Machine learning models for cross-sectional stock return prediction. Replicates and extends the feedforward neural network benchmark from Gu, Kelly, and Xiu (2020), and introduces a cross-sectional Transformer that learns stock-stock interactions via self-attention. Also experiments with the MSRR loss function from Kelly et al. (2025) that directly optimizes portfolio Sharpe ratio.

The MSRR loss directly optimizes portfolio Sharpe ratio instead of return prediction accuracy. Same architecture, same data — only the loss function differs. The SDF portfolio uses model outputs as portfolio weights directly (scale-invariant Sharpe).

The MSRR Transformer generates highly significant alpha unexplained by Fama-French 5 + Momentum factors. Only 33% of the SDF portfolio return is attributable to known risk factors. The FFN's returns are largely explained by existing factors (particularly profitability/RMW).

Full 19-year results (2001-2019) for the FFN are in MSE_ind_1yr_report.md (average Sharpe +1.07).

• MSE_ind_1yr_report.md — Full replication report for the NN5 FFN (2001-2019)
• Transformer_report.md — Cross-sectional Transformer report (2012-2019) with head-to-head comparison
• MSRR_Transformer_report.md — MSRR loss experiment (2016-2019), proof-of-concept

• train_nn.py — Data pipeline, FFN training, 8-experiment grid configurations
• train_transformer.py — Cross-sectional Transformer with MSE loss
• train_transformer_msrr.py — Cross-sectional Transformer with MSRR loss (Kelly et al. 2025)

The data files are not included in this repository due to licensing restrictions. You need to obtain them separately:

1. Stock characteristics (95 signals) and returns — derived from CRSP/Compustat via the 94 signals defined in Green, Hand, and Zhang (2017) and extended in GKX (2020). Available with a WRDS subscription. The processed signal files should be placed in gkx_full/.

2. Sector mapping (gkx_full/sector_mapping.csv) — SIC 2-digit industry codes per PERMNO, from CRSP.

3. Welch-Goyal macroeconomic predictors (welch_goyal_2024.xlsx) — publicly available from Amit Goyal's website: http://www.hec.unil.ch/agoyal/

The expected data layout is documented in MSE_ind_1yr_report.md section 10.2.

Python 3.10+
PyTorch 2.0+ (CUDA)
numpy, pandas, scipy, openpyxl
NVIDIA GPU with ≥16GB VRAM (tested on RTX 4080 SUPER)

# FFN (NN5), MSE_ind_1yr configuration
python train_nn.py

# Cross-sectional Transformer (MSE loss)
python train_transformer.py

# Cross-sectional Transformer (MSRR loss)
python train_transformer_msrr.py

Edit Config / TransformerConfig / MSRRConfig at the top of each file to change test years, hyperparameters, etc.

This work builds on:

Gu, S., Kelly, B., & Xiu, D. (2020). Empirical Asset Pricing via Machine Learning. The Review of Financial Studies, 33(5), 2223-2273. https://doi.org/10.1093/rfs/hhaa009

Kelly, B.T., Kuznetsov, B., Malamud, S., & Xu, T.A. (2025). Artificial Intelligence Asset Pricing Models. NBER Working Paper 33351.

If you use this code, please cite the original papers.

This repository is for research and educational purposes only. It is not investment advice. Past performance does not guarantee future results. The authors of this repository are not affiliated with Gu, Kelly, or Xiu.