*Article* **Robust Inference in the Capital Asset Pricing Model Using the Multivariate** *t***-Distribution**

**Manuel Galea 1,\*, David Cademartori 2, Roberto Curci 3 and Alonso Molina 1**


Received: 1 May 2020; Accepted: 9 June 2020; Published: 13 June 2020

**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.

**Keywords:** capital asset pricing model; estimation of systematic risk; tests of mean-variance efficiency; *t*-distribution; generalized method of moments; multifactor asset pricing model
