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Principal Portfolios: Recasting the Efficient Frontier

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  • M. Hossein Partovi

    (California State University, Sacramento)

  • Michael Caputo

    (University of Central Florida, Orlando)

Abstract

A new method of analyzing the efficient portfolio problem under the assumption that short sales are allowed is presented. It is based on the remarkable finding that the original asset set can be reorganized as a set of uncorrelated portfolios, here named principal portfolios. The original problem of portfolio selection from the existing, correlated assets is thereby traded for the reduced problem of choosing from a set of uncorrelated portfolios. These portfolios constitute a new investment environment of uncorrelated assets, thereby providing significant conceptual and practical simplification in any portfolio optimization process such as the determination of the efficient frontier. The principal portfolio analysis of the efficient frontier reveals new features of the volatility structure of the optimal portfolios.

Suggested Citation

  • M. Hossein Partovi & Michael Caputo, 2004. "Principal Portfolios: Recasting the Efficient Frontier," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-10.
    • Handle: RePEc:ebl:ecbull:eb-04g00003
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    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    3. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    Cited by:

    1. Juan Manuel Gómez R & José Alfredo Jiménez M, 2020. "Optimal portfolio selection based on first and second order Markov chains," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 92, pages 33-66, Enero-Jun.
    2. Zhang, Xinyu & Tong, Howell, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," LSE Research Online Documents on Economics 113566, London School of Economics and Political Science, LSE Library.
    3. Raphael Benichou & Yves Lemp'eri`ere & Emmanuel S'eri'e & Julien Kockelkoren & Philip Seager & Jean-Philippe Bouchaud & Marc Potters, 2016. "Agnostic Risk Parity: Taming Known and Unknown-Unknowns," Papers 1610.08818, arXiv.org.
    4. M. Hossein Partovi, 2013. "Hedging and Leveraging: Principal Portfolios of the Capital Asset Pricing Model," Papers 1306.4958, arXiv.org.
    5. Firoozye, Nikan & Tan, Vincent & Zohren, Stefan, 2023. "Canonical portfolios: Optimal asset and signal combination," Journal of Banking & Finance, Elsevier, vol. 154(C).
    6. Thorsten Poddig & Albina Unger, 2012. "On the robustness of risk-based asset allocations," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(3), pages 369-401, September.
    7. Gianni Pola, 2016. "On entropy and portfolio diversification," Journal of Asset Management, Palgrave Macmillan, vol. 17(4), pages 218-228, July.
    8. Xinyu Zhang & Howell Tong, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 543-565, April.
    9. Lončarski, Igor & Vidovič, Luka, 2019. "Sorting out the financials: Making economic sense out of statistical factors," Finance Research Letters, Elsevier, vol. 31(C), pages 110-118.
    10. Kentaro Imajo & Kentaro Minami & Katsuya Ito & Kei Nakagawa, 2020. "Deep Portfolio Optimization via Distributional Prediction of Residual Factors," Papers 2012.07245, arXiv.org.
    11. M. Hossein Partovi, 2013. "Hedging and Leveraging: Principal Portfolios of the Capital Asset Pricing Model," Economics Bulletin, AccessEcon, vol. 33(4), pages 2930-2937.
    12. Masafumi Nakano & Akihiko Takahashi, 2019. "A New Investment Method with AutoEncoder: Applications to Cryptocurrencies," CIRJE F-Series CIRJE-F-1128, CIRJE, Faculty of Economics, University of Tokyo.
    13. Libin Yang & William Rea & Alethea Rea, 2015. "Can PCA Structure Changes Indicate that it is Time to Trade?," Working Papers in Economics 15/13, University of Canterbury, Department of Economics and Finance.
    14. David Hallac & Peter Nystrup & Stephen Boyd, 2019. "Greedy Gaussian segmentation of multivariate time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 727-751, September.
    15. Simone Bernardi & Markus Leippold & Harald Lohre, 2018. "Maximum diversification strategies along commodity risk factors," European Financial Management, European Financial Management Association, vol. 24(1), pages 53-78, January.
    16. Ngo, Vu Minh & Nguyen, Huan Huu & Van Nguyen, Phuc, 2023. "Does reinforcement learning outperform deep learning and traditional portfolio optimization models in frontier and developed financial markets?," Research in International Business and Finance, Elsevier, vol. 65(C).
    17. 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.

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    JEL classification:

    • G0 - Financial Economics - - General
    • C0 - Mathematical and Quantitative Methods - - General

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