Optimizing the Model Investment Portfolios Based on Coherent Risk Measures under Conditions of Asymmetric Financial Market Volatility

This article is dedicated to the optimization of model investment portfolios by integrating asymmetric volatility forecasting using GJR-GARCH models, considering the minimization of Conditional Value at Risk (CVaR). The advantages and disadvantages of classical Markowitz theory are examined. The use of the coherent risk measure CVaR, which quantitatively evaluates losses in the distribution at the «tail», is explored and proposed in combination with the GJR-GARCH model. The GJR-GARCH model, in turn, accounts for the asymmetric volatility response to positive and negative market shocks. Empirical analysis is performed on global index data covering 2005–2023, which includes global crises and periods of high volatility. The proposed methodology comprises two stages. In the first stage, the dynamics of asset volatility are modeled using the EGARCH/GJR-GARCH framework, taking into account asymmetry. In the second stage, portfolio weights are optimized and risk is minimized. The formalization of the problem is carried out using linear programming. The results indicate that the GJR-CVaR model demonstrates better efficiency than traditional approaches, providing higher risk-adjusted returns, lower maximum drawdown, and a higher Sortino ratio, which, in turn, indicates the ability to respond proactively to market fluctuations and manage risks more effectively during periods of instability. The article demonstrates that an important direction in modern investing is the combination of asymmetric volatility models with coherent risk measures. This approach provides instruments for efficient portfolio risk management. Future research directions may include the development of multivariate volatility models to account for correlations between assets over time and the integration of scenario analysis approaches to assess the impact of changing market conditions on portfolio structure