We study magnetic behaviour of the Yb$^{3+}$ ions on a frustrated pyrochlore lattice in the spinel {CYS}. The crystal-electric field parameters deduced from high-energy inelastic neutron scattering reveal well-isolated ytterbium ground state doublet with a weakly Ising character. Magnetic order studied by powder neutron diffraction evolves from the $XY$-type antiferromagnetic $Gamma_5$ state to a splayed ice-like ferromagnet (both with k=0) in applied magnetic field with $B_c$=3 T. Low-energy inelastic neutron scattering identifies weakly dispersive magnetic bands around 0.72 meV starting at $midbf{Q}mid$ = 1.1 AA$^{-1}$~ at zero field, which diminish with field and vanish above 3 T. We explain the observed magnetic behaviour in framework of the nearest-neighbour anisotropic exchange model for effective $S=1/2$ Kramers doublets on the pyrochlore lattice. The estimated exchanges position the {CYS} spinel close to the phase boundary between the $Gamma_5$ and splayed ferromagnet states, similar to the Yb-pyrochlores suggesting an important role of the competition between these phases.
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