Mean–variance portfolio selection with correlation risk

Abstract

The Markowitz mean–variance portfolio selection (MVPS) problem is the building block of modern portfolio theory. Since Markowitz (1952) published his seminal study, there have been numerous extensions to the continuous-time MVPS problem under different market conditions. This paper further enriches the literature by taking account of correlation risk among risky asset returns. Empirical studies reveal that correlations among economic variables change randomly over time and affect hedging and investment demand in different correlation regimes. By incorporating correlation risk into the dynamic MVPS through the Wishart variance–covariance matrix process, this paper derives the explicit closed-form solution to the optimal portfolio policy and determines the market regime in which the optimal policy is stable and well-behaved. This stable market regime is found to be fully characterized by the correlation between market returns and their variance–covariance matrix or, equivalently, the effects of market leverage.