Reinterpreting the mutual fund theorem: the risk portfolio as a tactical overlay

Abstract

The Mutual Fund Theorem is an elegant way of describing how investors with different attitudes towards risk should construct their portfolios. It is, however, often misinterpreted. This paper revisits the topic by defining the Risk Portfolio as a self-financed tactical overlay portfolio in which all the overweight and underweight positions cancel each other out. In this sense no net resources are ever allocated to the Risk Portfolio and all the investment is allocated to the Minimum Variance Portfolio. Under these circumstances the Mutual Fund Theorem implies that the ratio of Bonds to Stocks in the Total Portfolio would depend on investor´s risk aversion; as it is actually observed in practice. The paper also argues that the Asset Allocation puzzle, as traditionally stated in the literature, only arises because of a misconception about the 'the facto' definition of the Risk Portfolio.