The question of whether security return distributions have a finite or an infinite variance has been debated for many years. The possibility that the security return-generating process actually has an infinite variance is particularly vexing since it implies that all statistical techniques and theoretical frameworks utilizing the second (or higher) moment are invalid. While this is clearly not a disaster—alternatives do exist—much of the work which has been done in the field of finance has assumed the existence of the second moment. It is, therefore, important to determine whether or not the security return distribution actually has a finite variance.