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Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach

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Author Info
Keith Vorkink (Mariott School of Management, Brigham Young University, Provo UT 84602, USA)
Douglas J. Hodgson (Department of Economics, University of Rochester, NY 14627-0156, USA)
Oliver Linton (Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

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Abstract

We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is necessary and sufficient for the validity of the CAPM. Our test is based on semiparametric efficient estimation procedures for a seemingly unrelated regression model where the multivariate error density is elliptically symmetric, but otherwise unrestricted. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. The elliptically symmetric family includes a number of thick-tailed distributions and so is potentially relevant in financial applications. Our estimated betas are lower than the OLS estimates, and our parameter estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates. Copyright © 2002 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.646
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File URL: http://qed.econ.queensu.ca:80/jae/2002-v17.6/
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Publisher Info
Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 6 ()
Pages: 617-639
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Handle: RePEc:jae:japmet:v:17:y:2002:i:6:p:617-639

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February. [Downloadable!] (restricted)
  2. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May. [Downloadable!] (restricted)
  3. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, Blackwell Publishing, vol. 66(1), pages 1-26, January.
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  4. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February. [Downloadable!] (restricted)
  5. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation, Yale University. [Downloadable!]
  6. Hodgson, Douglas J., 1998. "Adaptive Estimation Of Error Correction Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 44-69, February. [Downloadable!]
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  7. repec:cup:etheor:v:10:y:1994:i:2:p:316-56 is not listed on IDEAS
  8. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March. [Downloadable!] (restricted)
  9. Douglas J. Hodgson & Keith Vorkink, 2001. "Efficient Estimation of Conditional Asset Pricing Models," Cahiers de recherche CREFE / CREFE Working Papers 144, CREFE, Université du Québec à Montréal. [Downloadable!]
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  10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  11. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  12. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation, Yale University. [Downloadable!]
  13. 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 1121-52, September. [Downloadable!] (restricted)
  14. Wesselman, A. M. & Van Praag, B. M. S., 1987. "Elliptical regression operationalized," Economics Letters, Elsevier, vol. 23(3), pages 269-274. [Downloadable!] (restricted)
  15. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March. [Downloadable!] (restricted)
  16. MacKinlay, A. Craig, 1987. "On multivariate tests of the CAPM," Journal of Financial Economics, Elsevier, vol. 18(2), pages 341-371, June. [Downloadable!] (restricted)
  17. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
  18. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May. [Downloadable!] (restricted)
  19. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  20. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June. [Downloadable!] (restricted)
  21. Hodgson, Douglas J., 1998. "Adaptive estimation of cointegrating regressions with ARMA errors," Journal of Econometrics, Elsevier, vol. 85(2), pages 231-267, August. [Downloadable!] (restricted)
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  22. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September. [Downloadable!] (restricted)
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  23. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2004. "Testing forward exchange rate unbiasedness efficiently: a semiparametric approach," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 325-353, November. [Downloadable!]
  2. Douglas J. Hodgson & Keith Vorkink, 2001. "Efficient Estimation of Conditional Asset Pricing Models," Cahiers de recherche CREFE / CREFE Working Papers 144, CREFE, Université du Québec à Montréal. [Downloadable!]
    Other versions:
  3. BEAULIEU, Marie-Claude & DUFOUR, Jean-Marie & KHALAF, Lynda, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," Cahiers de recherche 2005-04, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  4. George A. Christodoulakis & Stephen E Satchell, 2006. "Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility," Working Papers 32, Bank of Greece. [Downloadable!]
  5. Fernando A. Quintana & Pilar L. Iglesias & Manuel Galea-Rojas, 2005. "Bayesian robust estimation of systematic risk using product partition models," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 1(5), pages 313-320, September. [Downloadable!] (restricted)
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