Can we predict the value of the Higgs mass?

In the framework of the Standard Model the mass of the physical Higgs boson is an arbitrary parameter. In this note we examine whether it is possible to determine the ratio of $m_H\mathrm{/}M$, where $M$ denotes any other mass in the theory, such as the $W$ or the $Z$-boson mass. We show that no such relation can be stable under renormalisation.