DeepRiskModel

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

Discover risk factors with deep neural networks.

Factor model:

r_{1,t} = X_1 @ b_t + u_{1,t}
r_{2,t} = X_2 @ b_t + u_{2,t}

R_1 = [r_{1,t-T}, r_{1,t-T+1}, ..., r_{1,t-1}]' = X_1 @ [b_{t-T}, b_{t-T+1}, ..., b_{t-1}] = X_1 @ B + U_1
R_2 = [r_{2,t-T}, r_{2,t-T+1}, ..., r_{2,t-1}]' = X_2 @ [b_{t-T}, b_{t-T+1}, ..., b_{t-1}] = X_2 @ B + U_2

cov(R_1, R_2) = X_1 @ cov(B, B) @ X_2 + std(U_1) * std(U_2)

How to specify X:

• Fundamental Risk Model (FRM): X is pre-defined by human experts (e.g., Size, Value, Momentum, etc)
• Statistical Risk Model (SRM): X is obtained by PCA or Factor Analysis
• Deep Risk Model (DRM): X is a learned embedding of input data (thus we are the superset of FRM)

Methodology

Model Design

• GAT: cross-sectional information (e.g., return relative to industry)
• RNN: temporal information (e.g., historical momentum)

We use two RNNs to leverage both types of information:

• RNN1: x -> (GAT) -> x_agg -> (RNN1) -> F1
• RNN2: x -> (RNN2) -> F2

F1 and F2 are concatenated as the output risk factors.

Loss Design

1. R^2
2. Multicollinearity: regularized inverse correlation matrix
3. Stability: multi-task learning

Experiments

See run.sh for more information.

Citation

@inproceedings{lin2021deep,
  title={Deep risk model: a deep learning solution for mining latent risk factors to improve covariance matrix estimation},
  author={Lin, Hengxu and Zhou, Dong and Liu, Weiqing and Bian, Jiang},
  booktitle={Proceedings of the Second ACM International Conference on AI in Finance},
  pages={1--8},
  year={2021}
}

@article{yang2020qlib,
  title={Qlib: An ai-oriented quantitative investment platform},
  author={Yang, Xiao and Liu, Weiqing and Zhou, Dong and Bian, Jiang and Liu, Tie-Yan},
  journal={arXiv preprint arXiv:2009.11189},
  year={2020}
}