Diffolio: A Diffusion Model for Multivariate Probabilistic Financial Time-Series Forecasting and Portfolio Construction

TL;DR

This work tackles probabilistic forecasting for multivariate financial time-series to support portfolio construction. It introduces Diffolio, a conditional diffusion model built on a two-stage hierarchical attention network and a correlation-guided regularizer that uses a stable Ledoit-Wolf target to capture cross-asset dependencies. Empirical results on 12 industry portfolios show Diffolio achieves state-of-the-art multivariate forecasting (lowest energy score) and strongest cross-asset dependency alignment, while delivering superior risk-adjusted portfolio performance (highest MVP-SR and GOP-CE) and robust, market-beating behavior over time. The combination of asset-specific and systematic covariates with the correlation-aware training signal provides practical advantages for both forecasting accuracy and economic decision-making in portfolio management.

Abstract

Probabilistic forecasting is crucial in multivariate financial time-series for constructing efficient portfolios that account for complex cross-sectional dependencies. In this paper, we propose Diffolio, a diffusion model designed for multivariate financial time-series forecasting and portfolio construction. Diffolio employs a denoising network with a hierarchical attention architecture, comprising both asset-level and market-level layers. Furthermore, to better reflect cross-sectional correlations, we introduce a correlation-guided regularizer informed by a stable estimate of the target correlation matrix. This structure effectively extracts salient features not only from historical returns but also from asset-specific and systematic covariates, significantly enhancing the performance of forecasts and portfolios. Experimental results on the daily excess returns of 12 industry portfolios show that Diffolio outperforms various probabilistic forecasting baselines in multivariate forecasting accuracy and portfolio performance. Moreover, in portfolio experiments, portfolios constructed from Diffolio's forecasts show consistently robust performance, thereby outperforming those from benchmarks by achieving higher Sharpe ratios for the mean-variance tangency portfolio and higher certainty equivalents for the growth-optimal portfolio. These results demonstrate the superiority of our proposed Diffolio in terms of not only statistical accuracy but also economic significance.

Figures (7)

• Figure 1: The structure of the hierarchical attention denoising network of Diffolio.
• Figure 2: Example of predicted excess returns for 12 assets in 2023 generated by Diffolio. The plot shows the mean, median, and the 10%-90% quantile range from 100 generated sample paths, along with the ground truth.
• Figure 3: Comparison of CorrScores for Diffolio and the baselines. A lower CorrScore indicates a better result.
• Figure 4: Comparison of correlation matrices estimated via samples from real data (left) and the mean sample path of Diffolio's synthetic data (right).
• Figure 5: Cumulative excess returns of the MVP for Diffolio, baseline models, and the market benchmark. The returns are plotted on a logarithmic scale.