Research and policy discussion about the diverging fortunes of children from advantaged and disadvantaged households have focused on the skill disparities between these children – how they might arise and how they might be remediated. Analysis of data from the National Longitudinal Study of Adolescent Health reveals another important mechanism in the determinants of educational attainment – differential returns to skills for children in different circumstances. Though the returns to cognitive ability are generally consistent across family background groups, personality traits have very different effects on educational attainment for young men and women with access to different levels of parental resources. These results are consistent with a model in which the provision of focused effort in school is complementary with parental inputs while openness, associated with imagination and exploration, is a substitute for information provision by educated parents and thus contributes to resilience in low-resource environments. In designing interventions to improve outcomes for disadvantaged children, we need to be cognizant of interactions between a child's skills and their circumstances.