The positron fraction observed by PAMELA and other experiments up to \sim 100 GeV is analyzed in terms of models of cosmic-ray propagation . It is shown that generically we expect the positron fraction to reach \sim 0.6 at energies of several TeV , and its energy dependence bears an intimate but subtle connection with that of the boron to carbon ratio in cosmic rays . The observed positron fraction can be fitted in a model that assumes a significant fraction of the boron below \sim 10 GeV is generated through spallation of cosmic-ray nuclei in a cocoonlike region surrounding the sources , and the positrons of energy higher than a few GeV are almost exclusively generated through cosmic-ray interactions in the general interstellar medium . Such a model is consistent with the bounds on cosmic-ray anisotropies and other observations .