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

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  • Douglas J Hodgson
  • Oliver Linton
  • Keith Vorkink

Abstract

We develop new tests of the capital asset pricing model which 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. 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.

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File URL: http://eprints.lse.ac.uk/2197/
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Bibliographic Info

Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 2197.

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Length: 37 pages
Date of creation: Jul 2000
Date of revision:
Handle: RePEc:ehl:lserod:2197

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Keywords: Adaptive estimation; capital asset pricing model; efficiency.;

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References

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Citations

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Cited by:
  1. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
  2. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C65-C101, November.
  3. 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.
  4. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series 38-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  5. Hafner, C.M. & Rombouts, J.V.K., 2004. "Semiparametric multivariate volatility models," Econometric Institute Research Papers EI 2004-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. 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.
  7. 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.
  8. Hodgson, Douglas J & Vorkink, Keith P, 2003. "Efficient Estimation of Conditional Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 269-83, April.
  9. 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.
  10. 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.
  11. 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.
  12. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  13. Sakhanenko, Lyudmila, 2008. "Testing for ellipsoidal symmetry: A comparison study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 565-581, December.
  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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