Financial Management Perspective

Financial Management Perspective

Robust Portfolio Optimization Based on Conditional Value-at-Risk Using GJR-GARCH and Asymmetric Dependence

Document Type : Original Article

Authors
Seyed Ramin Abolfazli 1
Gholamhosein Golarzi, 2
Farid Tondnevis 3
1 Financial engineering, Faculty of economic and management, Semnan Uneversity, Semnan, Iran
2 Department of Management and Economic, Faculty of Management and Economics, Semnan University, Semnan, Iran.
3 Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.
10.48308/jfmp.2026.243687.1580
Abstract
Emerging financial markets are characterized by asymmetric volatility, heavy-tailed return distributions, and nonlinear dependence structures, which pose significant challenges for risk measurement and portfolio optimization. Traditional mean–variance frameworks based on normality assumptions often fail to adequately capture the true nature of financial risk, particularly during periods of market distress and extreme fluctuations. Consequently, portfolio allocation decisions based solely on variance-based measures may underestimate downside risk and lead to suboptimal investment outcomes. This study proposes an empirical framework for portfolio optimization based on Conditional Value-at-Risk (CVaR) and provides a comparative evaluation of standard and robust optimization approaches in the context of the Iranian stock market. The analysis is conducted using daily returns of ten major industry sectors listed on the Tehran Stock Exchange over the period 2015–2025.



In the first stage, GJR-GARCH models are employed to capture conditional heteroskedasticity, volatility clustering, and leverage effects and to extract standardized residuals. The empirical results confirm the existence of asymmetric volatility dynamics across most industries, indicating that negative shocks exert a stronger impact on volatility than positive shocks of similar magnitude. Subsequently, Extreme Value Theory (EVT) is applied to model extreme downside risks. The EVT estimates reveal substantial heterogeneity in tail risk across industries, suggesting that exposure to severe losses differs considerably among sectors and highlighting the limitations of conventional risk measures based on normality assumptions.



To model nonlinear dependence among industry returns, Archimedean copulas, including Clayton, Frank, and Gumbel specifications, are estimated. The results indicate that dependence structures among industries are not purely linear and that tail dependence plays an important role in the transmission of market risk. Based on the estimated copula structures, joint return scenarios are generated and incorporated into two portfolio optimization frameworks: Mean–CVaR and Robust-CVaR.



The optimization results show that the robust framework produces a more balanced allocation of portfolio weights and a higher degree of diversification than the classical Mean–CVaR approach. While the conventional model tends to concentrate portfolio weights in a limited number of sectors, the robust framework reduces sensitivity to estimation errors and parameter uncertainty. In-sample evidence further indicates improvements in risk-adjusted performance under the Robust-CVaR specification.



To assess the robustness and generalizability of the findings, an out-of-sample evaluation based on six expanding rolling windows covering the period 2020–2025 is conducted. The results demonstrate that the robust portfolio performs similarly to or better than the classical portfolio in most evaluation periods and consistently achieves higher Sharpe ratios under the Clayton copula specification. Moreover, the rolling-window analysis reveals that copula dependence parameters vary over time, providing empirical evidence of parameter instability and uncertainty in the portfolio construction process.



Overall, the findings suggest that integrating GJR-GARCH, Extreme Value Theory, Archimedean copulas, and robust CVaR optimization provides a coherent framework for risk measurement, dependence modeling, and portfolio construction in emerging financial markets. The results also underscore the importance of accounting for asymmetric dependence structures and parameter uncertainty in asset allocation decisions and demonstrate that robust portfolio optimization can improve portfolio stability while mitigating the adverse effects of estimation errors.
Keywords
Robust Optimization
Conditional Value-at-Risk (CVaR)
Industry indices
Extreme Value Theory (EVT)
Archimedean Copula
GJR-GARCH model
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