Attention Factors for Statistical Arbitrage
Attention Factors for Statistical Arbitrage
This paper introduces the Attention Factor model for statistical arbitrage, which jointly learns conditional latent factors and an arbitrage trading policy in a one-step framework. The factors are constructed using an attention mechanism that maps firm characteristics to factor portfolio weights, capturing complex interactions. Residuals from the factor model are fed into a LongConv sequence model to generate trading signals, and the entire system is optimized to maximize the net Sharpe ratio after transaction and shorting costs. The approach addresses limitations of two-step methods where factors are estimated solely to explain variance, leading to high turnover and poor net performance.
Empirically, the model is tested on daily returns of the 500 largest U.S. stocks from 1998 to 2021, using 39 firm characteristics. With 30 attention factors, it achieves an out-of-sample gross Sharpe ratio of 3.97 and a net Sharpe ratio of 2.28, substantially outperforming PCA-based benchmarks (net Sharpe 1.57) and parametric models (negative net Sharpe). The strategy remains market-neutral (beta ≈ 0.05) and generates 16% annualized return. The paper also shows that weak factors (higher-order factors) contribute to performance, and that past return characteristics are the primary drivers, while other characteristics have limited impact. The factor loadings exhibit clear industry clustering, providing interpretability. Overall, the Attention Factor model sets a new state-of-the-art for statistical arbitrage under realistic trading frictions.
Highlights
- 1Proposes Attention Factors, a conditional latent factor model jointly learned with an arbitrage trading strategy to maximize net Sharpe ratio after transaction costs.
- 2Achieves out-of-sample Sharpe ratio above 4 (gross) and 2.3 (net) on the 500 largest U.S. equities over 24 years, significantly outperforming prior work.
- 3Demonstrates that weak factors (higher-order factors) are important for identifying profitable arbitrage opportunities.
- 4Provides interpretable factor structure where loadings cluster by industry sectors, and shows past returns are the key driver of performance.
Methods
- MAttention Factor Model: Uses attention mechanism to construct conditional latent factor portfolios from firm characteristic embeddings, with loadings derived via ridge regression.
- MLongConv Sequence Model: Applies long convolution to past residual returns to generate time-series signals for arbitrage portfolio weights.
- MJoint Optimization: Maximizes a combined objective of net Sharpe ratio (including transaction and shorting costs) and explained variance, estimated end-to-end with Adam optimizer.
Results
- RAttention Factor model with 30 factors achieves annualized gross Sharpe ratio of 3.97 and net Sharpe ratio of 2.28, compared to PCA-based two-step approach (gross 2.79, net 1.57) and parametric OU threshold model (gross 0.18, net -6.45).
- RNet Sharpe ratio of 2.3 with 100 factors represents an 84% improvement over the state-of-the-art PCA+LongConv benchmark.
- RThe strategy yields an annual return of 16% with near-zero market beta (0.05), indicating market neutrality.
- RRemoving past return characteristics drastically reduces net Sharpe ratio to 0.59, while other characteristic groups have negligible impact.
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