Equities

Market-Based Variance of Market Portfolio and of Entire Market ArXiv ID: 2510.13790 “View on arXiv” Authors: Victor Olkhov Abstract We present the unified market-based description of returns and variances of the trades with shares of a particular security, of the trades with shares of all securities in the market, and of the trades with the market portfolio. We consider the investor who doesn’t trade the shares of his portfolio he collected at time t0 in the past. The investor observes the time series of the current trades with all securities made in the market during the averaging interval. The investor may convert these time series into the time series that model the trades with all securities as the trades with a single security and into the time series that model the trades with the market portfolio as the trades with a single security. That establishes the same description of the returns and variances of the trades with a single security, the trades with all securities in the market, and the market portfolio. We show that the market-based variance, which accounts for the impact of random change of the volumes of consecutive trades with securities, takes the form of Markowitz’s (1952) portfolio variance if the volumes of consecutive trades with all market securities are assumed constant. That highlights that Markowitz’s (1952) variance ignores the effects of random volumes of consecutive trades. We compare the market-based variances of the market portfolio and of the trades with all market securities, consider the importance of the duration of the averaging interval, and explain the economic obstacles that limit the accuracy of the predictions of the returns and variances at best by Gaussian distributions. The same methods describe the returns and variances of any portfolio and the trades with its securities. ...

On Evaluating Loss Functions for Stock Ranking: An Empirical Analysis With Transformer Model ArXiv ID: 2510.14156 “View on arXiv” Authors: Jan Kwiatkowski, Jarosław A. Chudziak Abstract Quantitative trading strategies rely on accurately ranking stocks to identify profitable investments. Effective portfolio management requires models that can reliably order future stock returns. Transformer models are promising for understanding financial time series, but how different training loss functions affect their ability to rank stocks well is not yet fully understood. Financial markets are challenging due to their changing nature and complex relationships between stocks. Standard loss functions, which aim for simple prediction accuracy, often aren’t enough. They don’t directly teach models to learn the correct order of stock returns. While many advanced ranking losses exist from fields such as information retrieval, there hasn’t been a thorough comparison to see how well they work for ranking financial returns, especially when used with modern Transformer models for stock selection. This paper addresses this gap by systematically evaluating a diverse set of advanced loss functions including pointwise, pairwise, listwise for daily stock return forecasting to facilitate rank-based portfolio selection on S&P 500 data. We focus on assessing how each loss function influences the model’s ability to discern profitable relative orderings among assets. Our research contributes a comprehensive benchmark revealing how different loss functions impact a model’s ability to learn cross-sectional and temporal patterns crucial for portfolio selection, thereby offering practical guidance for optimizing ranking-based trading strategies. ...

Attention Factors for Statistical Arbitrage ArXiv ID: 2510.11616 “View on arXiv” Authors: Elliot L. Epstein, Rose Wang, Jaewon Choi, Markus Pelger Abstract Statistical arbitrage exploits temporal price differences between similar assets. We develop a framework to jointly identify similar assets through factors, identify mispricing and form a trading policy that maximizes risk-adjusted performance after trading costs. Our Attention Factors are conditional latent factors that are the most useful for arbitrage trading. They are learned from firm characteristic embeddings that allow for complex interactions. We identify time-series signals from the residual portfolios of our factors with a general sequence model. Estimating factors and the arbitrage trading strategy jointly is crucial to maximize profitability after trading costs. In a comprehensive empirical study we show that our Attention Factor model achieves an out-of-sample Sharpe ratio above 4 on the largest U.S. equities over a 24-year period. Our one-step solution yields an unprecedented Sharpe ratio of 2.3 net of transaction costs. We show that weak factors are important for arbitrage trading. ...

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. ...

Identifying and Quantifying Financial Bubbles with the Hyped Log-Periodic Power Law Model ArXiv ID: 2510.10878 “View on arXiv” Authors: Zheng Cao, Xingran Shao, Yuheng Yan, Helyette Geman Abstract We propose a novel model, the Hyped Log-Periodic Power Law Model (HLPPL), to the problem of quantifying and detecting financial bubbles, an ever-fascinating one for academics and practitioners alike. Bubble labels are generated using a Log-Periodic Power Law (LPPL) model, sentiment scores, and a hype index we introduced in previous research on NLP forecasting of stock return volatility. Using these tools, a dual-stream transformer model is trained with market data and machine learning methods, resulting in a time series of confidence scores as a Bubble Score. A distinctive feature of our framework is that it captures phases of extreme overpricing and underpricing within a unified structure. We achieve an average yield of 34.13 percentage annualized return when backtesting U.S. equities during the period 2018 to 2024, while the approach exhibits a remarkable generalization ability across industry sectors. Its conservative bias in predicting bubble periods minimizes false positives, a feature which is especially beneficial for market signaling and decision-making. Overall, this approach utilizes both theoretical and empirical advances for real-time positive and negative bubble identification and measurement with HLPPL signals. ...

Mean-Field Price Formation on Trees with Multi-Population and Non-Rational Agents ArXiv ID: 2510.11261 “View on arXiv” Authors: Masaaki Fujii Abstract This work solves the equilibrium price formation problem for the risky stock by combining mean-field game theory with the binomial tree framework, adapting the classic approach of Cox, Ross & Rubinstein. For agents with exponential and recursive utilities of exponential-type, we prove the existence of a unique mean-field market-clearing equilibrium and derive an explicit analytic formula for equilibrium transition probabilities of the stock price on the binomial lattice. The agents face stochastic terminal liabilities and incremental endowments that depend on unhedgeable common and idiosyncratic factors, in addition to the stock price path. We also incorporate an external order flow. Furthermore, the analytic tractability of the proposed approach allows us to extend the framework in two important directions: First, we incorporate multi-population heterogeneity, allowing agents to differ in functional forms for their liabilities, endowments, and risk coefficients. Second, we relax the rational expectations hypothesis by modeling agents operating under subjective probability measures which induce stochastically biased views on the stock transition probabilities. Our numerical examples illustrate the qualitative effects of these components on the equilibrium price distribution. ...

Integrating Large Language Models and Reinforcement Learning for Sentiment-Driven Quantitative Trading ArXiv ID: 2510.10526 “View on arXiv” Authors: Wo Long, Wenxin Zeng, Xiaoyu Zhang, Ziyao Zhou Abstract This research develops a sentiment-driven quantitative trading system that leverages a large language model, FinGPT, for sentiment analysis, and explores a novel method for signal integration using a reinforcement learning algorithm, Twin Delayed Deep Deterministic Policy Gradient (TD3). We compare the performance of strategies that integrate sentiment and technical signals using both a conventional rule-based approach and a reinforcement learning framework. The results suggest that sentiment signals generated by FinGPT offer value when combined with traditional technical indicators, and that reinforcement learning algorithm presents a promising approach for effectively integrating heterogeneous signals in dynamic trading environments. ...

ATLAS: Adaptive Trading with LLM AgentS Through Dynamic Prompt Optimization and Multi-Agent Coordination ArXiv ID: 2510.15949 “View on arXiv” Authors: Charidimos Papadakis, Angeliki Dimitriou, Giorgos Filandrianos, Maria Lymperaiou, Konstantinos Thomas, Giorgos Stamou Abstract Large language models show promise for financial decision-making, yet deploying them as autonomous trading agents raises fundamental challenges: how to adapt instructions when rewards arrive late and obscured by market noise, how to synthesize heterogeneous information streams into coherent decisions, and how to bridge the gap between model outputs and executable market actions. We present ATLAS (Adaptive Trading with LLM AgentS), a unified multi-agent framework that integrates structured information from markets, news, and corporate fundamentals to support robust trading decisions. Within ATLAS, the central trading agent operates in an order-aware action space, ensuring that outputs correspond to executable market orders rather than abstract signals. The agent can incorporate feedback while trading using Adaptive-OPRO, a novel prompt-optimization technique that dynamically adapts the prompt by incorporating real-time, stochastic feedback, leading to increasing performance over time. Across regime-specific equity studies and multiple LLM families, Adaptive-OPRO consistently outperforms fixed prompts, while reflection-based feedback fails to provide systematic gains. ...

A Deterministic Limit Order Book Simulator with Hawkes-Driven Order Flow ArXiv ID: 2510.08085 “View on arXiv” Authors: Sohaib El Karmi Abstract We present a reproducible research framework for market microstructure combining a deterministic C++ limit order book (LOB) simulator with stochastic order flow generated by multivariate marked Hawkes processes. The paper derives full stability and ergodicity proofs for both linear and nonlinear Hawkes models, implements time-rescaling and goodness-of-fit diagnostics, and calibrates exponential and power-law kernels on Binance BTCUSDT and LOBSTER AAPL datasets. Empirical results highlight the nearly-unstable subcritical regime as essential for reproducing realistic clustering in order flow. All code, datasets, and configuration files are publicly available at https://github.com/sohaibelkarmi/High-Frequency-Trading-Simulator ...

Diffusion-Augmented Reinforcement Learning for Robust Portfolio Optimization under Stress Scenarios ArXiv ID: 2510.07099 “View on arXiv” Authors: Himanshu Choudhary, Arishi Orra, Manoj Thakur Abstract In the ever-changing and intricate landscape of financial markets, portfolio optimisation remains a formidable challenge for investors and asset managers. Conventional methods often struggle to capture the complex dynamics of market behaviour and align with diverse investor preferences. To address this, we propose an innovative framework, termed Diffusion-Augmented Reinforcement Learning (DARL), which synergistically integrates Denoising Diffusion Probabilistic Models (DDPMs) with Deep Reinforcement Learning (DRL) for portfolio management. By leveraging DDPMs to generate synthetic market crash scenarios conditioned on varying stress intensities, our approach significantly enhances the robustness of training data. Empirical evaluations demonstrate that DARL outperforms traditional baselines, delivering superior risk-adjusted returns and resilience against unforeseen crises, such as the 2025 Tariff Crisis. This work offers a robust and practical methodology to bolster stress resilience in DRL-driven financial applications. ...