Portfolio Optimization by Mean-Variance-Kullback-Leibler Divergence Measure Using the AR-GJR-GARCH Filtration

This study introduces a reliable portfolio optimization framework that utilizes Mean-Variance (MV) Optimization together with Kullback-Leibler (KL) divergence under the AR-GJR-GARCH filtering process for capturing non-normality, volatility clustering, and model uncertainty in the returns of financial assets. The introduced Mean-Variance-KL (MV-KL) method incorporates the maximization of expected return, risk, and proximity to investor-specific target return distributions, while increasing the efficiency and robustness of the portfolio through portfolio diversification. The MV-KL portfolio is developed based on the returns from the African and worldwide financial assets using the AR-GJR-GARCH model to extract the conditional mean and volatility processes before constructing the optimal portfolios. The portfolio evaluation metrics used include residual return, residual volatility, Sharpe and Sortino ratios, as well as VaR and CVaR. The results indicate that although the classical MV approach generates the best stable risk-adjusted returns among the other methods. The proposed hybrid MV-KL method is more diversified and provides better downside risk management than the conventional portfolio techniques. The integration of KL divergence allows superior flexibility in adapting investor preferences and improves portfolio resilience under varying market conditions. These findings add to the increasing literature on robust portfolio optimization by providing an information-theoretic approach to dynamic asset allocation.