Hierarchical PCA and Applications to Portfolio Management

Asset returns in a multivariate market in which securities are grouped into sectors or blocks (e.g. GIC sectors, derivatives associated with different underlying assets). It is widely known that risk-factors derived from PCA beyond the first eigenportfolio are difficult to interpret (the “identification problem”) and hence to use in portfolio management. We explore a alternative approach (HPCA) which makes strong use of the partition of the market into sectors. We show that this approach leads to practically no loss of information with respect to PCA, in the case of equities (constituents of the S&P 500), and the associated risk-factors admit simple interpretations. The model can also be used in context in which the sectors have asynchronous price information, such as single-name credit default swaps, generalizing the works of Cont and Kan (2011) and Ivanov (2016).