The levels of diversification in U.S. investors' equity portfolios present a puzzle. Today's optimal level of diversification, measured by the rules of mean–variance portfolio theory, exceeds 300 stocks, but the average investor holds only 3 or 4 stocks. The diversification puzzle can be solved, however, in the context of behavioral portfolio theory. In behavioral portfolio theory, investors construct their portfolios as layered pyramids in which the bottom layers are designed for downside protection and the top layers are designed for upside potential. Risk aversion gives way to risk seeking at the uppermost layer as the desire to avoid poverty gives way to the desire for riches. But what motivates this behavior is the aspirations of investors, not their attitudes toward risk. Some investors fill the uppermost layer with the few stocks of an undiversified portfolio; others fill it with lottery tickets. Neither lottery buying nor undiversified portfolios are consistent with mean–variance portfolio theory, but both are consistent with behavioral portfolio theory.