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

Abstract

In this article, the authors present a novel and highly flexible concept to simulate correlation matrixes of financial markets. It produces realistic outcomes regarding stylized facts of empirical correlation matrixes and requires no asset return input data. The matrix generation is based on a multiobjective evolutionary algorithm, so the authors call the approach matrix evolutions. It is suitable for parallel implementation and can be accelerated by graphics processing units and quantum-inspired algorithms. The approach is useful for backtesting, pricing, and hedging correlation-dependent investment strategies and financial products. Its potential is demonstrated in a machine learning case study for robust portfolio construction in a multi-asset universe: An explainable machine learning program links the synthetic matrixes to the portfolio volatility spread of hierarchical risk parity versus equal risk contribution. TOPICS: Statistical methods, big data/machine learning, portfolio construction, performance measurement Key Findings ▪ The authors introduce the matrix evolutions concept based on an evolutionary algorithm to simulate correlation matrixes useful for financial market applications. ▪ They apply the resulting synthetic correlation matrixes to benchmark hierarchical risk parity (HRP) and equal risk contribution allocations of a multi-asset futures portfolio and find HRP to show lower portfolio risk. ▪ The authors evaluate three competing machine learning methods to regress the portfolio risk spread between both allocation methods against statistical features of the synthetic correlation matrixes and then discuss the local and global feature importance using the SHAP framework by Lundberg and Lee (2017).