Revisiting Modern Portfolio Theory and Its Misinterpretations

This paper revisits Modern Portfolio Theory and derives eleven properties of Efficient Allocations and Efficient Portfolios in order to analyze two misinterpretations of the Theory: the Mutual Fund Theorem and the Roles of Diversification in an Efficient Portfolio. A mean-variance efficient allocation is one in which the totality of the investment is allocated in the Minimum Variance Portfolio, whilst the Risk Portfolio comprises exclusively of shorts and longs that exactly cancel each other out. That is, no net resources are ever allocated in the Risk Portfolio and a change in investor´s risk-return preferences will leave the allocation between the Minimum Variance and Risk Portfolios completely unaltered - only changing the magnitudes of the shorts and longs within the Risk Portfolio. This interpretation of the Mutual Fund theorem contrasts with the traditional interpretation that a change in risk-return preferences will actually shift resources from the Minimum Variance to the Risk Portfolio. Secondly, in an Efficient Portfolio, Diversification acquires another important role. In addition to the traditional role of minimizing variance, Diversification is also an instrument to efficiently increase risk and the magnitudes of the shorts and longs within the Risk Portfolio.