A Multi-Level Extension of the Hierarchical PCA Framework with Applications to Portfolio Construction with Futures Contracts

Sammanfattning: With an increasingly globalised market and growing asset universe, estimating the market covariance matrix becomes even more challenging. In recent years, there has been an extensive development of methods aimed at mitigating these issues. This thesis takes its starting point in the recently developed Hierarchical Principal Component Analysis, in which a priori known information is taken into account when modelling the market correlation matrix. However, while showing promising results, the current framework only allows for fairly simple hierarchies with a depth of one. In this thesis, we introduce a generalisation of the framework that allows for an arbitrary hierarchical depth. We also evaluate the method in a risk-based portfolio allocation setting with Futures contracts.  Furthermore, we introduce a shrinkage method called Hierarchical Shrinkage, which uses the hierarchical structure to further regularise the matrix. The proposed models are evaluated with respect to how well-conditioned they are, how well they predict eigenportfolio risk and portfolio performance when they are used to form the Minimum Variance Portfolio. We show that the proposed models result in sparse and easy-to-interpret eigenvector structures, improved risk prediction, lower condition numbers and longer holding periods while achieving Sharpe ratios that are at par with our benchmarks.