On SAT exams and in professional basketball, women tend to compete differently from men.
Until recently, a wrong answer on the SAT had a cost. Penalized one quarter point, test takers had the incentive to skip a question if they were unsure of the answer.
There was only one problem.
The girls and boys responded differently to the incentive. Knowing they would receive a penalty for an incorrect answer, one point if they were right, and zero points for skipping the question, more girls avoided the risk. As a result, an Ohio State economist hypothesized that girls had lower math SAT scores than boys because they answered fewer questions.
Towards the end of a professional basketball game when the score is close, the response of the losing team depends on whether it is male or female. For an NBA team, the relative share of 3-point shots rises. However, in the WNBA, gambling less on chancy shots, women use precisely the opposite strategy.
The one exception is a high stakes playoff during a tournament. Then economists have concluded that there is no gender difference.
Our Bottom Line: Risk Aversion
So yes, we can say that evidence displays women can be more risk averse than men. Taking the next step though, we should ask whether we are talking about nature or nurture. We also might contemplate when it can be smart to be risk averse.
Our sources and more: Whether looking at SATs or basketball or chess, the studies on female risk aversion abound. However, there is a another group that says we should consider where risk taking preferences have been modified (in single sex schools and classes), that the statistics could have been misinterpreted, and that women in matrilineal groups like my favorite, the Khasi, do not display the same risk averse behaviors. And finally, I recommend this excellent Freakonomics podcast.