It is clear from several previous empirical studies that diversification reduces portfolio return variability and that the reduction of variability appears very quickly. The purpose of this paper is to reexamine the question of how diversification affects the distribution of portfolio returns. There is no doubt that increasing the number of securities in a portfolio will reduce the nonmarket related return variability. However, there are several areas of controversy. For example, it should be recognized that the term “variability” can have different definitions. Furthermore, the ability of diversication to eliminate independent elements of the variability of return is important only if this reduction can be incorporated into predictions of future risk. In addition, the method of portfolio formation may determine the extent to which diversification enables portfolio managers to more accurately assist future risk.