This Essay argues that it is impossible to achieve the following objectives simultaneously: (i) portfolio diversification, (ii) shareholder representation, and (iii) competition. In an economy in which everyone holds the market portfolio, all companies have the same shareholders. If, in addition, firms act in the interest of their shareholders (in other words, if the agency problem is solved), the equilibrium outcome is equivalent to an economy-wide monopoly. When managers are entrenched, however, the anticompetitive effects of common ownership are mitigated, yet they only disappear completely in the extreme case that managers are fully insulated from shareholder dissent. The trilemma highlights a fundamental systemic problem in stock market economies: their inherent tendency toward common ownership, and therefore away from market competition.