Equity

LLM-Based Routing in Mixture of Experts: A Novel Framework for Trading ArXiv ID: 2501.09636 “View on arXiv” Authors: Unknown Abstract Recent advances in deep learning and large language models (LLMs) have facilitated the deployment of the mixture-of-experts (MoE) mechanism in the stock investment domain. While these models have demonstrated promising trading performance, they are often unimodal, neglecting the wealth of information available in other modalities, such as textual data. Moreover, the traditional neural network-based router selection mechanism fails to consider contextual and real-world nuances, resulting in suboptimal expert selection. To address these limitations, we propose LLMoE, a novel framework that employs LLMs as the router within the MoE architecture. Specifically, we replace the conventional neural network-based router with LLMs, leveraging their extensive world knowledge and reasoning capabilities to select experts based on historical price data and stock news. This approach provides a more effective and interpretable selection mechanism. Our experiments on multimodal real-world stock datasets demonstrate that LLMoE outperforms state-of-the-art MoE models and other deep neural network approaches. Additionally, the flexible architecture of LLMoE allows for easy adaptation to various downstream tasks. ...

Finding the nonnegative minimal solutions of Cauchy PDEs in a volatility-stabilized market ArXiv ID: 2411.13558 “View on arXiv” Authors: Unknown Abstract The strong relative arbitrage problem in Stochastic Portfolio Theory seeks an investment strategy that almost surely outperforms a benchmark portfolio at the end of a given time horizon. The highest relative return in relative arbitrage opportunities is characterized by the smallest nonnegative continuous solution of a Cauchy problem for a partial differential equation (PDE). However, solving this type of PDE poses analytical and numerical challenges, due to the high dimensionality and its non-unique solutions. In this paper, we discuss numerical methods to address the relative arbitrage problem and the associated PDE in a volatility-stabilized market, using time-changed Bessel bridges. We present a practical algorithm and demonstrate numerical results through an example in volatility-stabilized markets. ...

Market efficiency, informational asymmetry and pseudo-collusion of adaptively learning agents ArXiv ID: 2411.05032 “View on arXiv” Authors: Unknown Abstract We examine the dynamics of informational efficiency in a market with asymmetrically informed, boundedly rational traders who adaptively learn optimal strategies using simple multiarmed bandit (MAB) algorithms. The strategies available to the traders have two dimensions: on the one hand, the traders must endogenously choose whether to acquire a costly information signal, on the other, they must determine how aggressively they trade by choosing the share of their wealth to be invested in the risky asset. Our study contributes to two strands of literature: the literature comparing the effects of competitive and strategic behavior on asset price efficiency under costly information as well as the actively growing literature on algorithmic tacit collusion and pseudo-collusion in financial markets. We find that for certain market environments (with low information costs) our model reproduces the results of Kyle [“1989”] in that the ability of traders to trade strategically leads to worse price efficiency compared to the purely competitive case. For other environments (with high information costs), on the other hand, our results show that a market with strategically acting traders can be more efficient than a purely competitive one. Furthermore, we obtain novel results on the ability of independently learning traders to coordinate on a pseudo-collusive behavior, leading to non-competitive pricing. Contrary to some recent contributions (see e.g. [“Cartea et al. 2022”]), we find that the pseudo-collusive behavior in our model is robust to a large number of agents, demonstrating that even in the setting of financial markets with a large number of independently learning traders non-competitive pricing and pseudo-collusive behavior can frequently arise. ...

Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels ArXiv ID: 2410.21858 “View on arXiv” Authors: Unknown Abstract We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications. We apply it to an extensive panel of monthly US stock excess returns from 1962 to 2021, using macroeconomic and firm-specific covariates as conditioning variables. The estimator effectively captures time-varying cross-sectional dependencies, demonstrating robust statistical and economic performance. We find that idiosyncratic risk explains, on average, more than 75% of the cross-sectional variance. ...

Existence, uniqueness and positivity of solutions to the Guyon-Lekeufack path-dependent volatility model with general kernels ArXiv ID: 2408.02477 “View on arXiv” Authors: Unknown Abstract We show the existence and uniqueness of a continuous solution to a path-dependent volatility model introduced by Guyon and Lekeufack (2023) to model the price of an equity index and its spot volatility. The considered model for the trend and activity features can be written as a Stochastic Volterra Equation (SVE) with non-convolutional and non-bounded kernels as well as non-Lipschitz coefficients. We first prove the existence and uniqueness of a solution to the SVE under integrability and regularity assumptions on the two kernels and under a condition on the second kernel weighting the past squared returns which ensures that the activity feature is bounded from below by a positive constant. Then, assuming in addition that the kernel weighting the past returns is of exponential type and that an inequality relating the logarithmic derivatives of the two kernels with respect to their second variables is satisfied, we show the positivity of the volatility process which is obtained as a non-linear function of the SVE’s solution. We show numerically that the choice of an exponential kernel for the kernel weighting the past returns has little impact on the quality of model calibration compared to other choices and the inequality involving the logarithmic derivatives is satisfied by the calibrated kernels. These results extend those of Nutz and Valdevenito (2023). ...

KAN based Autoencoders for Factor Models ArXiv ID: 2408.02694 “View on arXiv” Authors: Unknown Abstract Inspired by recent advances in Kolmogorov-Arnold Networks (KANs), we introduce a novel approach to latent factor conditional asset pricing models. While previous machine learning applications in asset pricing have predominantly used Multilayer Perceptrons with ReLU activation functions to model latent factor exposures, our method introduces a KAN-based autoencoder which surpasses MLP models in both accuracy and interpretability. Our model offers enhanced flexibility in approximating exposures as nonlinear functions of asset characteristics, while simultaneously providing users with an intuitive framework for interpreting latent factors. Empirical backtesting demonstrates our model’s superior ability to explain cross-sectional risk exposures. Moreover, long-short portfolios constructed using our model’s predictions achieve higher Sharpe ratios, highlighting its practical value in investment management. ...

Investment strategies based on forecasts are (almost) useless ArXiv ID: 2408.01772 “View on arXiv” Authors: Unknown Abstract Several studies on portfolio construction reveal that sensible strategies essentially yield the same results as their nonsensical inverted counterparts; moreover, random portfolios managed by Malkiel’s dart-throwing monkey would outperform the cap-weighted benchmark index. Forecasting the future development of stock returns is an important aspect of portfolio assessment. Similar to the ostensible arbitrariness of portfolio selection methods, it is shown that there is no substantial difference between the performances of best'' and trivial’’ forecasts - even under euphemistic model assumptions on the underlying price dynamics. A certain significance of a predictor is found only in the following special case: the best linear unbiased forecast is used, the planning horizon is small, and a critical relation is not satisfied. ...

NeuralFactors: A Novel Factor Learning Approach to Generative Modeling of Equities ArXiv ID: 2408.01499 “View on arXiv” Authors: Unknown Abstract The use of machine learning for statistical modeling (and thus, generative modeling) has grown in popularity with the proliferation of time series models, text-to-image models, and especially large language models. Fundamentally, the goal of classical factor modeling is statistical modeling of stock returns, and in this work, we explore using deep generative modeling to enhance classical factor models. Prior work has explored the use of deep generative models in order to model hundreds of stocks, leading to accurate risk forecasting and alpha portfolio construction; however, that specific model does not allow for easy factor modeling interpretation in that the factor exposures cannot be deduced. In this work, we introduce NeuralFactors, a novel machine-learning based approach to factor analysis where a neural network outputs factor exposures and factor returns, trained using the same methodology as variational autoencoders. We show that this model outperforms prior approaches both in terms of log-likelihood performance and computational efficiency. Further, we show that this method is competitive to prior work in generating realistic synthetic data, covariance estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization. Finally, due to the connection to classical factor analysis, we analyze how the factors our model learns cluster together and show that the factor exposures could be used for embedding stocks. ...

A Hybrid Deep Learning Framework for Stock Price Prediction Considering the Investor Sentiment of Online Forum Enhanced by Popularity ArXiv ID: 2405.10584 “View on arXiv” Authors: Unknown Abstract Stock price prediction has always been a difficult task for forecasters. Using cutting-edge deep learning techniques, stock price prediction based on investor sentiment extracted from online forums has become feasible. We propose a novel hybrid deep learning framework for predicting stock prices. The framework leverages the XLNET model to analyze the sentiment conveyed in user posts on online forums, combines these sentiments with the post popularity factor to compute daily group sentiments, and integrates this information with stock technical indicators into an improved BiLSTM-highway model for stock price prediction. Through a series of comparative experiments involving four stocks on the Chinese stock market, it is demonstrated that the hybrid framework effectively predicts stock prices. This study reveals the necessity of analyzing investors’ textual views for stock price prediction. ...

“Microstructure Modes” – Disentangling the Joint Dynamics of Prices & Order Flow ArXiv ID: 2405.10654 “View on arXiv” Authors: Unknown Abstract Understanding the micro-dynamics of asset prices in modern electronic order books is crucial for investors and regulators. In this paper, we use an order by order Eurostoxx database spanning over 3 years to analyze the joint dynamics of prices and order flow. In order to alleviate various problems caused by high-frequency noise, we propose a double coarse-graining procedure that allows us to extract meaningful information at the minute time scale. We use Principal Component Analysis to construct “microstructure modes” that describe the most common flow/return patterns and allow one to separate them into bid-ask symmetric and bid-ask anti-symmetric. We define and calibrate a Vector Auto-Regressive (VAR) model that encodes the dynamical evolution of these modes. The parameters of the VAR model are found to be extremely stable in time, and lead to relatively high $R^2$ prediction scores, especially for symmetric liquidity modes. The VAR model becomes marginally unstable as more lags are included, reflecting the long-memory nature of flows and giving some further credence to the possibility of “endogenous liquidity crises”. Although very satisfactory on several counts, we show that our VAR framework does not account for the well known square-root law of price impact. ...