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

26 Pages Posted: 13 Sep 2001

See all articles by Douglas J. Hodgson

Douglas J. Hodgson

University of Quebec at Montreal (UQAM) - Department of Economics

Oliver B. Linton

University of Cambridge

Keith Vorkink

Brigham Young University - J. Willard and Alice S. Marriott School of Management

Multiple version iconThere are 2 versions of this paper

Date Written: June 8, 2001

Abstract

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

Keywords: Adaptive Estimation, Capital Asset Pricing Model, Elliptical Symmetry, Semiparametric Efficiency

JEL Classification: C22

Suggested Citation

Hodgson, Douglas J. and Linton, Oliver B. and Vorkink, Keith, Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach (June 8, 2001). Available at SSRN: https://ssrn.com/abstract=283364 or http://dx.doi.org/10.2139/ssrn.283364

Douglas J. Hodgson

University of Quebec at Montreal (UQAM) - Department of Economics ( email )

P.O. Box 8888, Downtown Station
Montreal, Quebec H3C 3P8
Canada

Oliver B. Linton

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Keith Vorkink (Contact Author)

Brigham Young University - J. Willard and Alice S. Marriott School of Management ( email )

Provo, UT 84602
United States

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