On the Use of Principal Components Analysis in Index Construction

Abstract

This paper presents an established method for the construction of indices using principal component analysis (PCA), but as 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. 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. This FMI potentially be used for a number of asset sub-groupings. The approach can also be used to facilitate synthetic replication of risk factors

Keywords: Principal Component Analysis, Index construction, Correlation Matrix.