Adaptive Seriational Risk Parity and Other Extensions for Heuristic Portfolio Construction Using Machine Learning and Graph Theory

Abstract

In this article, the authors present a conceptual framework named adaptive seriational risk parity (ASRP) to extend hierarchical risk parity (HRP) as an asset allocation heuristic. The first step of HRP (quasi-diagonalization), determining the hierarchy of assets, is required for the actual allocation done in the second step (recursive bisectioning). In the original HRP scheme, this hierarchy is found using single-linkage hierarchical clustering of the correlation matrix, which is a static tree-based method. The authors compare the performance of the standard HRP with other static and adaptive tree-based methods, as well as seriation-based methods that do not rely on trees. Seriation is a broader concept allowing reordering of the rows or columns of a matrix to best express similarities between the elements. Each discussed variation leads to a different time series reflecting portfolio performance using a 20-year backtest of a multi-asset futures universe. Unsupervised learningbased on these time-series creates a taxonomy that groups the strategies in high correspondence to the construction hierarchy of the various types of ASRP. Performance analysis of the variations shows that most of the static tree-based alternatives to HRP outperform the single-linkage clustering used in HRP on a risk-adjusted basis. Adaptive tree methods show mixed results, and most generic seriation-based approaches underperform. Key Findings ▪ The authors introduce the adaptive seriational risk parity (ASRP) framework as a hierarchy of decisions to implement the quasi-diagonalization step of hierarchical risk parity (HRP) with seriation-based and tree-based variations as alternatives to single linkage. Tree-based variations are further separated in static and adaptive versions. Altogether, 57 variations are discussed and connected to the literature. ▪ Backtests of the 57 different HRP-type asset allocation variations applied to a multi-asset futures universe lead to a correlation matrix of the resulting 57 portfolio return time series. This portfolio return correlation matrix can be visualized as a dendrogram using single-linkage clustering. The correlation hierarchy reflected by the dendrogram is similar to the construction hierarchy of the quasi-diagonalization step. Most seriation-based strategies seem to underperform HRP on a risk-adjusted basis. Most static tree-based variations outperform HRP, whereas adaptive tree-based methods show mixed results. ▪ The presented variations fit into a triple artificial intelligence approach to connect synthetic data generation with explainable machine learning. This approach generates synthetic market data in the first step. The second step applies an HRP-type portfolio allocation approach as discussed in this article. The third step uses a model-agnostic explanation such as the SHAP framework to explain the resulting performance with features of the synthetic market data and with model selection in the second step.