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Some properties of portfolios constructed from principal components of asset returns

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  • Thomas A. Severini

    (Northwestern University)

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.

Suggested Citation

  • Thomas A. Severini, 2022. "Some properties of portfolios constructed from principal components of asset returns," Annals of Finance, Springer, vol. 18(4), pages 457-483, December.
    • Handle: RePEc:kap:annfin:v:18:y:2022:i:4:d:10.1007_s10436-022-00412-z
    DOI: 10.1007/s10436-022-00412-z
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Gilles, Christian & LeRoy, Stephen F, 1991. "On the Arbitrage Pricing Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(3), pages 213-229, July.
    3. Serhiy Kozak & Stefan Nagel & Shrihari Santosh, 2018. "Interpreting Factor Models," Journal of Finance, American Finance Association, vol. 73(3), pages 1183-1223, June.
    4. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    5. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    6. Joel M. Vanden, 2021. "Equilibrium asset pricing and the cross section of expected returns," Annals of Finance, Springer, vol. 17(2), pages 153-186, June.
    7. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    8. Libin Yang & William Rea & Alethea Rea, 2017. "Financial Insights from the Last Few Components of a Stock Market PCA," IJFS, MDPI, vol. 5(3), pages 1-12, July.
    9. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    10. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    11. repec:ebl:ecbull:v:7:y:2004:i:3:p:1-10 is not listed on IDEAS
    12. M. Hossein Partovi & Michael Caputo, 2004. "Principal Portfolios: Recasting the Efficient Frontier," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-10.
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    More about this item

    Keywords

    Efficient frontier; Minimum-risk frontier; Dimension reduction; Factor models; Portfolio theory;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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