Stable photinos, the photino being the supersymmetry partner of the photon, can explain both the 'missing mass' in galactic halos and the cosmic-ray antiproton spectrum up to the highest energies observed so far. This requires a photino mass around 15 GeV; significantly higher masses are cosmologically disfavored. As a consequence, the observed cosmic-ray antiproton-to-proton ratio is predicted to decrease abruptly just above the measured energy range, at E = m(x). If observed, this striking effect would strongly support the hypothesis that photinos make up the missing matter in the galaxy and also lead to a measurement of the photino mass from cosmic-ray data.