I also did a quick check on S&P June 1st 2010 data and it was down. So the first data that I tested invalidates your theory. May 28 close 1089.41 June 1st close 1070.71
May be you should look at this: http://www.bespokeinvest.com/thinkbig/2011/5/31/its-the-first-of-the-month.html S&P was up 13 out 17 times. Good luck with your puts though because you are going to need it.