# Joint Return and Risk Modeling with Deep Neural Networks for Portfolio Construction

arXiv: https://arxiv.org/abs/2603.19288 · HTML: https://mlsanity.com/paper/2603.19288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 5 of 5)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Universal features of price formation in financial markets: perspectives from Deep Learning](https://mlsanity.com/paper/1803.06917/) (2018)
- [Classification-based Financial Markets Prediction using Deep Neural Networks](https://mlsanity.com/paper/1603.08604/) (2016)
- [Deep Learning in Finance](https://mlsanity.com/paper/1602.06561/) (2016)

## Abstract (arXiv)

Portfolio construction traditionally relies on separately estimating expected returns and covariance matrices using historical statistics, often leading to suboptimal allocation under time-varying market conditions. This paper proposes a joint return and risk modeling framework based on deep neural networks that enables end-to-end learning of dynamic expected returns and risk structures from sequential financial data. Using daily data from ten large-cap US equities spanning 2010 to 2024, the proposed model is evaluated across return prediction, risk estimation, and portfolio-level performance. Out-of-sample results during 2020 to 2024 show that the deep forecasting model achieves competitive predictive accuracy (RMSE = 0.0264) with economically meaningful directional accuracy (51.9%). More importantly, the learned representation effectively captures volatility clustering and regime shifts. When integrated into portfolio optimization, the proposed Neural Portfolio strategy achieves an annual return of 36.4% and a Sharpe ratio of 0.91, outperforming equal weight and historical mean-variance benchmarks in terms of risk-adjusted performance. These findings demonstrate that jointly modeling return and covariance dynamics can provide consistent improvements over traditional allocation approaches. The framework offers a scalable and practical alternative for data-driven portfolio construction under nonstationary market conditions.