Basic personality traits are typically assessed through questionnaires. Here we consider phone-based metrics as a way to asses personality traits. We use data from smartphones with custom data-collection software distributed to 730 individuals. The data includes information about location, physical motion, face-to-face contacts, online social network friends, text messages and calls. The data is further complemented by questionnaire-based data on basic personality traits. From the phone-based metrics, we define a set of behavioral variables, which we use in a prediction of basic personality traits. We find that predominantly, the Big Five personality traits extraversion and, to some degree, neuroticism are strongly expressed in our data. As an alternative to the Big Five, we investigate whether other linear combinations of the 44 questions underlying the Big Five Inventory are more predictable. In a tertile classification problem, basic dimensionality reduction techniques, such as independent component analysis, increase the predictability relative to the baseline from $11\%$ to $23\%$. Finally, from a supervised linear classifier, we were able to further improve this predictability to $33\%$. In all cases, the most predictable projections had an overweight of the questions related to extraversion and neuroticism. In addition, our findings indicate that the score system underlying the Big Five Inventory disregards a part of the information available in the 44 questions.