This paper proposes a deep learning framework to estimate a conditional asset pricing model for individual U.S. stock returns, addressing four key challenges: high-dimensional conditioning information, unknown functional form of the stochastic discount factor (SDF), time-varying risk exposures, and low signal-to-noise ratio of risk premia. The authors incorporate the fundamental no-arbitrage condition as a criterion function in a neural network, which separates the risk premium signal from noise. The model consists of three neural network components: a feedforward network for the SDF as a function of firm characteristics and macroeconomic states, an LSTM network to extract a small number of economic state processes from 178 macroeconomic time series, and a generative adversarial network (GAN) that constructs the most informative test assets (characteristic-managed portfolios) to identify the SDF parameters. The GAN approach is economically motivated by the Hansen-Jagannathan distance, selecting moment conditions that maximize pricing errors.

Empirically, using monthly returns from 1967 to 2016 for all U.S. stocks, 46 firm characteristics, and 178 macro series, the model significantly outperforms benchmark approaches including linear factor models (Fama-French 5-factor), linear no-arbitrage models, and deep learning prediction models (Gu, Kelly, Xiu 2020). The out-of-sample Sharpe ratio of the SDF portfolio is 2.6, compared to 1.7 for the linear no-arbitrage model and 0.8 for Fama-French. The model explains 8% of individual stock return variation and 23% of expected returns out-of-sample, and achieves cross-sectional R² above 90% on 46 anomaly-sorted decile portfolios. Key findings include: (1) economic constraints (no-arbitrage) improve machine learning performance; (2) non-linear interactions among characteristics are important; (3) the adversarial construction of test assets improves pricing by 20% in Sharpe ratio; (4) macroeconomic states matter and are best captured by LSTM networks that preserve time-series dynamics; (5) the framework complements multi-factor models like IPCA. The SDF structure is stable over time, and results are robust to small stocks, tuning parameters, and time periods.