Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors: An Exact Simulation-Based Approach

Marie-Claude Beaulieu, Jean-Marie Dufour () and Lynda Khalaf

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Keywords: catal asset icing model; CAPM; mean-variance efficiency; non-normality; multi-variate linear regression; uniform linear hythesis; exact test; Monte Carlo test; bootstra; nuisance rameters; scification test; diagnostics; GARCH; variance ratio test (search for similar items in EconPapers)
JEL-codes: C12 C15 C3 C33 G1 G12 G14 (search for similar items in EconPapers)
Pages: 32 ges pages
Date: 2002
New Economics Papers: this item is included in nep-cfn, nep-cmp, nep-ecm and nep-fin
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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http://hdl.handle.net/1866/488 (application/pdf)

Related works:
Working Paper: Testing mean-variance efficiency in CAPM with possibly non-gaussian errors: an exact simulation-based approach (2003)
Working Paper: Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors: an Exact Simulation-Based Approach (2002)
Working Paper: TESTING MEAN-VARIANCE EFFICIENCY IN CAPM WITH POSSIBLY NON-GAUSSIAN ERRORS: AN EXACT SIMULATION-BASED APPROACH (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2002-17

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