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

Abstract

We present an improved methodology to estimate the underlyingstructure of systematic risk in the Mexican Stock Exchange withthe use of Principal Component Analysis and Factor Analysis.We consider the estimation of risk factors in an Arbitrage PricingTheory (APT) framework under a statistical approach, where thesystematic risk factors are extracted directly from the observedreturns on equities, and there are two differentiated stages, namely,the risk extraction and the risk attribution processes. Ourempirical study focuses only on the former; it includes the testingof our models in two versions: returns and returns in excessof the riskless interest rate for weekly and daily databases, anda two-stage methodology for the econometric contrast. First, weextract the underlying systematic risk factors by way of both,the standard linear version of the Principal Component Analysisand the Maximum Likelihood Factor Analysis estimation. Then,we estimate simultaneously, for all the system of equations, thesensitivities to the systematic risk factors (betas) by weightedleast squares. Finally, we test the pricing model with the use ofan average cross-section methodology via ordinary least squares,corrected by heteroskedasticity and autocorrelation consistentcovariances estimation. Our results show that although APTis very sensitive to the extraction technique utilized and to thenumber of components or factors retained, the evidence foundpartially supports the APT according to the methodology presentedand the sample studied.