This paper studies gender disparities in performance and risk aversion under competition. We use data from the Anpec Exam, the Brazilian national exam for students applying for Graduate Programs in Economics. This particular exam assigns negative points to incorrect answers, which could lead to the more risk-averse students leaving more questions unanswered and possibly getting lower grades. We show that women tend to omit more questions compared to men and are consistently under represented at the top of the rankings. Using the Rasch Model we derive probabilities of answering each question correctly for each student and show that both men and women deviate from the optimal strategy that maximizes their expected score. We also investigate the scenario where all students guess the questions previously left unanswered, after recalculating the expected scores and new rankings in this scenario we find that on average the effect for women that were already at the top of the distribution is very small, and women that were closer to the bottom of the ranking benefit more.