Carole Bernard

Grenoble Ecole de Management (GEM) - Vrije Universiteit Brussel (VUB)

Recent literature has identified the coskewness as one of the most important factors of portfolio optimization.  In this paper, we study the impact of dependence uncertainty first on the expectation of a product $E(X_1, X_2,..., X_d)$ when $X_i$ has cdf $F_i$ for all $i$ is studied and then on the coskewness typically used in portfolio optimization. Under some conditions on the $F_i$, explicit sharp bounds are obtained, and a numerical method is provided to approximate them for arbitrary choices of the $F_i$. The results are applied to assess the impact of dependence uncertainty on coskewness. A novel notion of "standardized rank coskewness" is introduced, which is invariant under strictly increasing transformations and takes values in $[1, 1]$.