Mean-variance analysis of portfolios of dependent investments: An extension

Abstract

This paper extends portfolio-choice theory under risk aversion to the case of dependent investments. It establishes the circumstances in which optimal portfolios of dependent investments will be diversified or completely specialized, and reevaluates earlier statements in this connection arrived at without reference to risk preference. The model, which assumes two risky assets, focuses first on the normal case, in which one asset has both a higher mean and variance of expected returns and, second, on the perverse case, in which one of the two assets is both more profitable and less risky than the other. In the first case diversified portfolios are the rule irrespective of the degree of correlation between assets; completely specialized portfolios may only obtain as corner solutions generally resulting from low-risk aversion; complete specialization obtains when there is high-risk aversion only in the limiting normal case of equally profitable but unequally risky assets. In the second, or perverse case, a wider variety of diversified portfolios than previously thought is found to be optimal. Specifically, diversification may be optimal even if one security has an extremely higher yield and lower variance of returns than the other, provided asset correlation is sufficiently low or negative. There will be complete specialization in the more profitable and less risky asset only if the correlation coefficient between asset returns assumes positive values in an interval that will be narrower or wider depending on the assumed degree of risk aversion and other considerations.