Optimal portfolio allocation and asset centrality revisited

J. Olmo (2021). Optimal portfolio allocation and asset centrality revisited. Quantitative Finance 21:9, 1475-1490.

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.

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.