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

In this paper we present a novel and highly flexible method to simulate correlation matrices of financial markets. It produces realistic outcomes regarding stylized facts of empirical correlation matrices and requires no asset return input data. The matrix generation is based on a multi-objective evolutionary algorithm so we call the approach ‘Matrix Evolutions'. It is suitable for parallel implementation and can be accelerated by graphics processing units (GPUs) and quantum-inspired algorithms. The approach can be used for pricing, hedging and trading correlation-based financial products. We demonstrate the potential of Matrix Evolutions in a machine learning case study for robust portfolio construction in a multi-asset universe. In this study we organize an explainable machine learning program to establish a link from the simulated matrices to relative investment performance. The training data consists of the synthetic matrices produced by Matrix Evolutions and an automatic labeling by Monte-Carlo simulation of the relative investment performance of the following two approaches for portfolio construction: the novel Hierarchical Risk Parity approach by Lopez de Prado (2016b) which is based on representation learning and the traditional equal risk contribution approach