This paper revisits the relationship between eigenvector asset centrality and optimal asset allocation in a minimum variance portfolio. We show that the standard definition of eigenvector centrality is misleading when the adjacency matrix in a network can take negative values. This is, for example, the case when the network topology is induced by the correlation matrix between assets in a portfolio. To correct for this, we introduce the concept of positive and negative eigenvector centrality. Our results show that the loss function associated to the minimum variance portfolio is positively/negatively related to the positive and negative eigenvector centrality under short-selling constraints but cannot be generalized beyond that. Furthermore, in contrast to what is claimed in the related literature, this relationship does not imply any monotonic relationship between the centrality of an asset and its optimal portfolio allocation. These theoretical insights are illustrated empirically in a portfolio allocation exercise with assets from U.S. and U.K. financial markets.

本文重新审视了最小方差投资组合中特征向量资产中心性与最优资产配置之间的关系。我们表明，当网络中的邻接矩阵可以取负值时，特征向量中心性的标准定义会产生误导。例如，当网络拓扑由投资组合中资产之间的相关矩阵引起时，就是这种情况。为了纠正这一点，我们引入了正负特征向量中心性的概念。我们的结果表明，与最小方差投资组合相关的损失函数与卖空约束下的正负特征向量中心性正/负相关，但不能推广到此之外。此外，与相关文献中声称的相反，这种关系并不意味着资产的中心性与其最优投资组合配置之间存在任何单调关系。这些理论见解在美国和英国金融市场资产的投资组合分配实践中得到了实证说明。