We develop exact mean-variance efficiency tests of the market portfolio in the context of (conditional and unconditional) capital asset pricing models (CAPM), allowing for a wide class of possibly non-Gaussian error distributions. The proposed procedures are applicable in a general multivariate linear regression framework, and exactness is achieved through Monte Carlo test techniques. We also perform exact multivariate diagnostic checks. Empirical results show that the Gaussian assumption is rejected, temporal instabilities are apparent, and mean-variance efficiency is rejected over several subperiods, but finite-sample methods that allow for nonnormality and conditioning information substantially reduce the number of rejections.

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Journal of Business and Economic Statistics
Department of Economics

Beaulieu, M.-C. (Marie-Claude), Dufour, J.-M. (Jean-Marie), & Khalaf, L. (2007). Multivariate tests of mean-variance efficiency with possibly non-Gaussian errors: An exact simulation-based approach. Journal of Business and Economic Statistics, 25(4), 398–410. doi:10.1198/073500106000000468