A Deep Learning Framework for Medium-Term Covariance Forecasting in Multi-Asset Portfolios

Accurate covariance forecasting is central to portfolio allocation, risk management, and asset pricing, yet many existing methods struggle at medium-term horizons, where shifting market regimes and slower dynamics predominate. We propose a deep learning framework that combines three-dimensional convolutional neural networks, bidirectional long short-term memory layers, and multi-head attention to capture complex spatio-temporal dependencies. Using daily data on 14 exchange-traded funds from 2017 through 2023, we find that our model reduces Euclidean and Frobenius distance metrics by up to 20\% relative to classical benchmarks (e.g., shrinkage and GARCH approaches) and remains robust across distinct market regimes. Our portfolio experiments demonstrate significant economic value through lower volatility and moderate turnover. These findings highlight the potential of advanced deep learning architectures to improve medium-term covariance forecasts, offering practical benefits for institutional investors and risk managers.