Interpretable Deep Learning for Stock Returns: A Consensus-Bottleneck Asset Pricing Model
Interpretable Deep Learning for Stock Returns: A Consensus-Bottleneck Asset Pricing Model
The paper introduces the Consensus-Bottleneck Asset Pricing Model (CB-APM), a novel interpretable deep learning framework for stock return prediction. CB-APM employs a concept-bottleneck architecture that explicitly models analyst consensus as an intermediate layer, treating professional beliefs as a sufficient statistic for the market's high-dimensional information set. The model consists of two stages: a nonlinear function that synthesizes firm characteristics and macroeconomic variables into consensus-like latent expectations, and a linear pricing stage that maps these expectations to expected returns. This design achieves interpretability-by-design, as the bottleneck constraint acts as an endogenous regularizer that improves out-of-sample predictive accuracy while anchoring inference to economically meaningful drivers. The model is estimated jointly via a weighted loss function that balances return prediction and consensus approximation, with a hyperparameter controlling the strength of the bottleneck.
Empirically, using a comprehensive dataset of U.S. stocks from 1994 to 2023, CB-APM demonstrates substantial improvements in long-horizon return prediction, achieving an out-of-sample R² of 10.46% for annual returns compared to 7.63% for a standard deep learning benchmark. Portfolio-level analyses confirm the model's economic relevance: portfolios sorted on CB-APM forecasts exhibit strongly monotonic payoff structures, with high-minus-low spreads approaching 2.3% per month for regularized specifications. Long-short portfolios achieve economically significant and stable out-of-sample performance, with mean monthly log returns rising from 1.53% to 2.20% and annualized Sharpe ratios improving from 1.10 to 1.44 as the bottleneck tightens. Furthermore, Gibbons–Ross–Shanken tests reveal that traditional factor models increasingly fail to price portfolios formed on CB-APM's predicted returns, indicating that the model uncovers priced information not spanned by linear factor models. Double sorts on model-implied returns and analysts' earnings forecasts show that the expected-return spreads are largest in states of analyst pessimism, suggesting that CB-APM effectively distills the priced component of forecasted earnings while adjusting for optimism-driven noise. These results establish CB-APM as a principled framework that integrates interpretable deep learning with asset pricing theory, offering both strong predictive performance and economic transparency.
Highlights
- 1Introduces the Consensus-Bottleneck Asset Pricing Model (CB-APM), a concept-bottleneck architecture that embeds analyst consensus as a structural bottleneck for interpretable return prediction.
- 2Achieves interpretability-by-design, where the bottleneck constraint acts as an endogenous regularizer improving out-of-sample predictive accuracy while anchoring inference to economically interpretable drivers.
- 3Demonstrates that CB-APM forecasts yield strong monotonic return gradients in portfolio sorts, robust across macroeconomic regimes, with high-minus-low spreads up to 2.3% per month.
- 4Shows that learned consensus representations encode priced information not spanned by canonical factor models, revealing belief-driven risk heterogeneity missed by linear frameworks.
- 5Outperforms standard deep learning benchmarks in long-horizon return prediction, with out-of-sample R² of 10.46% for annual returns versus 7.63% for the benchmark.
Methods
- MConcept-bottleneck neural network architecture with a two-stage structure: a nonlinear consensus formation stage (f) mapping firm characteristics and macro variables to analyst consensus proxies, and a linear pricing stage (g) mapping consensus to expected returns.
- MJoint estimation via a weighted loss function combining return prediction MSE and consensus approximation MSE, with hyperparameter λ controlling the bottleneck strength.
- MAutoencoder-based nonlinear macro embeddings to represent macroeconomic information as latent vectors.
- MExpanding-window evaluation with portfolio sorts, GRS tests, and double sorts on model-implied returns and analyst earnings forecasts.
Results
- RCB-APM achieves out-of-sample R² of 10.46% for annual returns, significantly improving over a standard deep learning benchmark (7.63%).
- RPortfolios sorted on CB-APM predictions exhibit monotonic payoff structures; high-minus-low spreads reach 2.3% per month for λ ≥ 0.3.
- RLong-short portfolios based on CB-APM forecasts yield mean monthly log returns up to 2.20% and annualized Sharpe ratio up to 1.44.
- RGRS tests show that traditional factor models increasingly fail to price CB-APM-sorted portfolios as the bottleneck tightens, indicating the model captures priced variation beyond linear factors.
- RDouble sorts reveal that expected-return spreads are largest under analyst pessimism (low earnings forecasts), attenuating with optimism, suggesting CB-APM filters optimism-driven noise.
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