Wirth, Philipp;
(2025)
Graph and Tensor Models for Correlation Network-based Portfolio Construction.
Doctoral thesis (Ph.D), UCL (University College London).
Abstract
This thesis develops and evaluates novel methodologies from graph theory and higher-order tensor decomposition to enhance portfolio diversification by uncovering hidden market structures and higher-dimensional asset relationships. The Dynamic Modularity-Spectral Algorithm (DynMSA) is introduced, a graph-based method combining community detection, spectral clustering and Random Matrix Theory to dynamically cluster assets without predefined cluster parameters. Tucker and Tensor Train decompositions are utilised to identify latent, multidimensional factors influencing asset returns over time. Tucker decomposition is applied to the Fama-French 5-factor betas of US stocks to investigate any higher-order relationships in these factor influences on US stock prices. After that, Tensor Train decomposition is used on time-wise stacked correlation matrices of US stocks to find la- tent factors that drive the changes in correlation network structures. Empirical analyses reveal that both DynMSA and Tensor Train decomposition methods generate statistically significant outperformance in portfolio returns and effectively uncover hidden market microstructures, confirming their practical relevance for risk management and portfolio optimisation. While similar performance and factor relationship insights were not consistently observed when decomposing Fama-French factor sensitivities using Tucker Decomposition, the general results of this work highlight the capabilities of non-traditional method- ologies for portfolio construction.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Graph and Tensor Models for Correlation Network-based Portfolio Construction |
| Language: | English |
| Additional information: | All rights reserved |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Civil, Environ and Geomatic Eng |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10215837 |
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