Equities

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. ...

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. ...

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. ...

Adaptive Alpha Weighting with PPO: Enhancing Prompt-Based LLM-Generated Alphas in Quant Trading ArXiv ID: 2509.01393 “View on arXiv” Authors: Qizhao Chen, Hiroaki Kawashima Abstract This paper proposes a reinforcement learning framework that employs Proximal Policy Optimization (PPO) to dynamically optimize the weights of multiple large language model (LLM)-generated formulaic alphas for stock trading strategies. Formulaic alphas are mathematically defined trading signals derived from price, volume, sentiment, and other data. Although recent studies have shown that LLMs can generate diverse and effective alphas, a critical challenge lies in how to adaptively integrate them under varying market conditions. To address this gap, we leverage the deepseek-r1-distill-llama-70b model to generate fifty alphas for five major stocks: Apple, HSBC, Pepsi, Toyota, and Tencent, and then use PPO to adjust their weights in real time. Experimental results demonstrate that the PPO-optimized strategy achieves strong returns and high Sharpe ratios across most stocks, outperforming both an equal-weighted alpha portfolio and traditional benchmarks such as the Nikkei 225, S&P 500, and Hang Seng Index. The findings highlight the importance of reinforcement learning in the allocation of alpha weights and show the potential of combining LLM-generated signals with adaptive optimization for robust financial forecasting and trading. ...

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. ...

The Impact of Sequential versus Parallel Clearing Mechanisms in Agent-Based Simulations of Artificial Limit Order Book Exchanges ArXiv ID: 2509.01683 “View on arXiv” Authors: Matej Steinbacher, Mitja Steinbacher, Matjaz Steinbacher Abstract This study examines the impact of different computing implementations of clearing mechanisms on multi-asset price dynamics within an artificial stock market framework. We show that sequential processing of order books introduces a systematic and significant bias by affecting the allocation of traders’ capital within a single time step. This occurs because applying budget constraints sequentially grants assets processed earlier preferential access to funds, distorting individual asset demand and consequently their price trajectories. The findings highlight that while the overall price level is primarily driven by macro factors like the money-to-stock ratio, the market’s microstructural clearing mechanism plays a critical role in the allocation of value among individual assets. This underscores the necessity for careful consideration and validation of clearing mechanisms in artificial markets to accurately model complex financial behaviors. ...

Multi Scale Analysis of Nifty 50 Return Characteristics Valuation Dynamics and Market Complexity 1990 to 2024 ArXiv ID: 2509.00697 “View on arXiv” Authors: Chandradew Sharma Abstract This study presents a unified, distribution-aware, and complexity-informed framework for understanding equity return dynamics in the Indian market, using 34 years (1990 to 2024) of Nifty 50 index data. Addressing a key gap in the literature, we demonstrate that the price to earnings ratio, as a valuation metric, may probabilistically map return distributions across investment horizons spanning from days to decades. Return profiles exhibit strong asymmetry. One-year returns show a 74 percent probability of gain, with a modal return of 10.67 percent and a reward-to-risk ratio exceeding 5. Over long horizons, modal CAGRs surpass 13 percent, while worst-case returns remain negative for up to ten years, defining a historical trapping period. This horizon shortens to six years in the post-1999 period, reflecting growing market resilience. Conditional analysis of the P/E ratio reveals regime-dependent outcomes. Low valuations (P/E less than 13) historically show zero probability of loss across all horizons, while high valuations (P/E greater than 27) correspond to unstable returns and extended breakeven periods. To uncover deeper structure, we apply tools from complexity science. Entropy, Hurst exponents, and Lyapunov indicators reveal weak persistence, long memory, and low-dimensional chaos. Information-theoretic metrics, including mutual information and transfer entropy, confirm a directional and predictive influence of valuation on future returns. These findings offer actionable insights for asset allocation, downside risk management, and long-term investment strategy in emerging markets. Our framework bridges valuation, conditional distributions, and nonlinear dynamics in a rigorous and practically relevant manner. ...

Prospects of Imitating Trading Agents in the Stock Market ArXiv ID: 2509.00982 “View on arXiv” Authors: Mateusz Wilinski, Juho Kanniainen Abstract In this work we show how generative tools, which were successfully applied to limit order book data, can be utilized for the task of imitating trading agents. To this end, we propose a modified generative architecture based on the state-space model, and apply it to limit order book data with identified investors. The model is trained on synthetic data, generated from a heterogeneous agent-based model. Finally, we compare model’s predicted distribution over different aspects of investors’ actions, with the ground truths known from the agent-based model. ...

Equity Premium Prediction: Taking into Account the Role of Long, even Asymmetric, Swings in Stock Market Behavior ArXiv ID: 2509.10483 “View on arXiv” Authors: Kuok Sin Un, Marcel Ausloos Abstract Through a novel approach, this paper shows that substantial change in stock market behavior has a statistically and economically significant impact on equity risk premium predictability both on in-sample and out-of-sample cases. In line with Auer’s ‘‘Bullish ratio’’, a ‘‘Bullish index’’ is introduced to measure the changes in stock market behavior, which we describe through a ‘‘fluctuation detrending moving average analysis’’ (FDMAA) for returns. We consider 28 indicators. We find that a ‘‘positive shock’’ of the Bullish Index is closely related to strong equity risk premium predictability for forecasts based on macroeconomic variables for up to six months. In contrast, a ‘’negative shock’’ is associated with strong equity risk premium predictability with adequate forecasts for up to nine months when based on technical indicators. ...

Agent-based model of information diffusion in the limit order book trading ArXiv ID: 2508.20672 “View on arXiv” Authors: Mateusz Wilinski, Juho Kanniainen Abstract There are multiple explanations for stylized facts in high-frequency trading, including adaptive and informed agents, many of which have been studied through agent-based models. This paper investigates an alternative explanation by examining whether, and under what circumstances, interactions between traders placing limit order book messages can reproduce stylized facts, and what forms of interaction are required. While the agent-based modeling literature has introduced interconnected agents on networks, little attention has been paid to whether specific trading network topologies can generate stylized facts in limit order book markets. In our model, agents are strictly zero-intelligence, with no fundamental knowledge or chartist-like strategies, so that the role of network topology can be isolated. We find that scale-free connectivity between agents reproduces stylized facts observed in markets, whereas no-interaction does not. Our experiments show that regular lattices and Erdos-Renyi networks are not significantly different from the no-interaction baseline. Thus, we provide a completely new, potentially complementary, explanation for the emergence of stylized facts. ...