Enhancing Portfolio Allocation: A Random Matrix Theory Perspective

This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, which are particularly susceptible to insta...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-05, Vol.12 (9), p.1389
Main Authors: Vanni, Fabio, Hitaj, Asmerilda, Mastrogiacomo, Elisa
Format: Article
Language:English
Subjects:
Clustering
Correlation analysis
dependence structure
Eigenvalues
Eigenvectors
Empirical analysis
Financial markets
Hilbert transformation
Investment analysis
Linear programming
Matrix theory
Methods
Multivariate analysis
networks
Optimization
Optimization techniques
Portfolio management
portfolio selection
random matrix theory
Random variables
Risk management
Securities markets
Strategic planning (Business)
Time series
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Summary:This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, which are particularly susceptible to instabilities. To address this challenge, we combine a data preprocessing technique based on the Hilbert transformation of returns with RMT to refine the accuracy and robustness of correlation matrix estimation. By comparing empirical correlations with those generated through RMT, we reveal non-random properties and uncover underlying relationships within financial data. We then utilize this methodology to construct the correlation network dependence structure used in portfolio optimization. The empirical analysis presented in this paper validates the effectiveness of RMT in enhancing portfolio diversification and risk management strategies. This research contributes by offering investors and portfolio managers with methodological insights to construct portfolios that are more stable, robust, and diversified. At the same time, it advances our comprehension of the intricate statistical principles underlying multivariate financial data.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12091389