Dependence modeling and portfolio optimization with copula-GARCH: a European investment perspective - Vasiljeva, Anastasija; Matvejevs, Andrejs; Fjodorovs, Jegors (Frontiers in Applied Mathematics and Statistics, 2025)
This study investigates advanced portfolio optimization techniques that integrate copula functions and GARCH models to enhance risk-adjusted performance in the European stock market. Traditional methods, such as mean-variance optimization, often fail to capture non-linear dependencies and heavy-tailed behaviors observed in financial returns. The copula-GARCH framework addresses these limitations by jointly modeling dependence structures and time-varying volatility. Using high-performance computing (HPC) resources, approximately 10,000 portfolios were simulated to evaluate the effectiveness of different copula-GARCH configurations. Several GARCH-type specifications - standard GARCH, GJR-GARCH, and exponential GARCH (eGARCH) - were tested in combination with various copula families. The analysis focused on EURO STOXX 50 constituents, with model estimation based on 2014-2021 data and out-of-sample backtesting conducted across three market regimes: the bearish year 2022, the bullish recovery in 2023, and the neutral conditions of 2024. Performance was benchmarked against traditional mean-variance and historical Conditional Value at Risk (CVaR) optimization methods. The combination of a Student’s t copula [33, 34] with marginal Student’s t distributions and an eGARCH model consistently outperformed alternatives, achieving lower CVaR values while maintaining favorable return profiles. This configuration demonstrated superior ability to capture tail dependence and asymmetric volatility, which contributed to its robustness across diverse market conditions. The findings confirm that copula-GARCH models provide a more realistic and adaptable framework for portfolio construction under changing market dynamics. By capturing both non-linear dependencies and time-varying volatility, this approach improves downside-risk control without compromising returns. These results highlight the practical value of copula-GARCH optimization for risk-averse investors operating in the European equity market.