  The Kondo system CeRu$_4$Sn$_6$ shows a strong anisotropy in its electric,
optic and magnetic properties. We employ density functional theory plus
dynamical mean field theory and show that the predominant Ce-$f$ state has
total angular moment $J=5/2$ and $z$-component $m_J=\pm 1/2$ in agreement with
recent X-ray absorption experiments. Even though CeRu$_4$Sn$_6$ has the direct
gap of a Kondo insulator through most of the Brillouin zone it remains weakly
metallic. This is because of (i) a band crossing in the $z$-direction and (ii)
a negative indirect gap.
