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We ran a field experiment to investigate whether competing in rank-order tournaments with different prize spreads affects individual performance. Our experiment involved students from an Italian University who took an exam that was partly evaluated on the basis of relative performance. Students were matched in pairs on the basis of their high school grades and each pair was randomly assigned to one of three different tournaments. Random assignment neutralizes selection effects and allows us to investigate if larger prize spreads increase individual effort. We do not find any positive effect of larger prizes on performance. Furthermore, we show that the effect of prize spreads on students' performance depends on their degree of risk-aversion: competing in tournaments with large spreads negatively affects the performance of risk-averse students, while it does not produce any effect on students who are more prone to taking risks.