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

Abstract

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 $R^2$ 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.

arXiv commentPublished at ICAIF'21: ACM International Conference on AI in Finance

References in corpus (5)

• Adam: A Method for Stochastic Optimization
• Sequence to Sequence Learning with Neural Networks
• Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling
• High-dimensional covariance matrix estimation in approximate factor models
• Estimation of Covariance Matrices under Sparsity Constraints

Cited by in corpus (1)

• HireVAE: An Online and Adaptive Factor Model Based on Hierarchical and Regime-Switch VAE