Introduction

The characteristics of the efficient (in the mean-variance sense) 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 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 classical graphical technique for deriving the efficient portfolio frontier is incorrect.

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