Describing and quantifying animal personality is now an integral part of behavioural studies because individually distinctive behaviours have ecological and evolutionary consequences. Yet, to fully understand how personality traits may respond to selection, one must understand the underlying heritability and genetic correlations between traits. Previous studies have reported a moderate degree of heritability of personality traits, but few of these studies have either been conducted in the wild or estimated the genetic correlations between personality traits. Estimating the additive genetic variance and covariance in the wild is crucial to understand the evolutionary potential of behavioural traits. Enhanced environmental variation could reduce heritability and genetic correlations, thus leading to different evolutionary predictions. We estimated the additive genetic variance and covariance of docility in the trap, sociability (mirror image stimulation), and exploration and activity in two different contexts (open-field and mirror image simulation experiments) in a wild population of yellow-bellied marmots (Marmota flaviventris). We estimated both heritability of behaviours and of personality traits and found nonzero additive genetic variance in these traits. We also found nonzero maternal, permanent environment and year effects. Finally, we found four phenotypic correlations between traits, and one positive genetic correlation between activity in the open-field test and sociability. We also found permanent environment correlations between activity in both tests and docility and exploration in the MIS test. This is one of a handful of studies to adopt a quantitative genetic approach to explain variation in personality traits in the wild and, thus, provides important insights into the potential variance available for selection.