The role of asymmetry about investor preferences

Abstract

This article is about the role of asymmetry in the distribution of portfolio returns and investors’ preferences. It is well known that the skewness of the distribution can play some roles in preferences, but in economic theory this role is usually conflated with the concept of the utility function and, in particular, with expected utility maximization. This perspective seems to us unsatisfactory in two respects. First, the financial intuition about the possibility of accounting for asymmetries is too abstract and difficult for practitioners to grasp. Second, this strategy works only under some implicit conditions such as the existence of third moment; not such a weak assumption for financial returns. Here we propose a different strategy. It considers the comparison between the mean and the median of the distribution of returns. Thus, we obtain a representation that gives us an idea of the possibility of favouring a positive asymmetry and disfavoring a negative one. The main advantage of this representation is that it contains only probabilistic concepts (no utility theory) and is easily understood and communicated by practitioners. Moreover, in this way the existence of a third moment is not necessary, the first one is sufficient.