We present a study of the magnetic properties of oxidized Co nanoparticles with an average grain size of 3 nm, embedded in an amorphous Al2O3 matrix. These nanoparticles can be considered as imperfect Co-core CoO-shell systems. Magnetization measurements after magnetic field cooling show a vertical shift of the hysteresis loop, while no exchange bias is observed. With a simple model, we show that there is a critical grain size for hybrid ferromagnetic-antiferromagnetic particles, below which exchange bias is absent for any ratio of ferromagnetic and antiferromagnetic constituents. The reason is that the interfacial exchange energy dominates over other energies in the system due to a large surface-to-volume ratio in the nanoparticles. (c) 2005 American Institute of Physics.