Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit (1608.05024v2)

Abstract: The conventional wisdom of mean-variance (MV) portfolio theory asserts that the nature of the relationship between risk and diversification is a decreasing asymptotic function, with the asymptote approximating the level of portfolio systematic risk or undiversifiable risk. This literature assumes that investors hold an equally-weighted or a MV portfolio and quantify portfolio diversification using portfolio size. However, the equally-weighted portfolio and portfolio size are MV optimal if and only if asset returns distribution is exchangeable or investors have no useful information about asset expected return and risk. Moreover, the whole of literature, absolutely all of it, focuses only on risky assets, ignoring the role of the risk free asset in the efficient diversification. Therefore, it becomes interesting and important to answer this question: how valid is this conventional wisdom when investors have full information about asset expected return and risk and asset returns distribution is not exchangeable in both the case where the risk free rate is available or not? Unfortunately, this question have never been addressed in the current literature. This paper fills the gap.