Asset Pricing via the Conditional Quantile Variational Autoencoder

Abstract

We propose a new asset pricing model that is applicable to the big panel of return data. The main idea of this model is to learn the conditional distribution of the return, which is approximated by a step distribution function constructed from conditional quantiles of the return. To study conditional quantiles of the return, we propose a new conditional quantile variational autoencoder (CQVAE) network. The CQVAE network specifies a factor structure for conditional quantiles with latent factors learned from a VAE network and nonlinear factor loadings learned from a “multi-head” network. Under the CQVAE network, we allow the observed covariates such as asset characteristics to guide the structure of latent factors and factor loadings. Furthermore, we provide a two-step estimation procedure for the CQVAE network. Using the learned conditional distribution of return from the CQVAE network, we propose our asset pricing model from the mean of this distribution, and additionally, we use both the mean and variance of this distribution to select portfolios. Finally, we apply our CQVAE asset pricing model to analyze a large 60-year US equity return dataset. Compared with the benchmark conditional autoencoder model, the CQVAE model not only delivers much larger values of out-of-sample total and predictive R 2’s, but also earns at least 30.9% higher values of Sharpe ratios for both long-short and long-only portfolios.