q-fin.PM

arXiv:2501.12074v1 Announce Type: new Abstract: Optimizing portfolio performance is a fundamental challenge in financial modeling, requiring the integration of advanced clustering techniques and data-driven optimization strategies. This paper introduces a comparative backtesting approach that combines clustering-based portfolio segmentation and Sharpe ratio-based optimization to enhance investment decision-making. First, we segment a diverse set of financial assets into clusters based on their historical log-returns using K-Means clustering. This segmentation enables the grouping of assets with similar return characteristics, facilitating targeted portfolio construction. Next, for each cluster, we apply a Sharpe ratio-based optimization model to derive optimal weights that maximize risk-adjusted returns. Unlike traditional mean-variance optimization, this approach directly incorporates the trade-off between returns and volatility, resulting in a more balanced allocation of resources within each cluster. The proposed framework is evaluated through a backtesting study using historical data spanning multiple asset classes. Optimized portfolios for each cluster are constructed and their cumulative returns are compared over time against a traditional equal-weighted benchmark portfolio.

arXiv:2501.06701v1 Announce Type: cross Abstract: This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often high-dimensional. The results demonstrate that a dynamic strategy, which forms a portfolio based on perfect knowledge of the dependence structure and full market information over time, may not grow at a higher rate infinitely often than a constant strategy, which remains invariant over time. Specifically, if the market is stationary, implying that the dependence structure is statistically stable, the growth rate of an optimal dynamic strategy, utilizing the maximum capacity of the entire market information, almost surely decays over time into an equilibrium state, asymptotically converging to the growth rate of a constant strategy. Technically, this work reassesses the common belief that a constant strategy only attains the optimal limiting growth rate of dynamic strategies when the market process is identically and independently distributed. By analyzing the dynamic log-optimal portfolio strategy as the optimal benchmark in a stationary market with side information, we show that a random optimal constant strategy almost surely exists, even when a limiting growth rate for the dynamic strategy does not. Consequently, two approaches to learning algorithms for portfolio construction are discussed, demonstrating the safety of removing side information from the learning process while still guaranteeing an asymptotic growth rate comparable to that of the optimal dynamic strategy.

arXiv:2501.01763v1 Announce Type: cross Abstract: Following an analysis of existing AI-related exchange-traded funds (ETFs), we reveal the selection criteria for determining which stocks qualify as AI-related are often opaque and rely on vague phrases and subjective judgments. This paper proposes a new, objective, data-driven approach using natural language processing (NLP) techniques to classify AI stocks by analyzing annual 10-K filings from 3,395 NASDAQ-listed firms between 2011 and 2023. This analysis quantifies each company's engagement with AI through binary indicators and weighted AI scores based on the frequency and context of AI-related terms. Using these metrics, we construct four AI stock indices-the Equally Weighted AI Index (AII), the Size-Weighted AI Index (SAII), and two Time-Discounted AI Indices (TAII05 and TAII5X)-offering different perspectives on AI investment. We validate our methodology through an event study on the launch of OpenAI's ChatGPT, demonstrating that companies with higher AI engagement saw significantly greater positive abnormal returns, with analyses supporting the predictive power of our AI measures. Our indices perform on par with or surpass 14 existing AI-themed ETFs and the Nasdaq Composite Index in risk-return profiles, market responsiveness, and overall performance, achieving higher average daily returns and risk-adjusted metrics without increased volatility. These results suggest our NLP-based approach offers a reliable, market-responsive, and cost-effective alternative to existing AI-related ETF products. Our innovative methodology can also guide investors, asset managers, and policymakers in using corporate data to construct other thematic portfolios, contributing to a more transparent, data-driven, and competitive approach.

arXiv:2412.16175v1 Announce Type: cross Abstract: We study continuous-time mean--variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for diffusion processes, we present a general data-driven RL algorithm that learns the pre-committed investment strategy directly without attempting to learn or estimate the market coefficients. For multi-stock Black--Scholes markets without factors, we further devise a baseline algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of Sharpe ratio. For performance enhancement and practical implementation, we modify the baseline algorithm into four variants, and carry out an extensive empirical study to compare their performance, in terms of a host of common metrics, with a large number of widely used portfolio allocation strategies on S\&P 500 constituents. The results demonstrate that the continuous-time RL strategies are consistently among the best especially in a volatile bear market, and decisively outperform the model-based continuous-time counterparts by significant margins.