IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v5y1999i3p225-235.html
   My bibliography  Save this article

A three-dimensional risk-return relationship based upon the inefficiency of a portfolio: derivation and implications

Author

Listed:
  • G. P. Diacogiannis

Abstract

This paper derives a three-dimensional risk-return relationship employing a set of risky securities and a portfolio that is located inside the minimum-variance boundary of these securities. More specifically, it is proved that the inefficiency of a portfolio that has an expected return greater than the expected return of the global minimum variance portfolio, is a necessary and sufficient condition for expressing the expected return on any security under consideration as an exact linear function of its relative risk in that portfolio and an additional risk associated with moving inside the boundary portfolio set. Then two implications of the theoretical results are discussed, one related to the cost of equity capital and another related to past tests of the capital asset pricing model.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:eurjfi:v:5:y:1999:i:3:p:225-235
    DOI: 10.1080/135184799337064
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/135184799337064
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/135184799337064?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shanken, Jay, 1985. "Multivariate tests of the zero-beta CAPM," Journal of Financial Economics, Elsevier, vol. 14(3), pages 327-348, September.
    2. C. J. Adcock & E. A. Clark, 1999. "Beta lives - some statistical perspectives on the capital asset pricing model," The European Journal of Finance, Taylor & Francis Journals, vol. 5(3), pages 213-224.
    3. Friend, Irwin & Blume, Marshall E, 1970. "Measurement of Portfolio Performance Under Uncertainty," American Economic Review, American Economic Association, vol. 60(4), pages 561-575, September.
    4. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
    5. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    6. Green, Richard C, 1986. "Benchmark Portfolio Inefficiency and Deviations from the Security Market Line," Journal of Finance, American Finance Association, vol. 41(2), pages 295-312, June.
    7. Manaster, Steven, 1979. "Real and Nominal Efficient Sets," Journal of Finance, American Finance Association, vol. 34(1), pages 93-102, March.
    8. Long, John B., 1977. "Efficient portfolio choice with differential taxation of dividends and capital gains," Journal of Financial Economics, Elsevier, vol. 5(1), pages 25-53, August.
    9. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    10. 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.
    11. Roll, Richard, 1980. "Orthogonal Portfolios," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(5), pages 1005-1023, December.
    12. Michael C. Jensen, 1972. "Capital Markets: Theory and Evidence," Bell Journal of Economics, The RAND Corporation, vol. 3(2), pages 357-398, Autumn.
    13. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    14. Kandel, Shmuel & Stambaugh, Robert F., 1987. "On correlations and inferences about mean-variance efficiency," Journal of Financial Economics, Elsevier, vol. 18(1), pages 61-90, March.
    15. Ross, Stephen A, 1977. "The Capital Asset Pricing Model (CAPM), Short-Sale Restrictions and Related Issues," Journal of Finance, American Finance Association, vol. 32(1), pages 177-183, March.
    16. 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.
    17. Fung, W.K.H., 1981. "Taxes, clientele effect of dividend and risk, return linearity," Journal of Banking & Finance, Elsevier, vol. 5(3), pages 405-424, September.
    18. Zhou, Guofu, 1991. "Small sample tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 30(1), pages 165-191, November.
    19. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Juan-Pedro Gómez & Fernando Zapatero, 2001. "Asset pricing implications of benchmarking: A two-factor CAPM," Economics Working Papers 693, Department of Economics and Business, Universitat Pompeu Fabra.
    2. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han, Xing & Li, Kai & Li, Youwei, 2020. "Investor overconfidence and the security market line: New evidence from China," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    2. Grauer, Robert R. & Janmaat, Johannus A., 2009. "On the power of cross-sectional and multivariate tests of the CAPM," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 775-787, May.
    3. 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).
    4. Marie Brière & Bastien Drut & Valérie Mignon & Kim Oosterlinck & Ariane Szafarz, 2013. "Is the Market Portfolio Efficient? A New Test of Mean-Variance Efficiency when all Assets are Risky," Finance, Presses universitaires de Grenoble, vol. 34(1), pages 7-41.
    5. Marie Brière & Bastien Drut & Valérie Mignon & Kim Oosterlinck & Ariane Szafarz, 2011. "Is the Market Portfolio Efficient? A New Test to Revisit the Roll (1977) versus Levy and Roll (2010) Controversy," Working Papers hal-04140988, HAL.
    6. repec:dau:papers:123456789/9297 is not listed on IDEAS
    7. Shanken, Jay & Weinstein, Mark I., 2006. "Economic forces and the stock market revisited," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 129-144, March.
    8. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    9. Grauer, Robert R. & Janmaat, Johannus A., 2004. "The unintended consequences of grouping in tests of asset pricing models," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2889-2914, December.
    10. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
    11. Levy, Moshe & Levy, Haim, 2015. "Keeping up with the Joneses and optimal diversification," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 29-38.
    12. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The RQE-CAPM : New insights about the pricing of idiosyncratic risk," CIRANO Working Papers 2021s-28, CIRANO.
    13. Thomas A. Severini, 2015. "A note on the effects of market inefficiency and portfolio constraints on the relationship between the expected return of an asset and the market," Economics and Business Letters, Oviedo University Press, vol. 4(4), pages 175-182.
    14. Grauer, Robert R. & Janmaat, Johannus A., 2010. "Cross-sectional tests of the CAPM and Fama-French three-factor model," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 457-470, February.
    15. Shanken, Jay & Zhou, Guofu, 2007. "Estimating and testing beta pricing models: Alternative methods and their performance in simulations," Journal of Financial Economics, Elsevier, vol. 84(1), pages 40-86, April.
    16. 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.
    17. Bob Korkie & Harry J. Turtle, 2002. "A Mean-Variance Analysis of Self-Financing Portfolios," Management Science, INFORMS, vol. 48(3), pages 427-443, March.
    18. Benoit Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The political reception of innovations," Cahiers de recherche 2107, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    19. Kim, Soohun & Skoulakis, Georgios, 2018. "Ex-post risk premia estimation and asset pricing tests using large cross sections: The regression-calibration approach," Journal of Econometrics, Elsevier, vol. 204(2), pages 159-188.
    20. repec:wvu:wpaper:05-06 is not listed on IDEAS
    21. Miguel Cantillo Simon & Nick Wonder, 2019. "An analysis of asset pricing models using out of sample data from the NYSE: 1900-1925," Working Papers 201904, Universidad de Costa Rica, revised Jul 2019.
    22. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:eurjfi:v:5:y:1999:i:3:p:225-235. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.