Market Risk Assessment: A Comparison between CAPM and VaR Methodologies with High Volatility Episodes in the Mexican Stock Market

Bárbara Trejo-Becerril; Arturo Lorenzo-Valdés; Alberto Gallegos-David; Francisco Pérez-Soto

doi:10.32479/ijefi.21151

Authors

Bárbara Trejo-Becerril Faculty of Engineering, National Autonomous University of Mexico, Mexico City, Mexico
Arturo Lorenzo-Valdés Department of Mathematics, Popular Autonomous University of the State of Puebla–CONCYTEP Puebla, Mexico,
Alberto Gallegos-David Division of Economic and Administrative Sciences (DICEA), Chapingo Autonomous University, State of Mexico.
Francisco Pérez-Soto Division of Economic and Administrative Sciences (DICEA), Chapingo Autonomous University, State of Mexico.

DOI:

https://doi.org/10.32479/ijefi.21151

Keywords:

Value at Risk, Historical Simulation, Monte Carlo Simulation, Capital Asset Pricing Model, TGARCH, Expected Shortfall

Abstract

This study aims to estimate the β-CAPM for firms listed on the Mexican Stock Exchange Price Index (IPC) by incorporating Value at Risk (VaR) measures during periods of high market volatility. We apply five risk estimation methodologies: (1) Historical Simulation VaR (VaR-SH), (2) Delta-Normal VaR (VaR-δN), (3) Monte Carlo Simulation VaR (VaR-MC), (4) Threshold-GARCH-based VaR (TGARCH-VaR), and (5) Expected Shortfall (ES). The results demonstrate consistency across the different methodologies during high-volatility periods. Nonetheless, we identify two important limitations: β-CAPM is constrained to equity portfolios, and VaR-based methods may underestimate tail risk during extreme market events. This study enhances the understanding of market risk exposure in the Mexican stock market by offering a comparative analysis of multiple VaR methodologies. It provides a valuable reference for assessing the relative riskiness of individual securities against the market portfolio, especially under conditions of financial stress.