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Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach

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Author Info
Douglas J. Hodgson () (Center for Research on Economic Fluctuations and Employment, UQAM)
Oliver Linton () (London School of Economics)
Keith Vorkink () (Brigham Young University)

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Abstract

We develop new tests of the capital asset pricing model (CAPM) 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 avert 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.

Nous développons de nouveaux tests du modèle d'évaluation des actifs financiers (" CAPM ") qui tiennent compte de, et sont valides sous, l'hypothèse que les retours des actifs découlent d'un loi de probabilité elliptiquement symétrique. Cette hypothèse est nécessaire et suffisante pour la validité du CAPM. Notre test utilise un estimateur des paramètres du modèle qui a l'efficacité semiparamétrique quand on a un modèle de régression apparemment sans relation et qui a des erreurs qui suivent une loi elliptiquement symétrique. L'hypothèse de la symétrie elliptique nous permet d'éviter le problème d'estimer non-paramétriquement une fonction de haute dimension parce qu'on peut écrire la densité d'une loi elliptique comme une fonction d'une transformation unidimensionnelle de la variable aléatoire multidimensionnelle. La famille des lois elliptiquement symétriques inclue plusieurs lois leptokurtiques, donc elle est pertinente à des applications financières. Les bêtas obtenus avec notre estimateur sont plus bas que ceux qui sont obtenus en utilisant des moindres carrés, et sont moins compatibles avec le CAPM.

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Publisher Info
Paper provided by CREFE, Université du Québec à Montréal in its series Cahiers de recherche CREFE / CREFE Working Papers with number 143.

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Length: 29 pages
Date of creation: Oct 2001
Date of revision:
Handle: RePEc:cre:crefwp:143

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Related research
Keywords: Adaptive estimation; capital asset pricing model; elliptical symmetry; semiparametric efficiency;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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)
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  4. 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.
    Other versions:
  5. 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)
  6. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation, Yale University. [Downloadable!]
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  12. 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:
  13. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
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  15. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August. [Downloadable!] (restricted)
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  26. 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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  27. 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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Full references

Cited by:
(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. Douglas Hodgson & Barrett Slade & Keith Vorkink, 2006. "Constructing Commercial Indices: A Semiparametric Adaptive Estimator Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 32(2), pages 151-168, March. [Downloadable!] (restricted)
  6. Enrique Sentana & Gabriele Fiorentini, 2007. "On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI. [Downloadable!]
    Other versions:
  7. 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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