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.

由于构造简单和易于解释，相关网络已成为推断金融网络的一种流行方式。但是，可以将具有共同原因的两个变量关联起来，从而推断出虚假关系。为了解决这个问题，我们可以使用偏相关。在本文中，我们根据S＆P500的收益构建了相关和偏相关网络，并对两者进行了比较和对比。首先，我们证明了部分相关网络具有比相关网络更小的变量强度，但实际上却不那么稳定。我们使用度中心度和特征向量中心度来观察图中各个扇区的中心度，发现在2009年市场崩盘期间各部门的中心性一起移动，而金融部门在大多数数据集中通常具有较高的平均中心性。探索使用这些集中度度量进行投资组合构建时，我们显示出样本内集中度与样本外Sharpe比率之间存在温和的相关性，但是样本内集中度与样本外风险之间存在负的相关性。最后，我们使用社区检测方法来研究网络如何反映底层行业结构，并研究这些社区随着时间的推移如何稳定。我们显示，样本内中心度与样本外Sharpe比率之间存在轻微的相关性，但样本内中心度与样本外风险之间存在负相关性。最后，我们使用社区检测方法来研究网络如何反映底层行业结构，并研究这些社区随着时间的推移如何稳定。我们显示，样本内中心度与样本外Sharpe比率之间存在轻微的相关性，但样本内中心度与样本外风险之间存在负相关性。最后，我们使用社区检测方法来研究网络如何反映底层行业结构，并研究这些社区随着时间的推移如何稳定。