We propose a novel approach to estimate asset pricing models for individual stock returns that takes advantage of the vast amount of conditioning information, while keeping a fully flexible form and accounting for time-variation. Our general non-linear asset pricing model is estimated with deep neural networks applied to all U.S. equity data combined with a substantial set of macroeconomic and firm-specific information. We estimate the stochastic discount factor that explains all asset returns from the conditional moment constraints implied by no-arbitrage. Our asset pricing model outperforms out-of-sample all other benchmark approaches in terms of Sharpe ratio, explained variation and pricing errors. We trace its superior performance to including the no-arbitrage constraint in the estimation and to accounting for macroeconomic conditions and non-linear interactions between firm-specific characteristics. Our generative adversarial network enforces no-arbitrage by identifying the portfolio strategies with the most pricing information. Our recurrent Long-Short-Term-Memory network finds a small set of hidden economic state processes. A feedforward network captures the non-linear effects of the conditioning variables. Our model allows us to identify the key factors that drive asset prices and generate profitable investment strategies.
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