Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit

TL;DR

This paper revisits the relationship between risk and diversification in the Markowitz mean-variance model, questioning the conventional wisdom under full information and non-exchangeable return distributions, including the role of risk-free assets.

Contribution

It provides a theoretical analysis of risk reduction and diversification when investors have full information and considers the impact of including risk-free assets.

Findings

Challenged the traditional view of diversification asymptotes.

Analyzed the role of risk-free assets in diversification.

Provided insights into risk-return relationships under full information.

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.