In this paper the changes of magnetic properties with increasing disorder in the exchange-enhanced Pauli paramagnet ${\mathrm{YCo}}_{2}$ are discussed. The structural disorder is initially introduced by rapid quenching, while further changes on a micro- or nanoscale are caused by a high-pressure torsion (HPT). Values of the magnetic moment determined for the plastically deformed ribbons reach $0.10\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Co}$ atom (for a sample subjected to the deformation at a pressure of 4 GPa) and $0.25\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Co}$ (6 GPa) at 2 K. The magnetic moment arises not only from the surface of nanocrystals but also from volume. Ab initio calculations explained the influence of chemical disorder and different types of structural defects on the electronic structure and magnetic properties of ${\mathrm{YCo}}_{2}$-based Laves phases. The calculated magnetic ground states are in qualitative agreement with experimental results for all considered structures with point defects.