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

Abstract

The authors introduce the matrix evolutions concept based on an evolutionary algorithm to simulate correlation matrixes useful for financial market applications.n 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.n 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).

Financial Risk Management and Explainable, Trustworthy, Responsible AI

“…This is similar to the example in https://medium.com/turintech/optimising-aiwith-multiple-objectives-why-ai-efficiency-is-critical-for-scaling-ai-turintech-6638f3d77dc6 5. See for example https://en.wikipedia.org/wiki/Parallel_coordinates or https:// plotly.com/python/parallel-coordinates-plot/.…”

“…In the next step, each point in that frontier is displayed as a single line in a parallel-coordinate plot 5 . The coordinates correspond to the multiple objectives.…”

“…The model training quality and its interpretability can be amplified by artificially creating future market data scenarios that have never been observed before but nevertheless carry the statistical footprints of financial market behavior. An example of such a procedure is given in Papenbrock et al ( 2021 ) who use an alternative approach to GAN to produce correlated market data. The approach is based on an evolutionary search heuristic which can be parameterized in a way that allows the adoption of normal as well as extreme scenarios, both unobserved in the past.…”

Enhancing portfolio management using artificial intelligence: literature review

“…Schwendner et al ( 2021 ) present a conceptual framework named Adaptive Seriational Risk Parity (ASRP) to extend HRP as an asset allocation heuristic using the SHAP framework to explain the resulting performance with features of synthetic market data. Also, referring to synthetic data, Papenbrock et al ( 2021 ) evaluates three competing machine learning methods to regress the portfolio risk spread between both allocation methods against statistical features of the synthetic correlation matrices and then discusses the local and global feature importance using the SHAP framework. Benhamou et al ( 2021a ) apply Shapley values to provide a global understanding and local explanations of a proposed gradient boosting decision tree (GBDT) to plan regime changes of S&P 500 from a set of 150 technical, fundamental and macroeconomic features.…”

Interpretable Machine Learning for Diversified Portfolio Construction

“…The framework we introduced in this article would be a suitable testbed to challenge them against the classical HRP strategy from López de Prado. Moreover, the analysis can be enhanced by comparing other strategies or enriching the training dataset by generating more complex simulations using AI such as generative adversarial networks (see, e.g., Wiese et al 2019 andMarti 2019) or using the matrix evolutions scheme of Papenbrock et al (2021).…”