Asset Allocation

CHAPTER 6Correlation Asymmetry

FALLACY: DIVERSIFICATION IS SYMMETRIC

That investors should diversify their portfolios is a core principle of modern finance. The correlation coefficient, the parameter that quantifies the degree to which two assets tend to offset – or diversify – one another, took on new significance in 1952 when Harry Markowitz published his landmark article “Portfolio Selection.” Markowitz formalized the role of diversification in portfolio risk when he showed how to construct optimal portfolios given the expected returns, standard deviations, and correlations of their component assets. Nearly 70 years after it was introduced, the mean-variance paradigm has proved surprisingly robust. However, it makes two implicit assumptions about diversification that warrant careful consideration. Because it relies on a single parameter to approximate the way each pair of assets covary, mean-variance analysis assumes that correlations are symmetric on the upside and downside. Moreover, when we maximize the quadratic utility function that takes this single parameter as an input, we also assume that diversification is desirable on the upside as well as the downside.¹ The first assumption is occasionally correct, but the second assumption never is.

Diversification is most helpful to investors when the major engine of growth in the portfolio, typically domestic equities, performs poorly. They derive benefit from assets whose returns offset this poor performance. When the growth ...