Abstract
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.
Highlights
The Capital Asset Pricing Model (CAPM) is one of the most important asset pricing models in financial economics
The literature on the CAPM based on the multivariate normal distribution is vast, as seen, for instance, in the works published by Elton and Gruber (1995), Campbell et al (1997), Broquet et al (2004), Francis and Kim (2013), Johnson (2014), Brandimarte (2018) and Mazzoni (2018)
Multivariate normality is not required to ensure the validity of the CAPM
Summary
The Capital Asset Pricing Model (CAPM) is one of the most important asset pricing models in financial economics. It is widely used in estimating the cost of capital for companies and measuring portfolio (or investment fund) performance, among others applications; see, for instance, Campbell et al (1997), Amenc and Le Sourd (2003), Broquet et al (2004), Levy (2012) and Ejara et al (2019). The literature on the CAPM based on the multivariate normal distribution is vast, as seen, for instance, in the works published by Elton and Gruber (1995), Campbell et al (1997), Broquet et al (2004), Francis and Kim (2013), Johnson (2014), Brandimarte (2018) and Mazzoni (2018). The multivariate version of the CAPM is considered, primarily focusing on modeling non-normal returns due to excess kurtosis
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