Testing mean-variance efficiency in CAPM with possibly non-gaussian errors: an exact simulation-based approach

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

No 2003,01, Discussion Paper Series 1: Economic Studies from Deutsche Bundesbank

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 framework 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), Gibbons, 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 multivariate 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: capital assed pricing model; CAPM; mean-variance efficiency; nonnormality; multivariate linear regression; uniform linear hypothesis; exact test (search for similar items in EconPapers)
JEL-codes: C12 C15 C3 C33 G1 G12 G14 (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/19587/1/200301dkp.pdf (application/pdf)

Related works:
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)
Working Paper: TESTING MEAN-VARIANCE EFFICIENCY IN CAPM WITH POSSIBLY NON-GAUSSIAN ERRORS: AN EXACT SIMULATION-BASED APPROACH (2002)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:bubdp1:4196

Access Statistics for this paper

More papers in Discussion Paper Series 1: Economic Studies from Deutsche Bundesbank Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().