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An Analytic Derivation of the Efficient Portfolio Frontier

Published online by Cambridge University Press:  19 October 2009

Robert C. Merton
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Extract

The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 7 , Issue 4 , September 1972 , pp. 1851 - 1872
Copyright
Copyright © School of Business Administration, University of Washington 1972

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