Hierarchical PCA: Incorporate (fundamental) priors into PCA
PCA is a useful tool for quant trading (stat arb) but in its naive implementation suffers from several forms of instabilities which yield to unnecessary turnover (trading cost...) and spurious trades. In order to regularize the model, several techniques are available. We will discuss one in particular: The Hierarchical PCA (HPCA). With HPCA, we modify the empirical correlation matrix such that it incorporates information from a prior (fundamental) hierarchical classification: For example, sectors and industries for stocks and bonds; protocols, layers and use cases for cryptos. We will illustrate this presentation with some basic python code and results comparing PCA and HPCA for stocks and cryptos.