  The dependence of the $\rho$ parameter on the mass of the Higgs scalar and
the top quark is computed non--perturbatively using the $1/N_F$ expansion in
the standard model. We find an explicit expression for the $\rho$ parameter
that requires the presence of a physical cutoff. This should come as no
surprise since the theory is presumably trivial. By taking this cutoff into
account, we find that the $\rho$ parameter can take values only within a
limited range and has finite ambiguities that are suppressed by inverse powers
of the cutoff scale, the so called ``scaling--violations". We find that large
deviations from the perturbative results are possible, but only when the cutoff
effects are also large.
