Context : Aims : With available Virtual Observatory tools , we looked for new M dwarfs in the solar neighbourhood and M giants with high tangential velocities . Methods : From an all-sky cross-match between the optical Tycho-2 and the near-infrared 2MASS catalogues , we selected objects with proper motions \mu > 50 mas yr ^ { -1 } and very red V _ { T } - K _ { s } colours . For the most interesting targets , we collected multi-wavelength photometry , constructed spectral energy distributions , estimated effective temperatures and surface gravities from fits to atmospheric models , performed time-series analysis of ASAS V -band light curves , and assigned spectral types from low-resolution spectroscopy obtained with CAFOS at the 2.2 m Calar Alto telescope . Results : We got a sample of 59 bright red high proper-motion objects , including fifty red giants , four red dwarfs , and five objects reported in this work for the first time . The five new stars have magnitudes V _ { T } \approx 10.8–11.3 mag , reduced proper motions midway between known dwarfs and giants , near-infrared colours typical of giants , and effective temperatures T _ { eff } \approx 2900–3400 K. From our time-series analysis , we discovered a long secondary period in Ruber 4 and an extremely long primary period in Ruber 6 . With the CAFOS spectra , we confirmed the red giant nature of Ruber 7 and 8 , the last of which seems to be one of the brightest metal-poor M giants ever identified . Conclusions :