# Deep Risk Model: A Deep Learning Solution for Mining Latent Risk Factors to Improve Covariance Matrix Estimation

arXiv: https://arxiv.org/abs/2107.05201 · HTML: https://mlsanity.com/paper/2107.05201/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Learning Multiple Stock Trading Patterns with Temporal Routing Adaptor and Optimal Transport](https://mlsanity.com/paper/2106.12950/) (2021)
- [An Overview on the Estimation of Large Covariance and Precision Matrices](https://mlsanity.com/paper/1504.02995/) (2015)
- [Large Covariance Estimation through Elliptical Factor Models](https://mlsanity.com/paper/1507.08377/) (2015)

## Built on by (most cited first, 5 of 5)

- [E2EAI: End-to-End Deep Learning Framework for Active Investing](https://mlsanity.com/paper/2305.16364/) (2023)
- [Factor Investing with a Deep Multi-Factor Model](https://mlsanity.com/paper/2210.12462/) (2022)
- [Style Miner: Find Significant and Stable Explanatory Factors in Time Series with Constrained Reinforcement Learning](https://mlsanity.com/paper/2303.11716/) (2023)
- [HireVAE: An Online and Adaptive Factor Model Based on Hierarchical and Regime-Switch VAE](https://mlsanity.com/paper/2306.02848/) (2023)
- [MEME: Modeling the Evolutionary Modes of Financial Markets](https://mlsanity.com/paper/2602.11918/) (2026)

## Abstract (arXiv)

Modeling and managing portfolio risk is perhaps the most important step to achieve growing and preserving investment performance. Within the modern portfolio construction framework that built on Markowitz's theory, the covariance matrix of stock returns is a required input to calculate portfolio risk. Traditional approaches to estimate the covariance matrix are based on human-designed risk factors, which often require tremendous time and effort to design better risk factors to improve the covariance estimation. In this work, we formulate the quest of mining risk factors as a learning problem and propose a deep learning solution to effectively ``design'' risk factors with neural networks. The learning objective is also carefully set to ensure the learned risk factors are effective in explaining the variance of stock returns as well as having desired orthogonality and stability. Our experiments on the stock market data demonstrate the effectiveness of the proposed solution: our method can obtain 1.9% higher explained variance measured by R2 and also reduce the risk of a global minimum variance portfolio. The incremental analysis further supports our design of both the architecture and the learning objective.