Deep Factor Model

—

Deep Factor Model

Kei Nakagawa
Takumi Uchida
Tomohisa Aoshima
Published on 10/1/2018
Equities
Japan
Factor investing
Machine learning
Deep learning
Stock picking

The paper introduces the Deep Factor Model, a unified deep learning approach for both return forecasting and risk attribution in quantitative portfolio management. Traditional multifactor models assume linear relationships between factors and stock returns, which is restrictive given market complexity. The authors replace the linear return model with a deep neural network that captures nonlinear interactions among factors. To address the black-box nature of deep learning, they apply layer-wise relevance propagation (LRP) to decompose the predicted return into contributions from individual factors, effectively creating an interpretable risk model. Empirical tests on Japanese TOPIX constituents from 1990 to 2016 show that the deep factor model significantly outperforms linear regression, support vector regression, and random forest in both prediction accuracy (MAE, RMSE) and portfolio profitability (Sharpe ratio). Notably, the deeper network (6 layers) achieves a higher Sharpe ratio (1.50) than the shallower network (1.41), while the shallower network has slightly better accuracy. LRP analysis reveals that quality and value factors dominate predictions, and that factor contributions differ from simple correlations, demonstrating the value of nonlinear attribution. The work bridges the gap between high-performance deep learning and the need for interpretability in financial applications.

Highlights

  • 1Proposes a unified deep learning framework for both return prediction and risk decomposition in multifactor models.
  • 2Applies layer-wise relevance propagation (LRP) to interpret deep learning predictions for stock returns.
  • 3Demonstrates superior predictive performance over linear models, SVR, and random forest on Japanese stock market data.
  • 4Shows that the deep factor model achieves higher Sharpe ratios compared to traditional methods.
  • 5Provides factor-level attribution analysis, revealing that quality and value factors dominate predictions.

Methods

  • M
    Deep neural networks with ReLU activation and Adam optimization for return prediction.
  • M
    Layer-wise relevance propagation (LRP) for decomposing predictions into factor contributions.
  • M
    Cross-sectional regression framework with historical factor means as constants.
  • M
    Rolling window training (60 months) with monthly re-estimation and portfolio construction.

Results

  • R
    Deep factor model achieves MAE of 0.0663 and RMSE of 0.0951, outperforming linear model (MAE 0.0679, RMSE 0.0965).
  • R
    Deep model (6 layers) yields annualized return of 10.31% and Sharpe ratio of 1.50, vs. linear model's 8.17% and 1.00.
  • R
    Quality and value factors contribute over 50% to predicted returns in top quintile portfolio.
  • R
    LRP reveals that value factor has high contribution but low correlation with predicted returns, highlighting nonlinear interactions.
  • R
    Shallow model (3 layers) has better prediction accuracy, while deeper model yields higher profitability.
0/5

Analyze Paper

Generate insights from "Deep Factor Model".

Suggested Actions