  The small-scale distribution of dark matter in Galactic halos is poorly
known. Several studies suggest that it could be very clumpy, which turns out to
be of paramount importance when investigating the annihilation signal from
exotic particles (e.g. supersymmetric or Kaluza-Klein). In this paper we focus
on the annihilation signal in positrons. We estimate the associated
uncertainty, due to the fact that we do not know exactly how the clumps are
distributed in the Galactic halo. To this aim, we perform a statistical study
based on analytical computations, as well as numerical simulations. In
particular, we study the average and variance of the annihilation signal over
many Galactic halos having the same statistical properties. We find that the
so-called boost factor used by many authors should be handled with care, as i)
it depends on energy and ii) it may be different for positrons, antiprotons and
gamma rays, a fact which has not received any attention before. As an
illustration, we use our results to discuss the positron spectrum measurements
by the HEAT experiment.
