  Supermassive black hole -- host galaxy relations are key to the computation
of the expected gravitational wave background (GWB) in the pulsar timing array
(PTA) frequency band. It has been recently pointed out that standard relations
adopted in GWB computations are in fact biased-high. We show that when this
selection bias is taken into account, the expected GWB in the PTA band is a
factor of about three smaller than previously estimated. Compared to other
scaling relations recently published in the literature, the median amplitude of
the signal at $f=1$yr$^{-1}$ drops from $1.3\times10^{-15}$ to
$4\times10^{-16}$. Although this solves any potential tension between
theoretical predictions and recent PTA limits without invoking other dynamical
effects (such as stalling, eccentricity or strong coupling with the galactic
environment), it also makes the GWB detection more challenging.
