  We study the impact of dependence uncertainty on the expectation of the
product of $d$ random variables, $\mathbb{E}(X_1X_2\cdots X_d)$ when $X_i \sim
F_i$ for all~$i$. 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. In this regard, we introduce a novel
notion of "standardized rank coskewness," which is invariant under strictly
increasing transformations and takes values in $[-1,\ 1]$.
