Expanding the frontier one asset at a time

We add a new risky asset to a set of n risky assets and derive the analytical relation between the original and the new mean-variance efficient frontiers. The two frontiers have a tangency point. A new mutual fund theorem holds. All portfolios in the new minimum-variance set are portfolio combinations of three mutual funds: The two funds located on the original frontier and the third fund containing all assets. We discuss implications of the new results for models of financial innovation, studies of portfolio re-balancing and trading volume, and for empirical tests of the CAPM (Roll critique).