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

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  • Dufour, Jean-Marie
  • Beaulieu, Marie-Claude
  • Khalaf, Lynda

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. -- In diesem Papier schlagen wir exakte likelihood-basierte Tests auf Mittelwert-Varianz- Effizienz im Rahmen des CAPM vor. Dabei wird eine breite Klasse von Verteilungen für den stochastischen Term zugelassen. Normalverteilung ist ein Spezialfall. Die Tests werden im Rahmen von multivariablen linearen Regressionen (MLR) entwickelt. Bekanntlich sind Standardtests, die auf MLR basieren und asymptotisch gerechtfertigt werden, nicht zuverlässig. In der Finanzökonometrie sind exakte Tests für einige wenige Hypothesen vorgeschlagen worden. Die meisten hängen von der Annahme der Normalverteilung ab (Jobson und Korkie (1982), Mac Kinley (1987), Gibbons, Ross und Shanken (1989), Zhou (1993)). Für das gaussianische Modell entsprechen unsere Tests denen von Gibbons, Ross und Shanken. Im nichtgaussianischen Modell betrachten wir Mittelwert-Varianz-Effizienz-Tests, wobei multivariate-Student-t und ?gemischte? Normalverteilungen zugelassen werden. Unser Ansatz gibt mehr Aufschluß darüber, ob die Annahme der Normalverteilung zu restriktiv ist, wenn das CAPM gestestet wird. Wir schlagen auch exakte multivariate Diagnosen (einschließlich Tests für multivariate GARCH-Modelle und multivariate Verallgemeinerungen der bekannten Varianz- Relationen-Tests) sowie Tests auf die Anpassungsgüte und eine Schätzung für die störenden Verschmutzungsparameter vor. Unsere Ergebnisse (für 5-Jahres-Perioden) zeigen das Folgende: (i) multivariate Normalität wird für die meisten Perioden verworfen (ii) die Überprüfung der Residuen zeigt keine signifikante Abweichung von der Annahme einer multivariaten i.i.d. Verteilung (iii), wenn man nichtnormalverteilte Fehler zulässt, werden Mittelwert-Varianz-Effizienz Tests des Marktportfolios seltener verworfen.

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2003,01.

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Date of creation: 2003
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Handle: RePEc:zbw:bubdp1:4196

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Keywords: capital assed pricing model; CAPM; mean-variance efficiency; nonnormality; multivariate linear regression; uniform linear hypothesis; exact test;

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Cited by:
  1. Kaïs Dachraoui & Georges Dionne, 2004. "Conditions Ensuring the Separability of Asset Demand for All Risk-Averse Investors," Cahiers de recherche 0411, CIRPEE.
  2. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2010. "Market Efficiency of Oil Spot and Futures: A Mean-Variance and Stochastic Dominance Approach," Working Papers in Economics 10/18, University of Canterbury, Department of Economics and Finance.
  3. Enrique Sentana, 2008. "The Econometrics Of Mean-Variance Efficiency Tests: A Survey," Working Papers wp2008_0807, CEMFI.
  4. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.

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