A Deep Learning Framework for Forecasting Medium‐Term Covariance in Multiasset Portfolios

ABSTRACT Forecasting the covariance matrix of asset returns is central to portfolio construction, risk management, and asset pricing. However, most existing models struggle at medium‐term horizons, several weeks to months, where shifting market regimes and slower dynamics prevail. We propose a novel deep learning framework that integrates three‐dimensional convolutional neural networks, bidirectional long short‐term memory, and multihead attention to capture complex spatiotemporal patterns in asset return dynamics. Using daily data on 14 exchange‐traded funds from 2017 to 2023, we demonstrate that our model improves out‐of‐sample covariance forecasts by reducing Euclidean and Frobenius distance metrics by up to 20% compared with classical benchmarks such as shrinkage estimators and GARCH‐type models. These gains persist across distinct market regimes, including bull and bear periods, and remain robust across various forecast horizons and under both raw and excess return specifications. Portfolio simulations based on global minimum variance strategies reveal that the proposed model consistently delivers lower volatility and moderate turnover, even under no‐short‐selling constraints. This balance between risk reduction and trading efficiency underscores the economic relevance of the forecasts, particularly for institutional investors managing portfolios at medium‐term horizons.