  We discuss the recently observed `excesses' in cosmic ray electron and
positron fluxes which have been widely interpreted as signals of dark matter.
By considering the production and acceleration of secondary electrons and
positrons in nearby supernova remnants, we predict an additional, harder
component that becomes dominant at high energies. The unknown spatial
distribution of the supernova remnants introduces a stochastic uncertainty
which we estimate analytically. Fitting the prediction for different source
distributions to the total electron + positron flux measured by Fermi--LAT
fixes all free parameters and allows us to `postdict' the rise in the positron
fraction seen by PAMELA. A similar rise in the B/C ratio is predicted at high
energies.
