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Orthogonal Portfolios

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  • Roll, Richard

Abstract

There is a false, but widely-held belief about orthogonal (“zero-beta”) portfolios: for a given market index, all zero-beta portfolios have the same expected return and the minimal-variance, zero-beta portfolio is unique. This is true only when the index is mean/variance efficient. Every nonefficient index possesses zero-beta portfolios at all levels of expected return. For a given index, minimal-variance zero-beta portfolios corresponding to different expected returns lie along an “orthogonal frontier” in the mean/variance space. The frontier has some unusual properties which turn out to be relevant for empirical work on asset pricing. It is functionally related to deviations about the “securities market line.”

Suggested Citation

  • Roll, Richard, 1980. "Orthogonal Portfolios," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(5), pages 1005-1023, December.
    • Handle: RePEc:cup:jfinqa:v:15:y:1980:i:05:p:1005-1023_01
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    1. repec:wvu:wpaper:05-06 is not listed on IDEAS
    2. Chavez-Bedoya, Luis & Rosales, Francisco, 2022. "Orthogonal portfolios to assess estimation risk," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 906-937.
    3. MacKinlay, A. Craig, 1995. "Multifactor models do not explain deviations from the CAPM," Journal of Financial Economics, Elsevier, vol. 38(1), pages 3-28, May.
    4. Guermat, Cherif, 2014. "Yes, the CAPM is testable," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 31-42.
    5. G. P. Diacogiannis, 1999. "A three-dimensional risk-return relationship based upon the inefficiency of a portfolio: derivation and implications," The European Journal of Finance, Taylor & Francis Journals, vol. 5(3), pages 225-235.
    6. Nijolė MAKNICKIENĖ & Jelena STANKEVIČIENĖ & Algirdas MAKNICKAS, 2020. "Comparison of Forex Market Forecasting Tools Based on Evolino Ensemble and Technical Analysis Indicators," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 134-148, September.
    7. Asgharian, Hossein & Hansson, Bjorn, 2005. "Evaluating the importance of missing risk factors using the optimal orthogonal portfolio approach," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 556-575, September.
    8. A. Craig MacKinlay, 1994. "Multifactor Models Do Not Explain Deviations from the CAPM," NBER Working Papers 4756, National Bureau of Economic Research, Inc.
    9. Kolari, James W. & Huang, Jianhua Z. & Butt, Hilal Anwar & Liao, Huiling, 2022. "International tests of the ZCAPM asset pricing model," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    10. Todd Prono, 2006. "GARCH-based identification of triangular systems with an application to the CAPM: still living with the roll critique," Working Papers 07-1, Federal Reserve Bank of Boston.
    11. Diacogiannis, George & Ioannidis, Christos, 2022. "Linear beta pricing with efficient/inefficient benchmarks and short-selling restrictions," International Review of Financial Analysis, Elsevier, vol. 81(C).
    12. Chi-Cheng Hsia, 1986. "Comparative Efficiency Of Market Indices: An Empirical Study," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 9(2), pages 123-135, June.

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