Portfolio Optimization

Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach ArXiv ID: 2508.10776 “View on arXiv” Authors: Juchan Kim, Inwoo Tae, Yongjae Lee Abstract Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio construction. However, most conventional statistical estimators and machine learning algorithms determine these parameters by minimizing mean-squared error (MSE), a criterion that can yield suboptimal investment decisions. In this paper, we adopt decision-focused learning (DFL) - an approach that directly optimizes decision quality rather than prediction error such as MSE - to derive the global minimum-variance portfolio (GMVP). Specifically, we theoretically derive the gradient of decision loss using the analytic solution of GMVP and its properties regarding the principal components of itself. Through extensive empirical evaluation, we show that prediction-focused estimation methods may fail to produce optimal allocations in practice, whereas DFL-based methods consistently deliver superior decision performance. Furthermore, we provide a comprehensive analysis of DFL’s mechanism in GMVP construction, focusing on its volatility reduction capability, decision-driving features, and estimation characteristics. ...

Comparing Normalization Methods for Portfolio Optimization with Reinforcement Learning ArXiv ID: 2508.03910 “View on arXiv” Authors: Caio de Souza Barbosa Costa, Anna Helena Reali Costa Abstract Recently, reinforcement learning has achieved remarkable results in various domains, including robotics, games, natural language processing, and finance. In the financial domain, this approach has been applied to tasks such as portfolio optimization, where an agent continuously adjusts the allocation of assets within a financial portfolio to maximize profit. Numerous studies have introduced new simulation environments, neural network architectures, and training algorithms for this purpose. Among these, a domain-specific policy gradient algorithm has gained significant attention in the research community for being lightweight, fast, and for outperforming other approaches. However, recent studies have shown that this algorithm can yield inconsistent results and underperform, especially when the portfolio does not consist of cryptocurrencies. One possible explanation for this issue is that the commonly used state normalization method may cause the agent to lose critical information about the true value of the assets being traded. This paper explores this hypothesis by evaluating two of the most widely used normalization methods across three different markets (IBOVESPA, NYSE, and cryptocurrencies) and comparing them with the standard practice of normalizing data before training. The results indicate that, in this specific domain, the state normalization can indeed degrade the agent’s performance. ...

Momentum-integrated Multi-task Stock Recommendation with Converge-based Optimization ArXiv ID: 2509.10461 “View on arXiv” Authors: Hao Wang, Jingshu Peng, Yanyan Shen, Xujia Li, Lei Chen Abstract Stock recommendation is critical in Fintech applications, which use price series and alternative information to estimate future stock performance. Although deep learning models are prevalent in stock recommendation systems, traditional time-series forecasting training often fails to capture stock trends and rankings simultaneously, which are essential consideration factors for investors. To tackle this issue, we introduce a Multi-Task Learning (MTL) framework for stock recommendation, \textbf{“M”}omentum-\textbf{“i”}ntegrated \textbf{“M”}ulti-task \textbf{“Stoc”}k \textbf{“R”}ecommendation with Converge-based Optimization (\textbf{“MiM-StocR”}). To improve the model’s ability to capture short-term trends, we novelly invoke a momentum line indicator in model training. To prioritize top-performing stocks and optimize investment allocation, we propose a list-wise ranking loss function called Adaptive-k ApproxNDCG. Moreover, due to the volatility and uncertainty of the stock market, existing MTL frameworks face overfitting issues when applied to stock time series. To mitigate this issue, we introduce the Converge-based Quad-Balancing (CQB) method. We conducted extensive experiments on three stock benchmarks: SEE50, CSI 100, and CSI 300. MiM-StocR outperforms state-of-the-art MTL baselines across both ranking and profitable evaluations. ...

Is Causality Necessary for Efficient Portfolios? A Computational Perspective on Predictive Validity and Model Misspecification ArXiv ID: 2507.23138 “View on arXiv” Authors: Alejandro Rodriguez Dominguez Abstract A recent line of research has argued that causal factor models are necessary for portfolio optimization, claiming that structurally misspecified models inevitably produce inverted signals and nonviable frontiers. This paper challenges that view. We show, through theoretical analysis, simulation counterexamples, and empirical validation, that predictive models can remain operationally valid even when structurally incorrect. Our contributions are fourfold. First, we distinguish between directional agreement, ranking, and calibration, proving that sign alignment alone does not ensure efficiency when signals are mis-scaled. Second, we establish that structurally misspecified signals can still yield convex and viable efficient frontiers provided they maintain directional alignment with true returns. Third, we derive and empirically confirm a quantitative scaling law that shows how Sharpe ratios contract smoothly with declining alignment, thereby clarifying the role of calibration within the efficient set. Fourth, we validate these results on real financial data, demonstrating that predictive signals, despite structural imperfections, can support coherent frontiers. These findings refine the debate on causality in portfolio modeling. While causal inference remains valuable for interpretability and risk attribution, it is not a prerequisite for optimization efficiency. Ultimately, what matters is the directional fidelity and calibration of predictive signals in relation to their intended use in robust portfolio construction. ...

HARLF: Hierarchical Reinforcement Learning and Lightweight LLM-Driven Sentiment Integration for Financial Portfolio Optimization ArXiv ID: 2507.18560 “View on arXiv” Authors: Benjamin Coriat, Eric Benhamou Abstract This paper presents a novel hierarchical framework for portfolio optimization, integrating lightweight Large Language Models (LLMs) with Deep Reinforcement Learning (DRL) to combine sentiment signals from financial news with traditional market indicators. Our three-tier architecture employs base RL agents to process hybrid data, meta-agents to aggregate their decisions, and a super-agent to merge decisions based on market data and sentiment analysis. Evaluated on data from 2018 to 2024, after training on 2000-2017, the framework achieves a 26% annualized return and a Sharpe ratio of 1.2, outperforming equal-weighted and S&P 500 benchmarks. Key contributions include scalable cross-modal integration, a hierarchical RL structure for enhanced stability, and open-source reproducibility. ...

Novel Risk Measures for Portfolio Optimization Using Equal-Correlation Portfolio Strategy ArXiv ID: 2508.03704 “View on arXiv” Authors: Biswarup Chakraborty Abstract Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration in a few securities. In this paper, we introduce novel risk measures grounded in the equal-correlation portfolio strategy, aiming to construct portfolios where each asset maintains an equal correlation with the overall portfolio return. We formulate a mathematical optimization framework that explicitly controls portfolio-wide correlation while preserving desirable risk-return trade-offs. The proposed models are empirically validated using historical stock market data. Our findings show that portfolios constructed via this approach demonstrate superior risk diversification and more stable returns under diverse market conditions. This methodology offers a compelling alternative to conventional diversification techniques and holds practical relevance for institutional investors, asset managers, and quantitative trading strategies. ...

Building crypto portfolios with agentic AI ArXiv ID: 2507.20468 “View on arXiv” Authors: Antonino Castelli, Paolo Giudici, Alessandro Piergallini Abstract The rapid growth of crypto markets has opened new opportunities for investors, but at the same time exposed them to high volatility. To address the challenge of managing dynamic portfolios in such an environment, this paper presents a practical application of a multi-agent system designed to autonomously construct and evaluate crypto-asset allocations. Using data on daily frequencies of the ten most capitalized cryptocurrencies from 2020 to 2025, we compare two automated investment strategies. These are a static equal weighting strategy and a rolling-window optimization strategy, both implemented to maximize the evaluation metrics of the Modern Portfolio Theory (MPT), such as Expected Return, Sharpe and Sortino ratios, while minimizing volatility. Each step of the process is handled by dedicated agents, integrated through a collaborative architecture in Crew AI. The results show that the dynamic optimization strategy achieves significantly better performance in terms of risk-adjusted returns, both in-sample and out-of-sample. This highlights the benefits of adaptive techniques in portfolio management, particularly in volatile markets such as cryptocurrency markets. The following methodology proposed also demonstrates how multi-agent systems can provide scalable, auditable, and flexible solutions in financial automation. ...

Large-scale portfolio optimization with variational neural annealing ArXiv ID: 2507.07159 “View on arXiv” Authors: Nishan Ranabhat, Behnam Javanparast, David Goerz, Estelle Inack Abstract Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a mixed-integer nonlinear program that current mixed-integer optimizers often struggle to solve. We propose mapping this problem onto a classical Ising-like Hamiltonian and solving it with Variational Neural Annealing (VNA), via its classical formulation implemented using autoregressive neural networks. We demonstrate that VNA can identify near-optimal solutions for portfolios comprising more than 2,000 assets and yields performance comparable to that of state-of-the-art optimizers, such as Mosek, while exhibiting faster convergence on hard instances. Finally, we present a dynamical finite-size scaling analysis applied to the S&P 500, Russell 1000, and Russell 3000 indices, revealing universal behavior and polynomial annealing time scaling of the VNA algorithm on portfolio optimization problems. ...

Behavioral Probability Weighting and Portfolio Optimization under Semi-Heavy Tails ArXiv ID: 2507.04208 “View on arXiv” Authors: Ayush Jha, Abootaleb Shirvani, Ali M. Jaffri, Svetlozar T. Rachev, Frank J. Fabozzi Abstract This paper develops a unified framework that integrates behavioral distortions into rational portfolio optimization by extracting implied probability weighting functions (PWFs) from optimal portfolios modeled under Gaussian and Normal-Inverse-Gaussian (NIG) return distributions. Using DJIA constituents, we construct mean-CVaR99 frontiers, alongwith Sharpe- and CVaR-maximizing portfolios, and estimate PWFs that capture nonlinear beliefs consistent with fear and greed. We show that increasing tail fatness amplifies these distortions and that shifts in the term structure of risk-free rates alter their curvature. The results highlight the importance of jointly modeling return asymmetry and belief distortions in portfolio risk management and capital allocation under extreme-risk environments. ...

Portfolio optimization in incomplete markets and price constraints determined by maximum entropy in the mean ArXiv ID: 2507.07053 “View on arXiv” Authors: Argimiro Arratia, Henryk Gzyl Abstract A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted expected value of the asset’s price under this measure. But if the market is incomplete, the risk neutral measure is not unique, and there is a range of possible prices for each asset, which can be identified with bid-ask ranges. We present in this paper an effective method to determine the current prices of a collection of assets in incomplete markets, and such that these prices comply with the cost constraints for a portfolio optimization problem. Our workhorse is the method of maximum entropy in the mean to adjust a distortion function from bid-ask market data. This distortion function plays the role of a risk neutral measure, which is used to price the assets, and the distorted probability that it determines reproduces bid-ask market values. We carry out numerical examples to study the effect on portfolio returns of the computation of prices of the assets conforming the portfolio with the proposed methodology. ...