Rethinking Beta: A Causal Take on CAPM ArXiv ID: 2509.05760 “View on arXiv” Authors: Naftali Cohen Abstract The CAPM regression is typically interpreted as if the market return contemporaneously \emph{“causes”} individual returns, motivating beta-neutral portfolios and factor attribution. For realized equity returns, however, this interpretation is inconsistent: a same-period arrow $R_{“m,t”} \to R_{“i,t”}$ conflicts with the fact that $R_m$ is itself a value-weighted aggregate of its constituents, unless $R_m$ is lagged or leave-one-out – the aggregator contradiction.'' We formalize CAPM as a structural causal model and analyze the admissible three-node graphs linking an external driver $Z$, the market $R_m$, and an asset $R_i$. The empirically plausible baseline is a \emph{"fork"}, $Z \to \{"R_m, R_i\"}$, not $R_m \to R_i$. In this setting, OLS beta reflects not a causal transmission, but an attenuated proxy for how well $R_m$ captures the underlying driver $Z$. Consequently, beta-neutral’’ portfolios can remain exposed to macro or sectoral shocks, and hedging on $R_m$ can import index-specific noise. Using stylized models and large-cap U.S.\ equity data, we show that contemporaneous betas act like proxies rather than mechanisms; any genuine market-to-stock channel, if at all, appears only at a lag and with modest economic significance. The practical message is clear: CAPM should be read as associational. Risk management and attribution should shift from fixed factor menus to explicitly declared causal paths, with ``alpha’’ reserved for what remains invariant once those causal paths are explicitly blocked. ...

Deep Learning for Conditional Asset Pricing Models ArXiv ID: 2509.04812 “View on arXiv” Authors: Hongyi Liu Abstract We propose a new pseudo-Siamese Network for Asset Pricing (SNAP) model, based on deep learning approaches, for conditional asset pricing. Our model allows for the deep alpha, deep beta and deep factor risk premia conditional on high dimensional observable information of financial characteristics and macroeconomic states, while storing the long-term dependency of the informative features through long short-term memory network. We apply this method to monthly U.S. stock returns from 1970-2019 and find that our pseudo-SNAP model outperforms the benchmark approaches in terms of out-of-sample prediction and out-of-sample Sharpe ratio. In addition, we also apply our method to calculate deep mispricing errors which we use to construct an arbitrage portfolio K-Means clustering. We find that the arbitrage portfolio has significant alphas. ...

Dynamics of Liquidity Surfaces in Uniswap v3 ArXiv ID: 2509.05013 “View on arXiv” Authors: Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang Abstract This paper presents a comprehensive study on the empirical dynamics of Uniswap v3 liquidity, which we model as a time-tick surface, $L_t(x)$. Using a combination of functional principal component analysis (FPCA) and dynamic factor methods, we analyze three distinct pools over multiple sample periods. Our findings offer three main contributions: a statistical characterization of automated market maker liquidity, an interpretable and portable basis for dimension reduction, and a robust analysis of liquidity dynamics using rolling window metrics. For the 5 bps pools, the leading empirical eigenfunctions explain the majority of cross-tick variation and remain stable, aligning closely with a low-order Legendre polynomial basis. This alignment provides a parsimonious and interpretable structure, similar to the dynamic Nelson-Siegel method for yield curves. The factor coefficients exhibit a time series structure well-captured by AR(1) models with clear GARCH-type heteroskedasticity and heavy-tailed innovations. ...

MM-DREX: Multimodal-Driven Dynamic Routing of LLM Experts for Financial Trading ArXiv ID: 2509.05080 “View on arXiv” Authors: Yang Chen, Yueheng Jiang, Zhaozhao Ma, Yuchen Cao, Jacky Keung, Kun Kuang, Leilei Gan, Yiquan Wu, Fei Wu Abstract The inherent non-stationarity of financial markets and the complexity of multi-modal information pose significant challenges to existing quantitative trading models. Traditional methods relying on fixed structures and unimodal data struggle to adapt to market regime shifts, while large language model (LLM)-driven solutions - despite their multi-modal comprehension - suffer from static strategies and homogeneous expert designs, lacking dynamic adjustment and fine-grained decision mechanisms. To address these limitations, we propose MM-DREX: a Multimodal-driven, Dynamically-Routed EXpert framework based on large language models. MM-DREX explicitly decouples market state perception from strategy execution to enable adaptive sequential decision-making in non-stationary environments. Specifically, it (1) introduces a vision-language model (VLM)-powered dynamic router that jointly analyzes candlestick chart patterns and long-term temporal features to allocate real-time expert weights; (2) designs four heterogeneous trading experts (trend, reversal, breakout, positioning) generating specialized fine-grained sub-strategies; and (3) proposes an SFT-RL hybrid training paradigm to synergistically optimize the router’s market classification capability and experts’ risk-adjusted decision-making. Extensive experiments on multi-modal datasets spanning stocks, futures, and cryptocurrencies demonstrate that MM-DREX significantly outperforms 15 baselines (including state-of-the-art financial LLMs and deep reinforcement learning models) across key metrics: total return, Sharpe ratio, and maximum drawdown, validating its robustness and generalization. Additionally, an interpretability module traces routing logic and expert behavior in real time, providing an audit trail for strategy transparency. ...

Painting the market: generative diffusion models for financial limit order book simulation and forecasting ArXiv ID: 2509.05107 “View on arXiv” Authors: Alfred Backhouse, Kang Li, Jakob Foerster, Anisoara Calinescu, Stefan Zohren Abstract Simulating limit order books (LOBs) has important applications across forecasting and backtesting for financial market data. However, deep generative models struggle in this context due to the high noise and complexity of the data. Previous work uses autoregressive models, although these experience error accumulation over longer-time sequences. We introduce a novel approach, converting LOB data into a structured image format, and applying diffusion models with inpainting to generate future LOB states. This method leverages spatio-temporal inductive biases in the order book and enables parallel generation of long sequences overcoming issues with error accumulation. We also publicly contribute to LOB-Bench, the industry benchmark for LOB generative models, to allow fair comparison between models using Level-2 and Level-3 order book data (with or without message level data respectively). We show that our model achieves state-of-the-art performance on LOB-Bench, despite using lower fidelity data as input. We also show that our method prioritises coherent global structures over local, high-fidelity details, providing significant improvements over existing methods on certain metrics. Overall, our method lays a strong foundation for future research into generative diffusion approaches to LOB modelling. ...

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator ArXiv ID: 2509.05065 “View on arXiv” Authors: Guillaume Maitrier, Grégoire Loeper, Jean-Philippe Bouchaud Abstract This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of executed volume. One of the most striking predictions of our model is the structure of the correlation between generalized order flow and returns, which is observed empirically and reproduced using our synthetic market generator. Furthermore, we were able to construct proxy metaorders from our simulated order flow that reproduce the square-root law of market impact, lending further credence to the proposal made in Ref. [“2”] to measure the impact of real metaorders from tape data (i.e. anonymized trades), which was long thought to be impossible. ...

Finance-Grounded Optimization For Algorithmic Trading ArXiv ID: 2509.04541 “View on arXiv” Authors: Kasymkhan Khubiev, Mikhail Semenov, Irina Podlipnova Abstract Deep Learning is evolving fast and integrates into various domains. Finance is a challenging field for deep learning, especially in the case of interpretable artificial intelligence (AI). Although classical approaches perform very well with natural language processing, computer vision, and forecasting, they are not perfect for the financial world, in which specialists use different metrics to evaluate model performance. We first introduce financially grounded loss functions derived from key quantitative finance metrics, including the Sharpe ratio, Profit-and-Loss (PnL), and Maximum Draw down. Additionally, we propose turnover regularization, a method that inherently constrains the turnover of generated positions within predefined limits. Our findings demonstrate that the proposed loss functions, in conjunction with turnover regularization, outperform the traditional mean squared error loss for return prediction tasks when evaluated using algorithmic trading metrics. The study shows that financially grounded metrics enhance predictive performance in trading strategies and portfolio optimization. ...

Hierarchical Risk Parity for Portfolio Allocation in the Latin American NUAM Market ArXiv ID: 2509.03712 “View on arXiv” Authors: Gonzalo Ramirez-Carrillo, David Ortiz-Mora, Alex Aguilar-Larrotta Abstract This study applies the Hierarchical Risk Parity (HRP) portfolio allocation methodology to the NUAM market, a regional holding that integrates the markets of Chile, Colombia and Peru. As one of the first empirical analyses of HRP in this newly formed Latin American context, the paper addresses a gap in the literature on portfolio construction under cross-border, emerging market conditions. HRP leverages hierarchical clustering and recursive bisection to allocate risk in a manner that is both interpretable and robust–avoiding the need to invert the covariance matrix, a common limitation in the traditional mean-variance optimization. Using daily data from 54 constituent stocks of the MSCI NUAM Index from 2019 to 2025, we compare the performance of HRP against two standard benchmarks: an equally weighted portfolio (1/N) and a maximum Sharpe ratio portfolio. Results show that while the Max Sharpe portfolio yields the highest return, the HRP portfolio delivers a smoother risk-return profile, with lower drawdowns and tracking error. These findings highlight HRP’s potential as a practical and resilient asset allocation framework for investors operating in the integrated, high-volatility markets like NUAM. ...

Non-Linear and Meta-Stable Dynamics in Financial Markets: Evidence from High Frequency Crypto Currency Market Makers ArXiv ID: 2509.02941 “View on arXiv” Authors: Igor Halperin Abstract This work builds upon the long-standing conjecture that linear diffusion models are inadequate for complex market dynamics. Specifically, it provides experimental validation for the author’s prior arguments that realistic market dynamics are governed by higher-order (cubic and higher) non-linearities in the drift. As the diffusion drift is given by the negative gradient of a potential function, this means that a non-linear drift translates into a non-quadratic potential. These arguments were based both on general theoretical grounds as well as a structured approach to modeling the price dynamics which incorporates money flows and their impact on market prices. Here, we find direct confirmation of this view by analyzing high-frequency crypto currency data at different time scales ranging from minutes to months. We find that markets can be characterized by either a single-well or a double-well potential, depending on the time period and sampling frequency, where a double-well potential may signal market uncertainty or stress. ...

Bridging Human Cognition and AI: A Framework for Explainable Decision-Making Systems ArXiv ID: 2509.02388 “View on arXiv” Authors: N. Jean, G. Le Pera Abstract Explainability in AI and ML models is critical for fostering trust, ensuring accountability, and enabling informed decision making in high stakes domains. Yet this objective is often unmet in practice. This paper proposes a general purpose framework that bridges state of the art explainability techniques with Malle’s five category model of behavior explanation: Knowledge Structures, Simulation/Projection, Covariation, Direct Recall, and Rationalization. The framework is designed to be applicable across AI assisted decision making systems, with the goal of enhancing transparency, interpretability, and user trust. We demonstrate its practical relevance through real world case studies, including credit risk assessment and regulatory analysis powered by large language models (LLMs). By aligning technical explanations with human cognitive mechanisms, the framework lays the groundwork for more comprehensible, responsible, and ethical AI systems. ...