Modeling and characterizing multiple factors is perhaps the most important step in achieving excess returns over market benchmarks. Both academia and industry are striving to find new factors that have good explanatory power for future stock returns and good stability of their predictive power. In practice, factor investing is still largely based on linear multi-factor models, although many deep learning methods show promising results compared to traditional methods in stock trend prediction and portfolio risk management. However, the existing non-linear methods have two drawbacks: 1) there is a lack of interpretation of the newly discovered factors, 2) the financial insights behind the mining process are unclear, making practitioners reluctant to apply the existing methods to factor investing. To address these two shortcomings, we develop a novel deep multi-factor model that adopts industry neutralization and market neutralization modules with clear financial insights, which help us easily build a dynamic and multi-relational stock graph in a hierarchical structure to learn the graph representation of stock relationships at different levels, e.g., industry level and universal level. Subsequently, graph attention modules are adopted to estimate a series of deep factors that maximize the cumulative factor returns. And a factor-attention module is developed to approximately compose the estimated deep factors from the input factors, as a way to interpret the deep factors explicitly. Extensive experiments on real-world stock market data demonstrate the effectiveness of our deep multi-factor model in the task of factor investing.

The paper proposes a new asset pricing model - the News Embedding UMAP Selection (NEUS) model, to explain and predict the stock returns based on the financial news. The proposed model is built on top of the recent achievements in asset pricing and natural language processing. From the asset pricing perspective, the NEUS model is based on the Adaptive Multi-Factor (AMF) model proposed by Zhu et al. [2020], which provides a modern and more general framework for multi-factor models. The AMF model contains the traditional well-known Fama-French 5-factor model (FF5) Fama and French [2015] as a special case. The finance theory behind the AMF model is the Generalized Arbitrage Pricing Theory (GAPT) proposed in Jarrow and Protter [2016] and Jarrow [2016] as a modern and more general framework of the traditional Arbitrage Pricing Theory (APT) proposed by Ross [1976].

The purpose of this paper is to test the multi-factor beta model implied by the generalized arbitrage pricing theory (APT) and the Adaptive Multi-Factor (AMF) model with the Groupwise Interpretable Basis Selection (GIBS) algorithm, without imposing the exogenous assumption of constant betas. The intercept (arbitrage) tests validate both the AMF and the Fama-French 5-factor (FF5) model. We do the time-invariance tests for the betas for both the AMF model and the FF5 in various time periods. We show that for nearly all time periods with length less than 6 years, the beta coefficients are time-invariant for the AMF model, but not the FF5 model. The beta coefficients are time-varying for both AMF and FF5 models for longer time periods. Therefore, using the dynamic AMF model with a decent rolling window (such as 5 years) is more powerful and stable than the FF5 model.

The purpose of this paper is to re-investigate the estimation of multiple factor models by relaxing the convention that the number of factors is small. We first obtain the collection of all possible factors and we provide a simultaneous test, security by security, of which factors are significant. Since the collection of risk factors selected for investigation is large and highly correlated, we use dimension reduction methods, including the Least Absolute Shrinkage and Selection Operator (LASSO) and prototype clustering, to perform the investigation. For comparison with the existing literature, we compare the multi-factor model's performance with the Fama-French 5-factor model. We find that both the Fama-French 5-factor and the multi-factor model are consistent with the behavior of "large-time scale" security returns. In a goodness-of-fit test comparing the Fama-French 5-factor with the multi-factor model, the multi-factor model has a substantially larger adjusted $R^{2}$. Robustness tests confirm that the multi-factor model provides a reasonable characterization of security returns.