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We study the mean-variance optimization problem when investment opportunities are changing. We add a new risky asset to a set of n risky assets. An analytical relation between the original and the new minimum-variance frontiers is established. The two frontiers have a tangency point. We derive a new mutual fund theorem. 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. Analytical framework developed in the paper has implications for studies of testability of the mean-variance efficiency of a market portfolio (Roll critique). Implications for models of financial innovation are discussed.


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© Elsevier. Final version published as: Ukhov, A. D. (2006). Expanding the frontier one asset at a time. Finance Research Letters, 3(3), 194-206. DOI: 10.1016/ Reprinted with permission. All rights reserved.