Optimal Portfolio Choice and Stock Centrality for Tail Risk Events

TL;DR

This paper introduces a new risk matrix combining VaR and Delta-CoVaR to optimize portfolios considering tail risks, revealing complex relationships between asset centrality and risk, with empirical evidence favoring highly connected networks.

Contribution

It develops a novel risk matrix incorporating tail dependence measures and analyzes the impact of stock centrality on optimal portfolio allocation.

Findings

Portfolio risk is not necessarily increasing with stock centrality.

High connectivity networks outperform low connectivity ones based on Sharpe ratio.

Closed-form solutions are derived for the quadratic risk function.

Abstract

We propose a novel risk matrix to characterize the optimal portfolio choice of an investor with tail concerns. The diagonal of the matrix contains the Value-at-Risk of each asset in the portfolio and the off-diagonal the pairwise Delta-CoVaR measures reflecting tail connections between assets. First, we derive the conditions under which the associated quadratic risk function has a closed-form solution. Second, we examine the relationship between portfolio risk and eigenvector centrality. Third, we show that portfolio risk is not necessarily increasing with respect to stock centrality. Forth, we demonstrate under certain conditions that asset centrality increases the optimal weight allocation of the asset to the portfolio. Overall, our empirical study indicates that a network topology which exhibits low connectivity is outperformed by high connectivity based on a Sharpe ratio test.