  We present radial velocity measurements of a sample of M5V-M9V stars from our
Red-Optical Planet Survey, ROPS, operating at 0.65-1.025 micron. Radial
velocities for 15 stars, with r.m.s. precision down to 2.5 m/s over a week long
time scale are achieved using Thorium-Argon reference spectra. We are sensitive
to planets with m_psin(i) >= 1.5 MEarth (3 MEarth at 2-sigma) in the classical
habitable zone and our observations currently rule out planets with m_psin(i) >
0.5 MJup at 0.03 AU for all our targets. A total of 9 of the 15 targets exhibit
r.m.s. < 16 m/s, which enables us to rule out the presence of planets with
m_psin(i) > 10 MEarth in 0.03 AU orbits.
  Since the mean rotation velocity is of order 8 km/s for an M6V star and 15
km/s by M9V, we avoid observing only slow rotators that would introduce a bias
towards low axial inclination i << 90 deg systems, which are unfavourable for
planet detection. Our targets with the highest vsini values exhibit radial
velocities significantly above the photon-noise limited precision, even after
accounting for vsini. We therefore monitored stellar activity via chromospheric
emission from the Halpha and Ca II infrared triplet lines. A clear trend of
log_10(Halpha/Lbol) with radial velocity r.m.s. is seen, implying that
significant starspot activity is responsible for the observed radial velocity
precision floor. The implication that most late M dwarfs are significantly
spotted, and hence exhibit time varying line distortions, indicates that
observations to detect orbiting planets need strategies to reliably mitigate
against the effects of activity induced radial velocity variations.
