Visualising dependence This month we look at the application of http:// en.wikipedia.org/wiki/Graph_(mathematics) graph theory to attempt to better visualise these connections. Our ultimate aim is, as always, to better understand the underlying dynamics and dependencies between assets in order to be able to better diversify our portfolios against the next crisis. In particular, we examine the use of http:// en.wikipedia.org/wiki/Partial_correlation Partial Correlation to help deepen our understanding of the co-relationships that exist and also to help filter out extraneous or spurious correlations. The Partial Correlation Matrix is calculated from the inverse matrix of either the standard Pearson product moment Correlation Matrix or the Variance- Co-Variance Matrix, preferably after ‘robustifying’ it through some or other form of shrinkage towards the global mean. In its univariate form, it can be thought of as the correlation of the residuals of X and Y after subtracting the returns of a third variable Z, from both. A Dependency matrix is then constructed by deducting the Partial Correlation from the Pearson Correlation to help identify those components with the highest level of interaction. It is hoped that the resulting matrix is more representative of the ‘true’ dependencies. The Dependency Matrix is then converted to an adjacency matrix, typically after further threshold filtering, and then to a Directed Adja......................

To view our full article please login

This article was published in Opalesque's New Managers a top-down monthly analysis, news and research publication on the global emerging manager space.