  We use the exact expression for the S parameter in the perturbative region of
the conformal window to establish its dependence on the explicit introduction
of fermion masses. We demonstrate that the relative ordering with which one
sends to zero either the fermion mass or the external momentum leads to
drastically different limiting values of S. Our results apply to any fermion
matter representation and can be used as benchmark for the determination of
certain relevant properties of the conformal window of any generic vector like
gauge theory with fermionic matter. We finally suggest the existence of a
universal lower bound on the opportunely normalized S parameter and explore its
theoretical and phenomenological implications. Our exact results constitute an
ideal framework to correctly interpret the lattice studies of the conformal
window of strongly interacting theories.
