Mobile phones contain a wealth of private information, so we try to keep them secure. We provide large-scale evidence that the psychological profiles of individuals and their relations with their peers can be predicted from seemingly anonymous communication traces -- calling and texting logs that service providers routinely collect. Based on two extensive longitudinal studies containing more than 900 college students, we use point process modeling to describe communication patterns. We automatically predict the peer relationship type and temporal dynamics, and assess user personality based on the modeling. For some personality traits, the results are comparable to the gold-standard performances obtained from survey self-report data. Findings illustrate how information usually residing outside the control of individuals can be used to reconstruct sensitive information.