  We show, using the trace formula, that any Newton stratum of a Shimura
variety of PEL-type of types (A) and (C) is non-empty at the primes of good
reduction. Furthermore we prove conditionally the non-emptiness for Shimura
data associated to odd Spin groups.
  Our results are conditional on Rapoport-Langlands conjecture and Arthur's
conjectures on the discrete spectrum. Both these results have been announced by
Arthur and Kisin in significant cases.
