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

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  • BEAULIEU, Marie-Claude
  • DUFOUR, Jean-Marie
  • 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 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.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-17.

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Length: 32 ges pages
Date of creation: 2002
Date of revision:
Handle: RePEc:mtl:montde:2002-17
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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;

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Find related papers by JEL classification:
  • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
  • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
  • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
  • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
  • G1 - Financial Economics - - General Financial Markets
  • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
  • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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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. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
  3. 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.
  4. Enrique Sentana, 2008. "The Econometrics Of Mean-Variance Efficiency Tests: A Survey," Working Papers wp2008_0807, CEMFI.

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