Portfolio selection based on graphs: Does it align with Markowitz-optimal portfolios?

Abstract

Some empirical studies suggest that the computation of certain graph structures from a (large) historical correlation matrix can be helpful in portfolio selection. In particular, a repeated finding is that information about the portfolio weights in the minimum variance portfolio (MVP) from classical Markowitz theory can be inferred from measurements of centrality in such graph structures. The present article compares the two concepts from a purely algebraic perspective. It is demonstrated that this heuristic relationship between graph centrality and the MVP does not originate from a structural similarity between the two portfolio selection mechanisms, but instead is due to specific features of observed correlation matrices. This means that empirically found relations between both concepts depend critically on the underlying historical data. Repeated empirical evidence for a strong relationship is hence shown to constitute a stylized fact of financial return time series.

Optimal Portfolio Choice and Stock Centrality for Tail Risk Events

“…More specifically, Peralta and Zareei (2016) concludes that optimal portfolio strategies should underweight the allocation to high central assets and overweight the allocation to low central assets. A similar finding is demonstrated by Huttner et al (2016). On the other hand, the study of Olmo (2021) concludes that higher asset centrality implies a larger allocation on the risky assets.…”

Matrix Evolutions: Synthetic Correlations and Explainable Machine Learning for Constructing Robust Investment Portfolios

“…Even smaller is the number of approaches to simulate such realistic correlation matrixes, maybe because finding such correlation matrixes is highly complex. For example, Huettner, Mai, and Mineo (2018) pointed out that "to the best of our knowledge, to date there exists no simulation algorithm that can reproduce all of them [the matrix evaluations], or even more than just one." The same authors later came up with a solution (Huettner and Mai 2019).…”

CORRGAN: Sampling Realistic Financial Correlation Matrices Using Generative Adversarial Networks

“…To the best of our knowlege, there are no previous attempt at generating realistic financial correlation matrices using GANs. No known model is able to capture, even approximately, all the known characteristics of financial correlation matrices [1]. We briefly review in the following subsection typical applications of GANs, and we highlight the lack of published results concerning financial data.…”