[Paper Review] Factor Investing with a Deep Multi-Factor Model

Zikai Wei, Bo Dai+1 more|arXiv (Cornell University)|Oct 22, 2022

Stock Market Forecasting Methods4 citations

TL;DR

This paper proposes a deep multi-factor model that integrates financial insights into graph-based deep learning for factor investing. By constructing a hierarchical, dynamic stock graph with industry- and universe-level relationships, and using graph attention and factor-attention modules, the model learns interpretable deep factors that outperform linear and non-interpretable deep baselines in cumulative returns and information ratio across Chinese stock indices.

ABSTRACT

Modeling and characterizing multiple factors is perhaps the most important step in achieving excess returns over market benchmarks. Both academia and industry are striving to find new factors that have good explanatory power for future stock returns and good stability of their predictive power. In practice, factor investing is still largely based on linear multi-factor models, although many deep learning methods show promising results compared to traditional methods in stock trend prediction and portfolio risk management. However, the existing non-linear methods have two drawbacks: 1) there is a lack of interpretation of the newly discovered factors, 2) the financial insights behind the mining process are unclear, making practitioners reluctant to apply the existing methods to factor investing. To address these two shortcomings, we develop a novel deep multi-factor model that adopts industry neutralization and market neutralization modules with clear financial insights, which help us easily build a dynamic and multi-relational stock graph in a hierarchical structure to learn the graph representation of stock relationships at different levels, e.g., industry level and universal level. Subsequently, graph attention modules are adopted to estimate a series of deep factors that maximize the cumulative factor returns. And a factor-attention module is developed to approximately compose the estimated deep factors from the input factors, as a way to interpret the deep factors explicitly. Extensive experiments on real-world stock market data demonstrate the effectiveness of our deep multi-factor model in the task of factor investing.

Motivation & Objective

• To address the lack of interpretability in deep learning-based factor investing by embedding financial insights into model components.
• To model complex, dynamic stock relationships through a hierarchical, multi-relational graph structure at industry and universe levels.
• To develop a factor-attention module that explicitly interprets how deep factors emerge from original style and macroeconomic factors.
• To improve predictive power and risk-adjusted returns in cross-sectional factor investing using non-linear, graph-based representations.
• To validate the model’s generalizability across market capitalizations (small-, mid-, and large-cap) in real-world data.

Proposed method

• Construct a dynamic, multi-relational stock graph with two edge types: intra-industry (industry graph) and inter-industry (universe graph) connections.
• Apply graph attention networks (GATs) to learn hierarchical influences—original, industry-neutralized, and universe-neutralized—on stock contexts.
• Use a context encoder to extract stock representations at multiple granularities, incorporating industry and market neutralization for financial realism.
• Employ a factor-attention module to estimate the contribution of original input factors (e.g., value, quality, momentum) to the final deep factor, enabling interpretability.
• Train the model via end-to-end optimization using validation loss minimization, with monthly rebalancing of a 10% long-only portfolio.
• Implement a multi-level architecture: stock nodes → industry and universe graphs → attention-based context fusion → deep factor prediction.

Experimental results

Research questions

• RQ1 Can a deep learning model with financial interpretability outperform traditional linear and black-box deep learning models in factor investing?
• RQ2 How do industry-level and universe-level stock relationships contribute to improved factor prediction and risk-adjusted returns?
• RQ3 To what extent can attention mechanisms reveal the economic logic behind learned deep factors in a transparent, interpretable manner?
• RQ4 Does the model generalize across different market capitalizations (small-, mid-, and large-cap stocks) in real-world equity markets?
• RQ5 Can hierarchical graph representation learning enhance the stability and explanatory power of deep factors compared to standard neural networks?

Key findings

• The proposed deep multi-factor model (DMFM) achieved consistently higher active returns and Sharpe ratios than linear, equal-weighted, MLP, and MLP&GAT baselines across all three Chinese stock indices (CSI1000, CSI500, CSI300).
• The model’s Sharpe ratio was positive across all benchmarks, while the baselines had negative Sharpe ratios (-0.11 to -0.20), indicating superior risk-adjusted performance.
• The factor-attention module revealed that quality factors received the highest average attention weights across all test periods, suggesting their dominant role in the deep factor’s formation.
• The dynamic graph structure effectively captured changes in stock relationships and constituents, with edge counts per stock fluctuating meaningfully over time, reflecting market dynamics.
• The model demonstrated strong generalizability across market caps, outperforming all baselines on small-cap (CSI1000), mid-cap (CSI500), and large-cap (CSI300) universes.
• The ICIR (Information Coefficient Information Ratio) and IR were significantly higher for DMFM, confirming improved predictive power and stability of the deep factors.