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Some properties of portfolios constructed from principal components of asset returns

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Abstract

Principal components analysis (PCA) is a well-known statistical method used to analyze the covariance structure of a random vector and for dimension reduction. When applied to an N-dimensional random vector of asset returns, PCA produces a set of N principal components, linear functions of the asset return vector that are mutually uncorrelated and which have some important statistical properties. The purpose of this paper is to consider the properties of portfolios based on such principal components, know as PC portfolios, including the efficiency of PC portfolios, the use of PC portfolios to reduce the return variance of a given portfolio, and the properties of factor models with PC portfolios as factors.

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Acknowledgements

I would like to thank a referee for a number of unusually helpful comments which have greatly improved the paper.

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  1. Department of Statistics, Northwestern University, 2006 Sheridan Road, Evanston, IL, 60208, USA

    Thomas A. Severini

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  1. Thomas A. Severini
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Correspondence to Thomas A. Severini.

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Severini, T.A. Some properties of portfolios constructed from principal components of asset returns. Ann Finance 18, 457–483 (2022). https://doi.org/10.1007/s10436-022-00412-z

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  • DOI: https://doi.org/10.1007/s10436-022-00412-z

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