Factor Investing

Not All Factors Crowd Equally: Modeling, Measuring, and Trading on Alpha Decay ArXiv ID: 2512.11913 “View on arXiv” Authors: Chorok Lee Abstract We derive a specific functional form for factor alpha decay – hyperbolic decay alpha(t) = K/(1+lambda*t) – from a game-theoretic equilibrium model, and test it against linear and exponential alternatives. Using eight Fama-French factors (1963–2024), we find: (1) Hyperbolic decay fits mechanical factors. Momentum exhibits clear hyperbolic decay (R^2 = 0.65), outperforming linear (0.51) and exponential (0.61) baselines – validating the equilibrium foundation. (2) Not all factors crowd equally. Mechanical factors (momentum, reversal) fit the model; judgment-based factors (value, quality) do not – consistent with a signal-ambiguity taxonomy paralleling Hua and Sun’s “barriers to entry.” (3) Crowding accelerated post-2015. Out-of-sample, the model over-predicts remaining alpha (0.30 vs. 0.15), correlating with factor ETF growth (rho = -0.63). (4) Average returns are efficiently priced. Crowding-based factor selection fails to generate alpha (Sharpe: 0.22 vs. 0.39 factor momentum benchmark). (5) Crowding predicts tail risk. Out-of-sample (2001–2024), crowded reversal factors show 1.7–1.8x higher crash probability (bottom decile returns), while crowded momentum shows lower crash risk (0.38x, p = 0.006). Our findings extend equilibrium crowding models (DeMiguel et al.) to temporal dynamics and show that crowding predicts crashes, not means – useful for risk management, not alpha generation. ...

Asset Pricing in Pre-trained Transformer ArXiv ID: 2505.01575 “View on arXiv” Authors: Shanyan Lai Abstract This paper proposes an innovative Transformer model, Single-directional representative from Transformer (SERT), for US large capital stock pricing. It also innovatively applies the pre-trained Transformer models under the stock pricing and factor investment context. They are compared with standard Transformer models and encoder-only Transformer models in three periods covering the entire COVID-19 pandemic to examine the model adaptivity and suitability during the extreme market fluctuations. Namely, pre-COVID-19 period (mild up-trend), COVID-19 period (sharp up-trend with deep down shock) and 1-year post-COVID-19 (high fluctuation sideways movement). The best proposed SERT model achieves the highest out-of-sample R2, 11.2% and 10.91% respectively, when extreme market fluctuation takes place followed by pre-trained Transformer models (10.38% and 9.15%). Their Trend-following-based strategy wise performance also proves their excellent capability for hedging downside risks during market shocks. The proposed SERT model achieves a Sortino ratio 47% higher than the buy-and-hold benchmark in the equal-weighted portfolio and 28% higher in the value-weighted portfolio when the pandemic period is attended. It proves that Transformer models have a great capability to capture patterns of temporal sparsity data in the asset pricing factor model, especially with considerable volatilities. We also find the softmax signal filter as the common configuration of Transformer models in alternative contexts, which only eliminates differences between models, but does not improve strategy-wise performance, while increasing attention heads improve the model performance insignificantly and applying the ’layer norm first’ method do not boost the model performance in our case. ...

Market-Neutral Strategies in Mid-Cap Portfolio Management: A Data-Driven Approach to Long-Short Equity ArXiv ID: 2412.12576 “View on arXiv” Authors: Unknown Abstract Mid-cap companies, generally valued between $2 billion and $10 billion, provide investors with a well-rounded opportunity between the fluctuation of small-cap stocks and the stability of large-cap stocks. This research builds upon the long-short equity approach (e.g., Michaud, 2018; Dimitriu, Alexander, 2002) customized for mid-cap equities, providing steady risk-adjusted returns yielding a significant Sharpe ratio of 2.132 in test data. Using data from 2013 to 2023, obtained from WRDS and following point-in-time (PIT) compliance, the approach guarantees clarity and reproducibility. Elements of essential financial indicators, such as profitability, valuation, and liquidity, were designed to improve portfolio optimization. Testing historical data across various markets conditions illustrates the stability and resilience of the tactic. This study highlights mid-cap stocks as an attractive investment route, overlooked by most analysts, which combine transparency with superior performance in managing portfolios. ...

GRU-PFG: Extract Inter-Stock Correlation from Stock Factors with Graph Neural Network ArXiv ID: 2411.18997 “View on arXiv” Authors: Unknown Abstract The complexity of stocks and industries presents challenges for stock prediction. Currently, stock prediction models can be divided into two categories. One category, represented by GRU and ALSTM, relies solely on stock factors for prediction, with limited effectiveness. The other category, represented by HIST and TRA, incorporates not only stock factors but also industry information, industry financial reports, public sentiment, and other inputs for prediction. The second category of models can capture correlations between stocks by introducing additional information, but the extra data is difficult to standardize and generalize. Considering the current state and limitations of these two types of models, this paper proposes the GRU-PFG (Project Factors into Graph) model. This model only takes stock factors as input and extracts inter-stock correlations using graph neural networks. It achieves prediction results that not only outperform the others models relies solely on stock factors, but also achieve comparable performance to the second category models. The experimental results show that on the CSI300 dataset, the IC of GRU-PFG is 0.134, outperforming HIST’s 0.131 and significantly surpassing GRU and Transformer, achieving results better than the second category models. Moreover as a model that relies solely on stock factors, it has greater potential for generalization. ...

Betting Against (Bad) Beta ArXiv ID: 2409.00416 “View on arXiv” Authors: Unknown Abstract Frazzini and Pedersen (2014) Betting Against Beta (BAB) factor is based on the idea that high beta assets trade at a premium and low beta assets trade at a discount due to investor funding constraints. However, as argued by Campbell and Vuolteenaho (2004), beta comes in “good” and “bad” varieties. While gaining exposure to low-beta, BAB factors fail to recognize that such a portfolio may tilt towards bad-beta. We propose a Betting Against Bad Beta factor, built by double-sorting on beta and bad-beta and find that it improves the overall performance of BAB strategies though its success relies on proper transaction cost mitigation. ...

Portfolio Construction using Black-Litterman Model and Factors ArXiv ID: 2311.04475 “View on arXiv” Authors: Unknown Abstract This paper presents a portfolio construction process, including mainly two parts, Factors Selection and Weight Allocations. For the factors selection part, We have chosen 20 factors by considering three aspects, the global market, different assets class, and stock idiosyncratic characteristics. Each factor is proxied by a corresponding ETF. Then, we would apply several weight allocation methods to those factors, including two fixed weight allocation methods, three optimisation methods, and a Black-Litterman model. In addition, we would also fit a Deep Learning model for generating views periodically and incorporating views with the prior to achieve dynamically updated weights by using the Black-Litterman model. In the end, the robustness checking shows how weights change with respect to time evolving and variance increasing. Results using shrinkage variance are provided to alleviate the impacts of representativeness of historical data, but there sadly has little impact. Overall, the model by using the Deep Learning plus Black-Litterman model results outperform the portfolio by other weight allocation schemes, even though further improvement and robustness checking should be performed. ...

E2EAI: End-to-End Deep Learning Framework for Active Investing ArXiv ID: 2305.16364 “View on arXiv” Authors: Unknown Abstract Active investing aims to construct a portfolio of assets that are believed to be relatively profitable in the markets, with one popular method being to construct a portfolio via factor-based strategies. In recent years, there have been increasing efforts to apply deep learning to pursue “deep factors’’ with more active returns or promising pipelines for asset trends prediction. However, the question of how to construct an active investment portfolio via an end-to-end deep learning framework (E2E) is still open and rarely addressed in existing works. In this paper, we are the first to propose an E2E that covers almost the entire process of factor investing through factor selection, factor combination, stock selection, and portfolio construction. Extensive experiments on real stock market data demonstrate the effectiveness of our end-to-end deep leaning framework in active investing. ...

Advanced Course in Asset Management (Presentation Slides) ArXiv ID: ssrn-3773484 “View on arXiv” Authors: Unknown Abstract These presentation slides have been written for the Advanced Course in Asset Management (theory and applications) given at the University of Paris-Saclay. They Keywords: Asset Management, Modern Portfolio Theory, Risk Management, Factor Investing, Multi-Asset Complexity vs Empirical Score Math Complexity: 7.5/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The slides present advanced mathematical theory including Markowitz optimization, CAPM, and Black-Litterman models with quadratic programming formulations and covariance matrix algebra. While it includes tutorial exercises and practice sections, it lacks empirical backtesting data, code implementations, or statistical performance metrics, remaining primarily theoretical and educational. flowchart TD A["Research Goal<br>Modern Asset Management"] --> B["Key Methodology<br>Portfolio Optimization"] B --> C["Data Inputs<br>Market Factors & Risk"] C --> D["Computational Process<br>Factor Analysis & MPT"] D --> E["Key Outcomes<br>Strategic Asset Allocation"] E --> F["Applications<br>Risk-Adjusted Returns"]

Fact, Fiction, and Value Investing ArXiv ID: ssrn-2595747 “View on arXiv” Authors: Unknown Abstract Value investing has been a part of the investment lexicon for at least the better part of a century. In particular the diversified systematic “value factor” or Keywords: Value Investing, Value Factor, Systematic Investing, Factor Investing, Equities Complexity vs Empirical Score Math Complexity: 1.5/10 Empirical Rigor: 8.0/10 Quadrant: Street Traders Why: The paper relies on accessible, industry-standard data for straightforward empirical tests, resulting in high empirical rigor, but uses minimal advanced mathematics or dense formulas, leading to low math complexity. flowchart TD A["Research Goal<br>Is the value factor robust<br>across time and geographies?"] --> B["Methodology<br>Longitudinal & cross-sectional analysis"] B --> C["Data Inputs<br>Global equities<br>Decades of historical data"] C --> D["Computational Process<br>Systematic value factor construction<br>Backtesting & attribution"] D --> E["Key Findings<br>Value factor persists but varies<br>Systematic implementation required"]