After reviewing the record in this case and considering the briefs and argument of the parties, we are satisfied that the district court did not abuse its discretion in denying the plaintiffs’ motion for leave to amend.

On the merits, the question of reliance in plaintiffs’ fraud-on-the-market case is controlled by Greenberg v. Crossroads Systems, Inc., 364 F.3d 657 (5th Cir. 2004). Under the reasoning of that case, we agree with the district court that the defendants *988 successfully rebutted the presumption that the plaintiffs purchased the Zonagen stock in reliance on defendants’ false statements. For these reasons and the reasons stated by the district court in its careful opinion of June 13, 2003, the district court’s judgment is.

AFFIRMED.