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Portfolio Inefficiency and the Cross-Section of Expected Returns

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  • Shmuel Kandel
  • Robert F. Stambaugh

Abstract

A plot of expected returns versus betas obeys virtually no relation to an inefficient index portfolio's mean-variance location. If the index portfolio is inefficient, then the coefficients and R- squared from an ordinary-least-squares regression of expected returns on betas can equal essentially any desired values. The mean-variance location of the index does determine the properties of a cross- sectional mean-beta relation fitted by generalized least squares (GLS). As the index portfolio moves closer to exact efficiency, the GLS mean-beta relation moves closer to the exact linear relation corresponding to an efficient portfolio with the same variance. The goodness-of-fit for the GLS regression is the index portfolio's squared relative efficiency, which measures closeness to efficiency in mean-variance space.

Suggested Citation

  • Shmuel Kandel & Robert F. Stambaugh, 1994. "Portfolio Inefficiency and the Cross-Section of Expected Returns," NBER Working Papers 4702, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:4702
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    References listed on IDEAS

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    1. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. Kandel, Shmuel & Stambaugh, Robert F, 1989. "A Mean-Variance Framework for Tests of Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 125-156.
    3. 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.
    4. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
    5. Shanken, Jay, 1985. "Multivariate tests of the zero-beta CAPM," Journal of Financial Economics, Elsevier, vol. 14(3), pages 327-348, September.
    6. 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.
    7. Ravi Jagannathan & Zhenyu Wang, 1993. "The CAPM is alive and well," Staff Report 165, Federal Reserve Bank of Minneapolis.
    8. 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.
    9. Shanken, Jay, 1987. "Multivariate proxies and asset pricing relations : Living with the Roll critique," Journal of Financial Economics, Elsevier, vol. 18(1), pages 91-110, March.
    10. Roll, Richard, 1985. "A note on the geometry of Shanken's CSR T2 test for mean/variance efficiency," Journal of Financial Economics, Elsevier, vol. 14(3), pages 349-357, September.
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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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