Modeling Portfolio Return and Risk using GARCH

Abstract

This study explores the application of GARCH and GJR-GARCH models in measuring portfolio return and risk using high-frequency daily return data from the S&P 500 and DAX indices over the period 2000–2020. The research aims to construct a parsimonious and practical volatility forecasting framework by integrating both symmetric and asymmetric shock models, as well as parametric and non-parametric approaches. The methodology follows foundational works by Engle (1982), Bollerslev (1986), and Glosten et al. (1993), and incorporates Value-at-Risk (VaR) to assess potential portfolio losses. Empirical results reveal that actual return distributions exhibit fat tails and skewness, invalidating the normality assumption and necessitating the use of Student’s t-distributions for better accuracy. The GJR-GARCH model proves superior in capturing asymmetric shock effects, as evidenced by higher predictive performance and alignment with observed volatility dynamics, particularly during financial turmoil such as the 2008 crisis. Furthermore, ARMA-enhanced GJR-GARCH models yield better fitting results, especially in forecasting conditional mean and variance. The findings indicate that DAX required higher risk compensation in multiple periods compared to S&P 500, which showed concentrated volatility during the crisis period only. The study highlights the practical implication of selecting appropriate volatility models for dynamic risk management and suggests the inclusion of autoregressive components to enhance return prediction accuracy. Ultimately, this research contributes to the advancement of financial econometric modeling by demonstrating the efficacy of advanced GARCH frameworks in real-world portfolio risk estimation.