  We address the $\simeq 4.4\sigma$ tension between local and the CMB
measurements of the Hubble Constant using simulated Type Ia Supernova (SN)
data-sets. We probe its directional dependence by means of a hemispherical
comparison through the entire celestial sphere as an estimator of the $H_0$
cosmic variance. We perform Monte Carlo simulations assuming isotropic and
non-uniform distributions of data points, the latter coinciding with the real
data. This allows us to incorporate observational features, such as the sample
incompleteness, in our estimation. We obtain that this tension can be
alleviated to $3.4\sigma$ for isotropic realizations, and $2.7\sigma$ for
non-uniform ones. We also find that the $H_0$ variance is largely reduced if
the data-sets are augmented to 4 and 10 times the current size. Future surveys
will be able to tell whether the Hubble Constant tension happens due to
unaccounted cosmic variance, or whether it is an actual indication of physics
beyond the standard cosmological model.
