the lower possibilistic mean and variance, and the upper possibilistic mean and variance. In particular, we mean to answer to the following research questions: first, to check whether, from a methodological and theoretical standpoint, it is possible to detect elements of superiority of one of the two approaches with respect to the other one; then, to check whether, from an operational point of view, one of the two approaches is more effective than the other one in terms of virtual-future performances. We disclosed that, on the basis of the results we obtained, the winner is the probabilistic approach.