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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper Series 1 ; No. 2003,01

Classification and Topics

• Classification: Wirtschaft ; Information and Market Efficiency; Event Studies; Insider Trading ; Statistical Simulation Methods: General ; Hypothesis Testing: General ; Asset Pricing; Trading Volume; Bond Interest Rates ; Multiple or Simultaneous Equation Models: Panel Data Models; Spatio-temporal Models
• Subject: capital assed pricing model ; CAPM ; mean-variance efficiency ; nonnormality ; multivariate linear regression ; uniform linear hypothesis ; exact test ; Capital Asset Pricing Model ; Schätztheorie ; Statistischer Test ; Schätzung ; Theorie ; USA

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Dufour, Jean-Marie ; Beaulieu, Marie-Claude ; Khalaf, Lynda
• Event: Veröffentlichung
• (who): Deutsche Bundesbank
• (where): Frankfurt a. M.
• (when): 2003

Further information

• Handle: http://hdl.handle.net/10419/19587
• Last update: 10.03.2025, 11:42 AM CET