Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis

AbstractWe present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied

Extraction of the underlying structure of systematic risk from non-Gaussian multivariate financial time series using independent component analysis: Evidence from the Mexican stock exchange

Regarding the problems related to multivariate non-Gaussianity of financial time series, i.e., unreliable results in extraction of underlying risk factors -via Principal Component Analysis or Factor Analysis-, we use Independent Component Analysis (ICA) to estimate the pervasive risk factors that explain the returns on stocks in the Mexican Stock Exchange. The extracted systematic risk factors are considered within a statistical definition of the Arbitrage Pricing Theory (APT), which is tested by means of a two-stage econometric methodology. Using the extracted factors, we find evidence of a suitable estimation via ICA and some results in favor of the APT.Peer ReviewedPostprint (published version

Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange

A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA’s assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the ‘bottleneck’ layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied.Peer ReviewedPostprint (published version

Extraction of the underlying structure of systematic risk from Non-Gaussian multivariate financial time series using Independent Component Analysis. Evidence from the Mexican Stock Exchange

Regarding the problems related to multivariate non-Gaussianity of financial time series, i.e.,unreliable results in extraction of underlying risk factors - via Principal Component Analysis or Factor Analysis-, we use Independent Component Analysis (ICA) to estimate the pervasive risk factors that explain the returns on stocks in the Mexican Stock Exchange. The extracted systematic risk factors are considered within a statistical definition of the Arbitrage Pricing Theory (APT), which is tested by means of a two-stage econometric methodology. Using the extracted factors, we find evidence of a suitable estimation via ICA and some results in favor of the APT

Neural Networks Principal Component Analysis for Estimating the Generative Multifactor Model of Returns under a Statistical Approach to the Arbitrage Pricing Theory: Evidence from the Mexican Stock Exchange

A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA's assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the 'bottleneck' layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied

Prospect theory in the financial decision-making process: An empirical study of two Argentine universities

Purpose: This paper aims to provide empirical evidence for using the prospect theory (PT) basic assumptions in the Argentine context. Mainly, this study analysed the financial decision-making process in students of the economic-administrative academic area of two universities, one public and one private, in Córdoba. Design/methodology/approach. The analysis methodology included (1) the descriptive statistical analysis to identify the presence of the certainty, reflection and isolation effects; (2) the construction of a set of indicators on the application of the PT; (3) the chi-squared independence test, to determine if the decisions made are independent of the degree course taken; (4) the non-parametric Kruskal–Wallis test, to determine if the decisions made by individuals vary according to the semesters taken or students' levels of progress; and (5) the non-parametric Mann–Whitney test, to determine if there are differences between the decisions made by men and women. Findings: The empirical results provided evidence on the effects of certainty, reflection and isolation in both universities, concluding that the study participants make financial decisions in situations of uncertainty based more on PT than on expected utility theory. Originality/value: This study contributes to the empirical evidence in a different Latin-American context, confirming that individuals make financial decisions based on the PT independently of their degree course, semester, level of advance, gender or the kind of university where they belong (public or private).Objetivo: Este artículo tiene como objetivo proporcionar evidencia empírica para el uso de los supuestos básicos de la teoría prospectiva (TP) en el contexto argentino. Principalmente, este estudio analizó el proceso de toma de decisiones financieras en estudiantes del área académica económico-administrativa de dos universidades, una pública y otra privada, de Córdoba. Diseño/metodología/enfoque: La metodología de análisis incluyó (1) el análisis estadístico descriptivo para identificar la presencia de los efectos de certeza, reflexión y aislamiento; (2) la construcción de un conjunto de indicadores sobre la aplicación del TP; (3) la prueba de independencia chi-cuadrado, para determinar si las decisiones tomadas son independientes de la carrera cursada; (4) la prueba no paramétrica de Kruskal-Wallis, para determinar si las decisiones tomadas por los individuos varían según los semestres cursados ​​o los niveles de progreso de los estudiantes; y (5) la prueba no paramétrica de Mann-Whitney, para determinar si existen diferencias entre las decisiones tomadas por hombres y mujeres. Hallazgos: Los resultados empíricos proporcionaron evidencia sobre los efectos de la certeza, la reflexión y el aislamiento en ambas universidades, concluyendo que los participantes del estudio toman decisiones financieras en situaciones de incertidumbre basándose más en el TP que en la teoría de la utilidad esperada. Originalidad/valor: Este estudio contribuye a la evidencia empírica en un contexto latinoamericano diferente, confirmando que los individuos toman decisiones financieras con base en el TP independientemente de su carrera, semestre, nivel de avance, género o tipo de universidad a la que pertenecen (público o privado)

Comparison of Statistical Underlying Systematic Risk Factors and Betas Driving Returns on Equities

The objective of this paper is to compare four dimension reduction techniques used for extracting the underlying systematic risk factors driving returns on equities of the Mexican Market. The methodology used compares the results of estimation produced by Principal Component Analysis (PCA), Factor Analysis (FA), Independent Component Analysis (ICA), and Neural Networks Principal Component Analysis (NNPCA) under three different perspectives. The results showed that in general: PCA, FA, and ICA produced similar systematic risk factors and betas; NNPCA and ICA produced the greatest number of fully accepted models in the econometric contrast; and, the interpretation of systematic risk factors across the four techniques was not constant. Additional research testing alternative extraction techniques, econometric contrast, and interpretation methodologies are recommended, considering the limitations derived from the scope of this work. The originality and main contribution of this paper lie in the comparison of these four techniques in both the financial and Mexican contexts. The main conclusion is that depending on the purpose of the analysis, one technique will be more suitable than another

Factores que explican el comportamiento del mercado accionario mexicano

The purpose of this research is to provide preliminary empirical evidence about a set of macroeconomic variables that could explain the behavior of the stock market in Mexico. The variable to explain is represented by the Prices and Quotations Index (IPC by its acronym in Spanish), and the explanatory variables are characterized by the exchange rate Mexican peso – United States dollar, the interest rate and the oil price. The methodology for the empirical analysis includes, first, a correlational study on the variables object of this research; and secondly, univariate (simple linear regression) and multivariate (multiple linear regression) cross-section econometric contrasts which are applied on the aforementioned indicators. The results of this research provide empirical evidence about the influence of two of these macroeconomic variables on the behavior of the Mexican Stock Exchange (BMV by its acronym in Spanish): the exchange rate and the oil price.El objetivo de la investigación es proporcionar evidencia empírica preliminar sobre un conjunto de variables macroeconómicas que pudieran explicar el comportamiento del mercado accionario en México. La variable a explicar se encuentra representada por el Índice de Precios y Cotizaciones de la Bolsa Mexicana de Valores (IPC) y las variables macroeconómicas explicativas están conformadas por: el tipo de cambio peso mexicano-dólar, la tasa de interés y el precio del petróleo. La metodología de análisis de esta investigación empírica incluye, primero, un estudio correlacional de las variables objeto de estudio y posteriormente, un contraste unifactorial (regresión lineal simple) y multifactorial (regresión lineal múltiple) de los indicadores mencionados. Se aplica una metodología econométrica de corte transversal de datos históricos reales mensuales, que permite determinar de manera inicial la importancia e influencia de estos factores en el IPC. Los resultados obtenidos en esta investigación proporcionan evidencia empírica de la influencia que tienen dos de las variables en el comportamiento del principal índice bursátil de la Bolsa Mexicana de Valores (BMV): el tipo de cambio y el precio del petróleo

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

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

Estimation of the underlying structure of systematic risk using principal component analysis and factor analysis

We present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied