Factor Models

A Deep Learning Approach for Trading Factor Residuals ArXiv ID: 2412.11432 “View on arXiv” Authors: Unknown Abstract The residuals in factor models prevalent in asset pricing presents opportunities to exploit the mis-pricing from unexplained cross-sectional variation for arbitrage. We performed a replication of the methodology of Guijarro-Ordonez et al. (2019) (G-P-Z) on Deep Learning Statistical Arbitrage (DLSA), originally applied to U.S. equity data from 1998 to 2016, using a more recent out-of-sample period from 2016 to 2024. Adhering strictly to point-in-time (PIT) principles and ensuring no information leakage, we follow the same data pre-processing, factor modeling, and deep learning architectures (CNNs and Transformers) as outlined by G-P-Z. Our replication yields unusually strong performance metrics in certain tests, with out-of-sample Sharpe ratios occasionally exceeding 10. While such results are intriguing, they may indicate model overfitting, highly specific market conditions, or insufficient accounting for transaction costs and market impact. Further examination and robustness checks are needed to align these findings with the more modest improvements reported in the original study. (This work was conducted as the final project for IEOR 4576: Data-Driven Methods in Finance at Columbia University.) ...

Benchmarking M6 Competitors: An Analysis of Financial Metrics and Discussion of Incentives ArXiv ID: 2406.19105 “View on arXiv” Authors: Unknown Abstract The M6 Competition assessed the performance of competitors using a ranked probability score and an information ratio (IR). While these metrics do well at picking the winners in the competition, crucial questions remain for investors with longer-term incentives. To address these questions, we compare the competitors’ performance to a number of conventional (long-only) and alternative indices using standard industry metrics. We apply factor models to measure the competitors’ value-adds above industry-standard benchmarks and find that competitors with more extreme performance are less dependent on the benchmarks. We also uncover that most competitors could not generate significant out-performance compared to randomly selected long-only and long-short portfolios but did generate out-performance compared to short-only portfolios. We further introduce two new strategies by picking the competitors with the best (Superstars) and worst (Superlosers) recent performance and show that it is challenging to identify skill amongst investment managers. We also discuss the incentives of winning the competition compared to professional investors, where investors wish to maximize fees over an extended period of time. ...

Kernel Three Pass Regression Filter ArXiv ID: 2405.07292 “View on arXiv” Authors: Unknown Abstract We forecast a single time series using a high-dimensional set of predictors. When these predictors share common underlying dynamics, an approximate latent factor model provides a powerful characterization of their co-movements Bai(2003). These latent factors succinctly summarize the data and can also be used for prediction, alleviating the curse of dimensionality in high-dimensional prediction exercises, see Stock & Watson (2002a). However, forecasting using these latent factors suffers from two potential drawbacks. First, not all pervasive factors among the set of predictors may be relevant, and using all of them can lead to inefficient forecasts. The second shortcoming is the assumption of linear dependence of predictors on the underlying factors. The first issue can be addressed by using some form of supervision, which leads to the omission of irrelevant information. One example is the three-pass regression filter proposed by Kelly & Pruitt (2015). We extend their framework to cases where the form of dependence might be nonlinear by developing a new estimator, which we refer to as the Kernel Three-Pass Regression Filter (K3PRF). This alleviates the aforementioned second shortcoming. The estimator is computationally efficient and performs well empirically. The short-term performance matches or exceeds that of established models, while the long-term performance shows significant improvement. ...

Portfolio Analysis in High Dimensions with TE and Weight Constraints ArXiv ID: 2402.17523 “View on arXiv” Authors: Unknown Abstract This paper explores the statistical properties of forming constrained optimal portfolios within a high-dimensional set of assets. We examine portfolios with tracking error constraints, those with simultaneous tracking error and weight restrictions, and portfolios constrained solely by weight. Tracking error measures portfolio performance against a benchmark (typically an index), while weight constraints determine asset allocation based on regulatory requirements or fund prospectuses. Our approach employs a novel statistical learning technique that integrates factor models with nodewise regression, named the Constrained Residual Nodewise Optimal Weight Regression (CROWN) method. We demonstrate its estimation consistency in large dimensions, even when assets outnumber the portfolio’s time span. Convergence rate results for constrained portfolio weights, risk, and Sharpe Ratio are provided, and simulation and empirical evidence highlight the method’s outstanding performance. ...

Stockformer: A Price-Volume Factor Stock Selection Model Based on Wavelet Transform and Multi-Task Self-Attention Networks ArXiv ID: 2401.06139 “View on arXiv” Authors: Unknown Abstract As the Chinese stock market continues to evolve and its market structure grows increasingly complex, traditional quantitative trading methods are facing escalating challenges. Particularly, due to policy uncertainty and the frequent market fluctuations triggered by sudden economic events, existing models often struggle to accurately predict market dynamics. To address these challenges, this paper introduces Stockformer, a price-volume factor stock selection model that integrates wavelet transformation and a multitask self-attention network, aimed at enhancing responsiveness and predictive accuracy regarding market instabilities. Through discrete wavelet transform, Stockformer decomposes stock returns into high and low frequencies, meticulously capturing long-term market trends and short-term fluctuations, including abrupt events. Moreover, the model incorporates a Dual-Frequency Spatiotemporal Encoder and graph embedding techniques to effectively capture complex temporal and spatial relationships among stocks. Employing a multitask learning strategy, it simultaneously predicts stock returns and directional trends. Experimental results show that Stockformer outperforms existing advanced methods on multiple real stock market datasets. In strategy backtesting, Stockformer consistently demonstrates exceptional stability and reliability across market conditions-whether rising, falling, or fluctuating-particularly maintaining high performance during downturns or volatile periods, indicating a high adaptability to market fluctuations. To foster innovation and collaboration in the financial analysis sector, the Stockformer model’s code has been open-sourced and is available on the GitHub repository: https://github.com/Eric991005/Multitask-Stockformer. ...

Sector Rotation by Factor Model and Fundamental Analysis ArXiv ID: 2401.00001 “View on arXiv” Authors: Unknown Abstract This study presents an analytical approach to sector rotation, leveraging both factor models and fundamental metrics. We initiate with a systematic classification of sectors, followed by an empirical investigation into their returns. Through factor analysis, the paper underscores the significance of momentum and short-term reversion in dictating sectoral shifts. A subsequent in-depth fundamental analysis evaluates metrics such as PE, PB, EV-to-EBITDA, Dividend Yield, among others. Our primary contribution lies in developing a predictive framework based on these fundamental indicators. The constructed models, post rigorous training, exhibit noteworthy predictive capabilities. The findings furnish a nuanced understanding of sector rotation strategies, with implications for asset management and portfolio construction in the financial domain. ...

Black-Litterman, Bayesian Shrinkage, and Factor Models in Portfolio Selection: You Can Have It All ArXiv ID: 2308.09264 “View on arXiv” Authors: Unknown Abstract Mean-variance analysis is widely used in portfolio management to identify the best portfolio that makes an optimal trade-off between expected return and volatility. Yet, this method has its limitations, notably its vulnerability to estimation errors and its reliance on historical data. While shrinkage estimators and factor models have been introduced to improve estimation accuracy through bias-variance trade-offs, and the Black-Litterman model has been developed to integrate investor opinions, a unified framework combining three approaches has been lacking. Our study debuts a Bayesian blueprint that fuses shrinkage estimation with view inclusion, conceptualizing both as Bayesian updates. This model is then applied within the context of the Fama-French approach factor models, thereby integrating the advantages of each methodology. Finally, through a comprehensive empirical study in the US equity market spanning a decade, we show that the model outperforms both the simple $1/N$ portfolio and the optimal portfolios based on sample estimators. ...

Online Universal Dirichlet Factor Portfolios ArXiv ID: 2308.07763 “View on arXiv” Authors: Unknown Abstract We revisit the online portfolio allocation problem and propose universal portfolios that use factor weighing to produce portfolios that out-perform uniform dirichlet allocation schemes. We show a few analytical results on the lower bounds of portfolio growth when the returns are known to follow a factor model. We also show analytically that factor weighted dirichlet sampled portfolios dominate the wealth generated by uniformly sampled dirichlet portfolios. We corroborate our analytical results with empirical studies on equity markets that are known to be driven by factors. ...

Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns ArXiv ID: 2308.05564 “View on arXiv” Authors: Unknown Abstract Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A stochastic gradient ascent algorithm is used to solve the variational optimization. The methodology is used to estimate skew-t factor copula models with up to 15 factors for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. In a moving window study we show that the asymmetric dependencies also vary over time, and that intraday predictive densities from the skew-t copula are more accurate than those from benchmark copula models. Portfolio selection strategies based on the estimated pairwise asymmetric dependencies improve performance relative to the index. ...

On Unified Adaptive Portfolio Management ArXiv ID: 2307.03391 “View on arXiv” Authors: Unknown Abstract This paper introduces a unified framework for adaptive portfolio management, integrating dynamic Black-Litterman (BL) optimization with the general factor model, Elastic Net regression, and mean-variance portfolio optimization, which allows us to generate investors views and mitigate potential estimation errors systematically. Specifically, we propose an innovative dynamic sliding window algorithm to respond to the constantly changing market conditions. This algorithm allows for the flexible window size adjustment based on market volatility, generating robust estimates for factor modeling, time-varying BL estimations, and optimal portfolio weights. Through extensive ten-year empirical studies using the top 100 capitalized assets in the S&P 500 index, accounting for turnover transaction costs, we demonstrate that this combined approach leads to computational advantages and promising trading performances. ...