Optimal portfolio allocation and asset centrality revisited

This paper revisits the relationship between eigenvector asset centrality and optimal asset
allocation in a minimum variance portfolio. We show that the standard denition of eigen-
vector centrality is misleading when the adjacency matrix in a network can take negative
values. To correct for this, we introduce the concept of positive and negative eigenvector
centrality. We also show that the relationship between the centrality of an asset and its
optimal allocation in an investment portfolio is not decreasing or monotonic. Our results
contradict recent results on the nancial networks literature claiming otherwise. As a
byproduct, we show that the marginal rate of substitution between positive and negative
asset centrality is positive implying that both centrality measures tend to move together
in the same direction to preserve the optimal allocation of an asset in a portfolio. These
theoretical insights are illustrated empirically in a portfolio allocation exercise with assets
from U.S. and U.K. nancial markets.