  The density functional plus dynamical mean-field theory is used to study the
spin excitation spectra of SrRu$_2$O$_6$. A good quantitative agreement with
experimental spin excitation spectra is found. Depending on the size of the
Hund's coupling $J_H$ the systems chooses either Mott insulator or covalent
insulator state when magnetic ordering is not allowed. We find that the nature
of the paramagnetic state has negligible influence on the charge and spin
excitation spectra. We find that antiferromagnetic correlations hide the
covalent insulator state for realistic choices of the interaction parameters.
