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

Pedro Reis, Ana Paula Serra, João Gama

TL;DR

The paper tackles medium-term covariance forecasting for multi-asset portfolios by introducing CAB, a deep learning framework that integrates 3D convolution, bidirectional LSTM, and multi-head attention, with symmetry and PSD enforcement and a shrinkage step. It benchmarks CAB against naive, de-noising, and GARCH models on daily ETF data (2017–2023), showing substantial improvements in forecast accuracy (lower $L_E$ and $L_F$) across diverse market regimes and horizons. The authors demonstrate that CAB yields meaningful economic value in GMV portfolio construction, achieving lower out-of-sample volatility with moderate turnover, and that its advantages persist under robustness checks including larger asset universes and both raw and excess return specifications. Overall, the study highlights the practical potential of sophisticated spatio-temporal DL architectures to enhance covariance forecasting and risk management in multi-asset settings, while acknowledging avenues for extending tail-risk modelling and incorporating costs.

Abstract

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.

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

TL;DR

The paper tackles medium-term covariance forecasting for multi-asset portfolios by introducing CAB, a deep learning framework that integrates 3D convolution, bidirectional LSTM, and multi-head attention, with symmetry and PSD enforcement and a shrinkage step. It benchmarks CAB against naive, de-noising, and GARCH models on daily ETF data (2017–2023), showing substantial improvements in forecast accuracy (lower and ) across diverse market regimes and horizons. The authors demonstrate that CAB yields meaningful economic value in GMV portfolio construction, achieving lower out-of-sample volatility with moderate turnover, and that its advantages persist under robustness checks including larger asset universes and both raw and excess return specifications. Overall, the study highlights the practical potential of sophisticated spatio-temporal DL architectures to enhance covariance forecasting and risk management in multi-asset settings, while acknowledging avenues for extending tail-risk modelling and incorporating costs.

Abstract

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.

Paper Structure

This paper contains 35 sections, 52 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Naïve Models
  4. Naïve ($NA$)
  5. Naïve full sample ($NA^F$)
  6. Exponential Weighted Moving Average ($EWMA$)
  7. De-noising Models
  8. Principal Component Analysis ($PCA$)
  9. Random Matrix Theory ($RMT$)
  10. Ledoit and Wolf ($LW$)
  11. Ledoit and Wolf full sample ($LW^F$)
  12. GARCH Models
  13. Constant Conditional Correlations ($CCC$)
  14. Dynamic Conditional Correlations ($DCC$)
  15. Nonlinear Shrinkage Dynamic Conditional Correlations ($DCC^{NL}$)
  16. ...and 20 more sections

Figures (2)

  • Figure 1: Upper Triangular Euclidean distance
  • Figure 2: Frobenius distance