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

Douglas Hodgson (), Oliver Linton and Keith Vorkink ()
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Keith Vorkink: Brigham Young University

No 143, Cahiers de recherche CREFE / CREFE Working Papers from CREFE, Université du Québec à Montréal

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.

Keywords: Adaptive estimation; capital asset pricing model; elliptical symmetry; semiparametric efficiency (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2001-10
New Economics Papers: this item is included in nep-cfn, nep-ecm, nep-fin and nep-fmk
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach (2002)
Journal Article: Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach (2002)
Working Paper: Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach (2001)
Working Paper: Testing the Capital Asset Pricing Model Efficiently under Elliptical Symmetry: A Semiparametric Approach (2000)
Working Paper: Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach (2000)
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