On the Use of Principal Components Analysis in Index Construction

This methodological paper presents a principal component analysis (PCA) derived way to construct equity indices. Although established in other disciplines, it represents a new application in finance. It is postulated that it can be useful to address entropy issues with non linear return time series that could potentially impact an index's ability to be a proxy for the market portfolio. In this approach, PCA is used to assign weights to individual equities, whilst the procedures to aggregate those equities are based on the PCA loadings. The method creates a factor model index (FMI) derived from PCA that delivers identifiable sub-sectors and weightings. The resultant portfolio recasts the efficient frontier and its weights can then be used to construct an index. The FMI can potentially be used for a number of asset sub-groupings. The approach can also be used to facilitate synthetic replication of risk factors