In this paper, we investigate the relationship between automatically extracted behavioral characteristics derived from rich smartphone data and self-reported Big-Five personality traits (Extraversion, Agreeableness, Conscientiousness, Emotional Stability and Openness to Experience). Our data stems from smartphones of 117 Nokia N95 smartphone users, collected over a continuous period of 17 months in Switzerland. From the analysis, we show that several aggregated features obtained from smartphone usage data can be indicators of the Big-Five traits. Next, we describe a machine learning method to detect the personality trait of a user based on smartphone usage. Finally, we study the benefits of using gender-specific models for this task. Apart from a psychological viewpoint, this study facilitates further research on the automated classification and usage of personality traits for personalizing services on smartphones.