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Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

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

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

Keywords: capital asset pricing model; mean-variance efficiency; non-normality; multivariate linear regression; stable distribution; skewness; kurtosis; asymmetry; uniform linear hypothesis; exact test; Monte Carlo test; nuisance parameter; specification test; diagnostics (search for similar items in EconPapers)
JEL-codes: C3 C12 C33 C15 G1 G12 G14 (search for similar items in EconPapers)
Date: 2005
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Working Paper: Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions (2005) Downloads
Working Paper: Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions (2005) Downloads
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