Techniques For Estimating the Generative Multifactor Model of Returns in a Statistical Approach to the Arbitrage Pricing Theory. Evidence from the Mexican Stock Exchange

Abstract

This dissertation focuses on the estimation of the generative multifactor model of returns on equities, under a statistical approach of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. Therefore, this research takes as frameworks two main issues: (i) the multifactor asset pricing models, specially the statistical risk factors approach, and (ii) the dimension reduction or feature extraction techniques: Principal Component Analysis, Factor Analysis, Independent Component Analysis and Non-linear Principal Component Analysis, utilized to extract the underlying systematic risk factors. The models estimated are tested using two methodologies: (i) capability of reproduction of the observed returns using the estimated generative multifactor model, and (ii) results of the econometric contrast of the APT using the extracted systematic risk factors. Finally, a comparative study among techniques is carried on based on their theoretical properties and the empirical results.

According to the above stated and as far as we concerned, this dissertation contributes to financial research by providing empirical evidence of the estimation of the generative multifactor model of returns on equities, extracting statistical underlying risk factors via classic and alternative dimension reduction or feature extraction techniques in the field of finance, in order to test the APT as an asset pricing model, in the context of an emerging financial market such as the Mexican Stock Exchange. In addition, this work presents an unprecedented theoretical and empirical comparative study among Principal Component Analysis, Factor Analysis, Independent Component Analysis and Neural Networks Principal Component Analysis, as techniques to extract systematic risk factors from a stock exchange, analyzing the level of sensitivity of the results in function of the technique carried on. In addition, this dissertation represents a mainly empirical exhaustive study where objective evidence about the Mexican stock market is provided by way of the application of four different techniques for extraction of systematic risk factors, to four datasets, in a test window that ranged from two to nine factors.