  In a generic Grand Unified Theory with a relatively small dispersion of the
spectrum around the $Z$-boson and the unification masses, a connection is
established, exact at one loop level, between $M_Z$, $G_{\rm F}$, $\alpha(M_Z)$
and the strong coupling constant $\alpha_3(M_Z)$. At this level of precision,
this avoids the logical and phenomenological inconsistency of predicting
$\alpha_3(M_Z)$ by means of the electroweak couplings as extracted from the
data in the Standard Model rather than in the complete theory. Attention is
paid to the independence of the physical results from regularization and/or
renormalization schemes. As a particularly relevant example, the analysis is
specialized to the case of the Minimal Supersymmetric Standard Model, with
emphasis on light charginos and neutralinos.
