{"title":"Some properties of portfolios constructed from principal components of asset returns","authors":"Thomas A. Severini","doi":"10.1007/s10436-022-00412-z","DOIUrl":null,"url":null,"abstract":"<div><p>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 <i>N</i>-dimensional random vector of asset returns, PCA produces a set of <i>N</i> 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.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Finance","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s10436-022-00412-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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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.
期刊介绍：
Annals of Finance provides an outlet for original research in all areas of finance and its applications to other disciplines having a clear and substantive link to the general theme of finance. In particular, innovative research papers of moderate length of the highest quality in all scientific areas that are motivated by the analysis of financial problems will be considered. Annals of Finance''s scope encompasses - but is not limited to - the following areas: accounting and finance, asset pricing, banking and finance, capital markets and finance, computational finance, corporate finance, derivatives, dynamical and chaotic systems in finance, economics and finance, empirical finance, experimental finance, finance and the theory of the firm, financial econometrics, financial institutions, mathematical finance, money and finance, portfolio analysis, regulation, stochastic analysis and finance, stock market analysis, systemic risk and financial stability. Annals of Finance also publishes special issues on any topic in finance and its applications of current interest. A small section, entitled finance notes, will be devoted solely to publishing short articles – up to ten pages in length, of substantial interest in finance. Officially cited as: Ann Finance
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