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

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  • Oliver Linton

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  • Douglas J.Hodgson
  • Keith Vorkink

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 neccessary and sufficient for the validity of the CAPM. Our test is based on semi-parametric efficient estimation procedures for a seemingly unrelated regression model where the multvariate 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 parametric estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates.

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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp382.

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Date of creation: Jun 2001
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Handle: RePEc:fmg:fmgdps:dp382

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Web page: http://www.lse.ac.uk/fmg/

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Citations

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Cited by:
  1. Sakhanenko, Lyudmila, 2008. "Testing for ellipsoidal symmetry: A comparison study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 565-581, December.
  2. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 251-280, April.
  3. 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.
  4. 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.
  5. Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," CIRANO Working Papers 2005s-03, CIRANO.
  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.
  7. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C65-C101, November.
  8. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  9. Vitali Alexeev & Alex Maynard, 2010. "Localized Level Crossing Random Walk Test Robust to the Presence of Structural Breaks," Working Papers 1001, University of Guelph, Department of Economics and Finance.
  10. 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.
  11. Asimit, Alexandru V. & Jones, Bruce L., 2007. "Extreme behavior of bivariate elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 53-61, July.
  12. 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.
  13. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
  14. Guermat, Cherif & Freeman, Mark C., 2010. "A net beta test of asset pricing models," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 1-9, January.

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