## 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.

Original language | English (US) |
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Pages (from-to) | 457-483 |

Number of pages | 27 |

Journal | Annals of Finance |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2022 |

## Keywords

- Dimension reduction
- Efficient frontier
- Factor models
- Minimum-risk frontier
- Portfolio theory

## ASJC Scopus subject areas

- Finance
- Economics, Econometrics and Finance(all)