Partial correlation financial networks

Correlation networks have been a popular way of inferring a financial network due to the simplicity of construction and the ease of interpretability. However two variables which share a common cause can be correlated, leading to the inference of spurious relationships. To solve this we can use partial correlation. In this paper we construct both correlation and partial correlation networks from S&P500 returns and compare and contrast the two. Firstly we show that the partial correlation networks have a smaller and much less variable intensity than the correlation networks, but in fact are less stable. We look at the centrality of the various sectors in the graph using degree centrality and eigenvector centrality, finding that sector centralities move together during the 2009 market crash and that the financial sector generally has a higher mean centrality over most of the dataset. Exploring the use of these centrality measures for portfolio construction, we shown there is mild correlation between the in-sample centrality and the out of sample Sharpe ratio but there is negative correlation between the in-sample centrality and out of sample risk. Finally we use a community detection method to study how the networks reflect the underlying sector structure and study how stable these communities are over time.