Random Matrix Theory (RMT)

Correlation structure analysis of the global agricultural futures market ArXiv ID: 2310.16849 “View on arXiv” Authors: Unknown Abstract This paper adopts the random matrix theory (RMT) to analyze the correlation structure of the global agricultural futures market from 2000 to 2020. It is found that the distribution of correlation coefficients is asymmetric and right skewed, and many eigenvalues of the correlation matrix deviate from the RMT prediction. The largest eigenvalue reflects a collective market effect common to all agricultural futures, the other largest deviating eigenvalues can be implemented to identify futures groups, and there are modular structures based on regional properties or agricultural commodities among the significant participants of their corresponding eigenvectors. Except for the smallest eigenvalue, other smallest deviating eigenvalues represent the agricultural futures pairs with highest correlations. This paper can be of reference and significance for using agricultural futures to manage risk and optimize asset allocation. ...

Random matrix theory and nested clustered portfolios on Mexican markets ArXiv ID: 2306.05667 “View on arXiv” Authors: Unknown Abstract This work aims to deal with the optimal allocation instability problem of Markowitz’s modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT) and the machine learning allocation methodology known as Nested Clustered Optimization~(NCO). The latter methodology is modified and reformulated in terms of the spectral clustering algorithm and Minimum Spanning Tree~(MST) to solve internal problems inherent to the original proposal. Markowitz’s classical mean-variance allocation and the modified NCO machine learning approach are tested on financial instruments listed on the Mexican Stock Exchange~(BMV) in a moving window analysis from 2018 to 2022. The modified NCO algorithm achieves stable allocations by incorporating RMT covariance estimators. In particular, the allocation weights are positive, and their absolute value adds up to the total capital without considering explicit restrictions in the formulation. Our results suggest that can be avoided the risky \emph{“short position”} investment strategy by means of RMT inference and statistical learning techniques. ...