Variational Autoencoder Asset Pricing models with economic restrictions

This paper proposes a Variational Autoencoder Asset Pricing model with Economic Restrictions (VAE-ER) that aims to reconcile predictive performance and economic interpretability in machine-learning-based asset pricing. The model builds on autoencoder factor frameworks by introducing variational regularization to stabilize latent factor estimation and economically motivated restrictions that anchor latent factors to macroeconomic states, without incorporating macro variables as direct inputs to the return-generating process. Using U.S. equity data, we show that the VAE-ER model consistently outperforms linear benchmarks and standard autoencoder models in out-of-sample predictive R-squared, information coefficients, Sharpe ratios, and cumulative long–short portfolio returns. These improvements are robust across factor dimensions, portfolio constructions, prediction horizons, and data frequencies, and extend to individual stock-level forecasts. Beyond predictive gains, the implied pricing kernel exhibits clear procyclicality and systematically predicts future macroeconomic conditions, consistent with the intertemporal CAPM. Overall, the results demonstrate that combining variational inference with economic restrictions yields a scalable and economically interpretable approach to asset pricing.