We conduct an experiment in which individuals select securities to reproduce the well-known relationship between portfolio risk and the number of securities. The standard result occurs on average but not for most individuals, many of whom effectively de-diversify as they add seemingly random securities. Moreover, only slightly better results are achieved using a random number generator. This finding challenges the belief that only a small number of securities are required for diversification and shows that it is applicable only to a large sample. The implications are important given that many individual investors hold very few stocks in their portfolios.