On the use of principal components analysis in index construction.

This paper introduces a novel application of principal component analysis (PCA) in constructing equity indices. While PCA is well-established in other fields, its use in financial index design remains underexplored. The proposed method addresses entropy concerns in nonlinear return time series. PCA is employed to determine equity weights, using factor loadings to guide its construction. This results in a factor model index (FMI) that identifies sub-sectors and assigns data-driven weights. The FMI framework is flexible, allowing adaptation to different asset sub-groups and facilitating synthetic replication of risk factors.