The Inference and Analysis of Correlation and Partial Correlation Financial Networks

Abstract

To understand risk in a financial market we must understand how asset prices are related. By using correlation measures we can quantify the relationships between asset pairs, and then using network science we can then attempt to study the system as a whole. In this thesis we explore the use of various correlation and partial correlation estimators to estimate a financial network from returns data. We then show how these networks differ from the standard Pearson correlation models and attempt to evaluate their use. We firstly explore the use of sparse precision matrix estimators, and compare their success in selecting a known underlying model to simply thresholding the sample covariance matrix. Surprisingly we find that thresholding the sample covariance matrix is competitive with these sparse precision matrix estimators. Next we look at using a selection of these estimators for portfolio optimization. We find that in general they do not outperform non-sparse methods, such as the Ledoit-Wolf shrinkage estimators, but can provide some added robustness, and do force diversification upon the portfolios. We then look at constructing networks using these precision matrix estimations. Firstly we use the Ledoit-Wolf shrinkage method to construct partial correlation networks of the S&P500. These partial correlation networks have a significantly less variable largest eigenvalue than a correlation network, indicating the effect of the market has been removed, but in fact are more unstable than their correlation counterparts, with both the largest eigenvector and community structure changing significantly more between adjacent time periods. Furthermore we have less success in uncovering the underlying sector structure in these partial correlation networks compared to the equivalent correlation ones. These Ledoit-Wolf estimated networks are dense, which can inhibit interpretability. Therefore next we look at using a sparse precision matrix estimator, the SPACE method. Again these networks seem quite unstable, with a large number of edge changes between networks adjacent in time, indicating that partial correlation networks in general are more unstable than their correlation counterparts. Next we explore the use of rank correlation methods for the construction of minimum spanning trees from financial returns, and explore how these compare to those constructed using Pearson correlation. We find that the trees constructed using these rank methods correlation tend to be more stable and maintain more edges over the dataset than those constructed using Pearson correlation and the trees have similar topologies. We also explore how deviations from Gaussianity drive differences in the trees. There is little correlation between MST differences and deviations from univariate Gaussianity, but if we use quantile normalization to force the dataset to be univariate Gaussian then the differences between the MSTs drops, indicating this does have an effect. Finally we look at how the similarity and stability of correlation networks changes during times of market calm and market stress. Using some simple measures, such as the change and standard deviation of the entries in the leading eigenvector and the mean L2 difference between nodes, we look at three different markets, the US, UK and Germany, and find that the UK and US markets become more similar and more stable during times of market stress, but the German market does not see such effects.

More information

Identifiers

ORCID for Mahesan Niranjan: orcid.org/0000-0001-7021-140X

Catalogue record

Export record