A Normalizing Flow Approach in Portfolio Optimization with NTS model with Volatility Clustering

We propose a novel portfolio optimization framework that integrates linear factor modeling, non-Gaussian innovations, and generative artificial intelligence to construct portfolios with superior risk-return trade-offs. The success of portfolio optimization critically depends on accurately capturing the joint dependence structure among asset returns. However, traditional covariance measures fail to describe asymmetric tail dependence, and widely used parametric copulas are often too restrictive for complex financial regimes. To overcome these limitations, we introduce a generative framework utilizing Real NVP, a subclass of normalizing flows, to flexibly learn and represent complex dependence structures among latent financial factors. Our approach builds on the tradition of CAPM and Fama–French models but departs by extracting factors statistically via Principal Component Analysis (PCA). Each factor is filtered through ARMA-GARCH dynamics, with residuals modeled using the Normal Tempered Stable (NTS) distribution to account for fat tails and asymmetry.
Empirical results from a 10-year backtest (2015–2024) demonstrate that our NTS-MLCopula method achieves superior statistical fidelity, evidenced by a lower Maximum Mean Discrepancy (MMD) as a non-parametric metric for goodness-of-fit compared to traditional multivariate models. Furthermore, the framework consistently produces portfolios with enhanced Conditional Value at Risk (CVaR) protection and higher Sharpe ratios, proving its robustness in mitigating extreme tail risks during catastrophic market events.