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Open AccessArticle

Robust Inference in the Capital Asset Pricing Model Using the Multivariate t-distribution

1
Departamento de Estadística, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago 7820436, Chile
2
Escuela de Comercio, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2830, Valparaíso 2340031, Chile
3
Brennan School of Business, Dominican University, River Forest, IL 60305, USA
*
Author to whom correspondence should be addressed.
J. Risk Financial Manag. 2020, 13(6), 123; https://doi.org/10.3390/jrfm13060123
Received: 1 May 2020 / Revised: 9 June 2020 / Accepted: 9 June 2020 / Published: 13 June 2020
(This article belongs to the Special Issue Financial Statistics and Data Analytics)
In this paper, we consider asset pricing models under the multivariate t-distribution with finite second moment. Such a distribution, which contains the normal distribution, offers a more flexible framework for modeling asset returns. The main objective of this work is to develop statistical inference tools, such as parameter estimation and linear hypothesis tests in asset pricing models, with an emphasis on the Capital Asset Pricing Model (CAPM). An extension of the CAPM, the Multifactor Asset Pricing Model (MAPM), is also discussed. A simple algorithm to estimate the model parameters, including the kurtosis parameter, is implemented. Analytical expressions for the Score function and Fisher information matrix are provided. For linear hypothesis tests, the four most widely used tests (likelihood-ratio, Wald, score, and gradient statistics) are considered. In order to test the mean-variance efficiency, explicit expressions for these four statistical tests are also presented. The results are illustrated using two real data sets: the Chilean Stock Market data set and another from the New York Stock Exchange. The asset pricing model under the multivariate t-distribution presents a good fit, clearly better than the asset pricing model under the assumption of normality, in both data sets. View Full-Text
Keywords: capital asset pricing model; estimation of systematic risk; tests of mean-variance efficiency; t-distribution; generalized method of moments; multifactor asset pricing model capital asset pricing model; estimation of systematic risk; tests of mean-variance efficiency; t-distribution; generalized method of moments; multifactor asset pricing model
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Galea, M.; Cademartori, D.; Curci, R.; Molina, A. Robust Inference in the Capital Asset Pricing Model Using the Multivariate t-distribution. J. Risk Financial Manag. 2020, 13, 123.

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