We derive sufficient conditions for the cross-correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects. The derived class is valid for any choice of covariance functions, and yields substantial flexibility between multiple processes. The key is to identify the cross-correlation coefficient matrix with a contraction m...

where X and Y are random returns. The main innovation introduced by Markowitz is to measure the risk of a portfolio via the joint (multivariate) distribution of returns of all assets. Multivariate distributions are characterized by the statistical (marginal) properties of all component random variables and by their dependence structure. Markowitz described the former by the first two moments of...