Always Possible Frontiers Available to Purchase

This note addresses the issue of impossible mean-variance frontiers – those on which there are no portfolios all of whose weights are positive. This is a concern because the market portfolio should be mean-variance efficient, and it has entirely positive weights. It has been argued that impossible frontiers are likely and occur with probability one as the number of assets increases. This criticism, however, is purely statistical in nature. Similar analysis shows that arbitrage is also ubiquitous. When we recognize that the returns available in the market are not randomly distributed, but are the consequence of equilibrium process, then both of these concerns vanish. Possible frontiers will always arise.