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Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

Author

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  • Marie-Claude Beaulieu
  • Jean-Marie Dufour
  • Lynda Khalaf
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. Dans cet article, nous proposons des méthodes d'inférence exactes pour des modèles d'évaluation d'actifs (CAPM) qui sont formulés dans le contexte des modèles de régression linéaires multivariés. De plus, ces méthodes permettent de considérer des lois de probabilité stables sur les erreurs du modèle. Il est bien connu que l'hypothèse de normalité des rendements boursiers est habituellement rejetée dans les études empiriques à cause de la présence d'asymétrie et d'aplatissement dans les distributions. Afin de modéliser de tels attributs, nous suggérons une approche qui accommode l'asymétrie et l'aplatissement dans les distributions sans avoir recours à des approximations de grands échantillons. Les méthodes suggérées sont basées sur des tests de Monte Carlo. Des tests diagnostiques multivariés sont formellement inclus dans l'analyse afin de s'assurer que les distributions d'erreurs considérées sont raisonnables pour les données étudiées. Ces tests permettent la construction de régions de confiance exactes pour les paramètres d'asymétrie et d'aplatissement des erreurs dans le cas de lois stables. Nous proposons des tests d'efficacité du portefeuille de référence (i.e., pour la nullité des constantes) qui tiennent explicitement compte de la présence de paramètres de nuisance dans les distributions stables. Les méthodes proposées sont appliquées aux rendements de 12 portefeuilles constitués d'actifs négociés à la bourse de New York (NYSE) sur la période s'étalant de 1926 à 1995 (par sous-périodes de cinq ans). Nos résultats montrent que l'utilisation de distributions stables possiblement asymétriques produit une amélioration statistique importante dans la représentation de la distribution et mène à moins de rejet de l'hypothèse d'efficacité du portefeuille de marché.

Suggested Citation

  • Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," CIRANO Working Papers 2005s-03, CIRANO.
    • Handle: RePEc:cir:cirwor:2005s-03
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    References listed on IDEAS

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    Cited by:

    1. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
    2. Tanya Araujo & João Dias & Samuel Eleutério & Francisco Louçã, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Working Papers Department of Economics 2012/21, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    3. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    4. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2009. "Finite sample multivariate tests of asset pricing models with coskewness," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2008-2021, April.
    5. Tanya Ara'ujo & Jo~ao Dias & Samuel Eleut'erio & Francisco Louc{c}~a, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Papers 1207.1202, arXiv.org.
    6. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.
    7. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    8. Araújo, Tanya & Dias, João & Eleutério, Samuel & Louçã, Francisco, 2013. "A measure of multivariate kurtosis for the identification of the dynamics of a N-dimensional market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3708-3714.

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    More about this item

    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; modèle d'évaluation d'actifs financiers; efficience de portefeuille; non-normalité; modèle de régression multivarié; loi stable; asymétrie; aplatissement; hypothèse linéaire uniforme; test exact; test de Monte Carlo; paramètres de nuisance; tests diagnostiques;
    All these keywords.

    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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