Neural Network-Driven Volatility Drag Mitigation under Aggressive Leverage

Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with point-in-time selection, commissions, financing, corporate actions, and market impact. Across the 26-year out-of-sample period, the neural estimator reduces annualized five-day volatility by approximately 20% and increases the Sharpe ratio by approximately 40% relative to the next-best covariance estimator. These improvements are consistent across realized risk, risk-adjusted performance, and drawdown control, remain after the modeled execution frictions, and are supported by a 99.9% Model Confidence Set that retains only the neural estimator.

This paper tests whether graph neural networks improve realized volatility forecasts and whether those forecasts improve portfolio performance. Using weekly realized volatility for 465 S&P 500 equities from 2015-2025, Heterogeneous Autoregressive and Long Short-Term Memory baselines are compared against GraphSAGE models built on rolling correlation, sector, and Granger-causal graphs, with and without macro regime features. The empirical finding is that the model with the lowest forecast MSE, the model with the highest cross-sectional ranking accuracy, and the model with the highest portfolio Sharpe ratio are three different models. Forecast accuracy, ranking quality, and portfolio performance are related but not interchangeable objectives. Graph volatility models add value only when the portfolio rule can exploit the cross-sectional structure they encode.

Financial volatility is regime dependent, yet incorporating regime information into neural networks can also destabilize training. This paper asks where such information should enter a neural cross-sectional volatility forecasting model. We study five-day realized-volatility forecasts for 1,027 U.S. equities using a rolling walk-forward evaluation framework in which information, model capacity, hyperparameter tuning, and random seeds are matched across architectures. We propose RG-ResMoE, a regime-gated residual mixture-of-experts architecture in which regime information is used only for expert routing rather than for direct forecasting. The base predictor models volatility from stock features, while a gating network uses regime state variables to route residual corrections. RG-ResMoE consistently outperforms a capacity-matched MLP in both forecasting accuracy and training stability in the main U.S. study. Similar gains are observed on an independent Japanese panel. The integration pathway is decisive: appending the same regime variables directly to the forecasting input degrades both predictive performance and training stability, whereas restricting them to the routing gate improves accuracy and Value-at-Risk calibration. Hard routing consistently underperforms soft routing. The results suggest that, in compact neural volatility forecasting models, the primary value of mixture-of-experts models lies less in increasing model capacity than in controlling how nonstationary regime information influences prediction.