In this article we compare the properties of two naive portfolio-building rules: equal weights and market value weights. Specifically, we study the risk composition of randomly selected portfolios of size one, two, four, and so forth, from two large, interdependent stock universes. On the basis of the rationale of simple random sampling without replacement we derive, analytically, the risk composition of these portfolios. We find that for all portfolio sizes, including portfolios of one stock, the risk measures of market-value-based portfolios are lower than equal-value-based portfolios. We conclude that this is so because risk is inversely related to size. Thus, market value weights understate risk for randomly selected portfolios. Our results complement findings of others who report inferior characteristics of market-value-weighted portfolios vis à vis equally weighted portfolios.