Factor Models

Forecasting the U.S. Treasury Yield Curve: A Distributionally Robust Machine Learning Approach ArXiv ID: 2601.04608 “View on arXiv” Authors: Jinjun Liu, Ming-Yen Cheng Abstract We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a decision rule that minimizes worst case expected loss over an ambiguity set of forecast error distributions. To this end, we propose a distributionally robust ensemble forecasting framework that integrates parametric factor models with high dimensional nonparametric machine learning models through adaptive forecast combinations. The framework consists of three machine learning components. First, a rolling window Factor Augmented Dynamic Nelson Siegel model captures level, slope, and curvature dynamics using principal components extracted from economic indicators. Second, Random Forest models capture nonlinear interactions among macro financial drivers and lagged Treasury yields. Third, distributionally robust forecast combination schemes aggregate heterogeneous forecasts under moment uncertainty, penalizing downside tail risk via expected shortfall and stabilizing second moment estimation through ridge regularized covariance matrices. The severity of the worst case criterion is adjustable, allowing the forecaster to regulate the trade off between robustness and statistical efficiency. Using monthly data, we evaluate out of sample forecasts across maturities and horizons from one to twelve months ahead. Adaptive combinations deliver superior performance at short horizons, while Random Forest forecasts dominate at longer horizons. Extensions to global sovereign bond yields confirm the stability and generalizability of the proposed framework. ...

High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions ArXiv ID: 2511.01271 “View on arXiv” Authors: Zhaoxing Gao, Sihan Tu, Ruey S. Tsay Abstract This paper investigates estimation and inference of a Spatial Arbitrage Pricing Theory (SAPT) model that integrates spatial interactions with multi-factor analysis, accommodating both observable and latent factors. Building on the classical mean-variance analysis, we introduce a class of Spatial Capital Asset Pricing Models (SCAPM) that account for spatial effects in high-dimensional assets, where we define {"\it spatial rho"} as a counterpart to market beta in CAPM. We then extend SCAPM to a general SAPT framework under a {"\it complete"} market setting by incorporating multiple factors. For SAPT with observable factors, we propose a generalized shrinkage Yule-Walker (SYW) estimation method that integrates ridge regression to estimate spatial and factor coefficients. When factors are latent, we first apply an autocovariance-based eigenanalysis to extract factors, then employ the SYW method using the estimated factors. We establish asymptotic properties for these estimators under high-dimensional settings where both the dimension and sample size diverge. Finally, we use simulated and real data examples to demonstrate the efficacy and usefulness of the proposed model and method. ...

Evaluating Investment Performance: The p-index and Empirical Efficient Frontier ArXiv ID: 2510.11074 “View on arXiv” Authors: Jing Li, Bowei Guo, Xinqi Xie, Kuo-Ping Chang Abstract The empirical results have shown that firstly, with one-week holding period and reinvesting, for SSE Composite Index stocks, the highest p-ratio investment strategy produces the largest annualized rate of return; and for NYSE Composite Index stocks, all the three strategies with both one-week and one-month periods generate negative returns. Secondly, with non-reinvesting, for SSE Composite Index stocks, the highest p-ratio strategy with one-week holding period yields the largest annualized rate of return; and for NYSE Composite stocks, the one-week EEF strategy produces a medium annualized return. Thirdly, under the one-week EEF investment strategy, for NYSE Composite Index stocks, the right frontier yields a higher annualized return, but for SSE Composite Index stocks, the left frontier (stocks on the empirical efficient frontier) yields a higher annualized return than the right frontier. Fourthly, for NYSE Composite Index stocks, there is a positive linear relationship between monthly return and the p-index, but no such relationship is evident for SSE Composite Index stocks. Fifthly, for NYSE Composite Index stocks, the traditional five-factor model performs poorly, and adding the p-index as a sixth factor provides incremental information. ...

Is All the Information in the Price? LLM Embeddings versus the EMH in Stock Clustering ArXiv ID: 2509.01590 “View on arXiv” Authors: Bingyang Wang, Grant Johnson, Maria Hybinette, Tucker Balch Abstract This paper investigates whether artificial intelligence can enhance stock clustering compared to traditional methods. We consider this in the context of the semi-strong Efficient Markets Hypothesis (EMH), which posits that prices fully reflect all public information and, accordingly, that clusters based on price information cannot be improved upon. We benchmark three clustering approaches: (i) price-based clusters derived from historical return correlations, (ii) human-informed clusters defined by the Global Industry Classification Standard (GICS), and (iii) AI-driven clusters constructed from large language model (LLM) embeddings of stock-related news headlines. At each date, each method provides a classification in which each stock is assigned to a cluster. To evaluate a clustering, we transform it into a synthetic factor model following the Arbitrage Pricing Theory (APT) framework. This enables consistent evaluation of predictive performance in a roll forward, out-of-sample test. Using S&P 500 constituents from from 2022 through 2024, we find that price-based clustering consistently outperforms both rule-based and AI-based methods, reducing root mean squared error (RMSE) by 15.9% relative to GICS and 14.7% relative to LLM embeddings. Our contributions are threefold: (i) a generalizable methodology that converts any equity grouping: manual, machine, or market-driven, into a real-time factor model for evaluation; (ii) the first direct comparison of price-based, human rule-based, and AI-based clustering under identical conditions; and (iii) empirical evidence reinforcing that short-horizon return information is largely contained in prices. These results support the EMH while offering practitioners a practical diagnostic for monitoring evolving sector structures and provide academics a framework for testing alternative hypotheses about how quickly markets absorb information. ...

Time-Varying Factor-Augmented Models for Volatility Forecasting ArXiv ID: 2508.01880 “View on arXiv” Authors: Duo Zhang, Jiayu Li, Junyi Mo, Elynn Chen Abstract Accurate volatility forecasts are vital in modern finance for risk management, portfolio allocation, and strategic decision-making. However, existing methods face key limitations. Fully multivariate models, while comprehensive, are computationally infeasible for realistic portfolios. Factor models, though efficient, primarily use static factor loadings, failing to capture evolving volatility co-movements when they are most critical. To address these limitations, we propose a novel, model-agnostic Factor-Augmented Volatility Forecast framework. Our approach employs a time-varying factor model to extract a compact set of dynamic, cross-sectional factors from realized volatilities with minimal computational cost. These factors are then integrated into both statistical and AI-based forecasting models, enabling a unified system that jointly models asset-specific dynamics and evolving market-wide co-movements. Our framework demonstrates strong performance across two prominent asset classes-large-cap U.S. technology equities and major cryptocurrencies-over both short-term (1-day) and medium-term (7-day) horizons. Using a suite of linear and non-linear AI-driven models, we consistently observe substantial improvements in predictive accuracy and economic value. Notably, a practical pairs-trading strategy built on our forecasts delivers superior risk-adjusted returns and profitability, particularly under adverse market conditions. ...

Multilayer Perceptron Neural Network Models in Asset Pricing: An Empirical Study on Large-Cap US Stocks ArXiv ID: 2505.01921 “View on arXiv” Authors: Shanyan Lai Abstract In this study, MLP models with dynamic structure are applied to factor models for asset pricing tasks. Concretely, the MLP pyramid model structure was employed on firm-characteristic-sorted portfolio factors for modelling the large-capital US stocks. It was further developed as a practicable factor investing strategy based on the predictions. The main findings in this chapter were evaluated from two angles: model performance and investing performance, which were compared from the periods with and without COVID-19. The empirical results indicated that with the restrictions of the data size, the MLP models no longer perform “deeper, better”, while the proposed MLP models with two and three hidden layers have higher flexibility to model the factors in this case. This study also verified the idea of previous works that MLP models for factor investing have more meaning in the downside risk control than in pursuing the absolute annual returns. ...

Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure ArXiv ID: 2504.06566 “View on arXiv” Authors: Unknown Abstract Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion processes, bridging econometrics with modern generative AI to address the challenges of the curse of dimensionality and data scarcity in financial simulation. By exploiting the low-dimensional factor structure inherent in asset returns, we decompose the score function–a key component in diffusion models–using time-varying orthogonal projections, and this decomposition is incorporated into the design of neural network architectures. We derive rigorous statistical guarantees, establishing nonasymptotic error bounds for both score estimation at O(d^{“5/2”} n^{"-2/(k+5)"}) and generated distribution at O(d^{“5/4”} n^{"-1/2(k+5)"}), primarily driven by the intrinsic factor dimension k rather than the number of assets d, surpassing the dimension-dependent limits in the classical nonparametric statistics literature and making the framework viable for markets with thousands of assets. Numerical studies confirm superior performance in latent subspace recovery under small data regimes. Empirical analysis demonstrates the economic significance of our framework in constructing mean-variance optimal portfolios and factor portfolios. This work presents the first theoretical integration of factor structure with diffusion models, offering a principled approach for high-dimensional financial simulation with limited data. Our code is available at https://github.com/xymmmm00/diffusion_factor_model. ...

Generalized Factor Neural Network Model for High-dimensional Regression ArXiv ID: 2502.11310 “View on arXiv” Authors: Unknown Abstract We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression. Our approach introduces PCA and Soft PCA layers, which can be embedded at any stage of a neural network architecture, allowing the model to alternate between factor modeling and non-linear transformations. This flexibility makes our method especially effective for processing hierarchical compositional data. We explore ours and other techniques for imposing low-rank structures on neural networks and examine how architectural design impacts model performance. The effectiveness of our method is demonstrated through simulation studies, as well as applications to forecasting future price movements of equity ETF indices and nowcasting with macroeconomic data. ...

FactorGCL: A Hypergraph-Based Factor Model with Temporal Residual Contrastive Learning for Stock Returns Prediction ArXiv ID: 2502.05218 “View on arXiv” Authors: Unknown Abstract As a fundamental method in economics and finance, the factor model has been extensively utilized in quantitative investment. In recent years, there has been a paradigm shift from traditional linear models with expert-designed factors to more flexible nonlinear machine learning-based models with data-driven factors, aiming to enhance the effectiveness of these factor models. However, due to the low signal-to-noise ratio in market data, mining effective factors in data-driven models remains challenging. In this work, we propose a hypergraph-based factor model with temporal residual contrastive learning (FactorGCL) that employs a hypergraph structure to better capture high-order nonlinear relationships among stock returns and factors. To mine hidden factors that supplement human-designed prior factors for predicting stock returns, we design a cascading residual hypergraph architecture, in which the hidden factors are extracted from the residual information after removing the influence of prior factors. Additionally, we propose a temporal residual contrastive learning method to guide the extraction of effective and comprehensive hidden factors by contrasting stock-specific residual information over different time periods. Our extensive experiments on real stock market data demonstrate that FactorGCL not only outperforms existing state-of-the-art methods but also mines effective hidden factors for predicting stock returns. ...

Regression and Forecasting of U.S. Stock Returns Based on LSTM ArXiv ID: 2502.05210 “View on arXiv” Authors: Unknown Abstract This paper analyses the investment returns of three stock sectors, Manuf, Hitec, and Other, in the U.S. stock market, based on the Fama-French three-factor model, the Carhart four-factor model, and the Fama-French five-factor model, in order to test the validity of the Fama-French three-factor model, the Carhart four-factor model, and the Fama-French five-factor model for the three sectors of the market. French five-factor model for the three sectors of the market. Also, the LSTM model is used to explore the additional factors affecting stock returns. The empirical results show that the Fama-French five-factor model has better validity for the three segments of the market under study, and the LSTM model has the ability to capture the factors affecting the returns of certain industries, and can better regress and predict the stock returns of the relevant industries. Keywords- Fama-French model; Carhart model; Factor model; LSTM model. ...