The menstrual cycle has many complicated and largely disregarded effects on a woman's life and behavior.
Chen et al. (2005) used an auction-bidding game to compare how men and women took risks and maximized earnings. Interestingly, they found that women's bidding, while it differed from men's through most of the month, did not significantly differ from men's during menstruation; when estrogen levels were at their lowest, the gender gap disappeared. The authors say this is consistent with previous understanding of women's risk-taking strategies.
St Leger et al. (2006) found that recreational female scuba divers encountered more problems while diving at certain points in their cycle.
Walpurger et al. (2004) found that a woman's classification response to auditory stimuli was faster during menstruation than at other times in the cycle.
I find it terribly amusing that these studies suggest that menstruation (an event often used to differentiate the experience of womanhood) is the time when a woman seems to be most similar to a man, hormonally. I barely remember what it was like, to be honest. Menstruation wasn't really that big a deal for me, although I saw it wreak havoc on the bodies of the people around me. I can't say I noticed any particular difference in alertness or risk-taking, either, since the swings in libido ran over subtler distinctions rough-shod. Sadly, much like I've experienced with testosterone, it's impossible to tell which effects were real, and which were placebo caused by my own expectations.