Asset pricing with contrastive adversarial variational Bayes

Machine learning techniques have gained considerable attention in the field of empirical asset pricing. Conditioning on a broad set of firm characteristics, one of the most popular no-arbitrage workhorses is a nonlinear conditional asset pricing model that consists of two modules within a neural network structure, i.e., factor and beta estimates, for which we propose a novel contrastive adversarial variational Bayes (CAVB) framework. To exploit the factor structure, we employ adversarial variational Bayes that transforms the maximum-likelihood problem into a zero-sum game between a variational autoencoder (VAE) and a generative adversarial network (GAN), where an auxiliary discriminative network brings in arbitrary expressiveness to the inference model. To tackle the problem of learning indistinguishable feature representations in the beta network, we introduce a contrastive loss to learn distinctive hidden features of the factor loadings in correspondence to conditional quantiles of return distributions. CAVB establishes a robust relation between the cross-section of asset returns and the common latent factors with nonlinear factor loadings. Extensive experiments show that CAVB not only significantly outperforms prominent models in the existing literature in terms of total and predictive R-squares, but also delivers superior Sharpe ratios after transaction costs for both long-only and long-short portfolios.