Hausdorff Distance and Convex Hull

Given two sets of points A and B, both in $R^d$, is there a relation between the convex hulls of A and B, i.e. conv(A) and conv(B), w.r.t. the Hausdorff distance between A and B? In other words, does the computation of the hulls for the two point sets in question pose any advantage when computing the Hausdorff distance between the point sets? Would be nice if someone could reference a paper that helps understand this relation.