Random matrix theory and nested clustered portfolios on Mexican markets

TL;DR

This paper combines Random Matrix Theory and a modified Nested Clustered Optimization method to improve the stability and risk profile of portfolio allocations on the Mexican Stock Exchange.

Contribution

It introduces a novel integration of RMT covariance estimators with spectral clustering-based NCO for portfolio optimization.

Findings

RMT-based covariance estimators lead to more stable allocations.

The modified NCO avoids risky short positions.

The approach performs well on Mexican market data from 2018 to 2022.

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.