Portfolio Optimization

Denoising Complex Covariance Matrices with Hybrid ResNet and Random Matrix Theory: Cryptocurrency Portfolio Applications ArXiv ID: 2510.19130 “View on arXiv” Authors: Andres Garcia-Medina Abstract Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical interactions among assets. Motivated by this observation, we introduce a power-law covariance model to characterize collective market dynamics and propose a hybrid estimator that integrates Random Matrix Theory (RMT) with deep Residual Neural Networks (ResNets). The RMT component regularizes the eigenvalue spectrum in high-dimensional noisy settings, while the ResNet learns data-driven corrections that recover latent structural dependencies encoded in the eigenvectors. Monte Carlo simulations show that the proposed ResNet-based estimators consistently minimize both Frobenius and minimum-variance losses across a range of population covariance models. Empirical experiments on 89 cryptocurrencies over the period 2020-2025, using a training window ending at the local Bitcoin peak in November 2021 and testing through the subsequent bear market, demonstrate that a two-step estimator combining hierarchical filtering with ResNet corrections produces the most profitable and well-balanced portfolios, remaining robust across market regime shifts. Beyond finance, the proposed hybrid framework applies broadly to high-dimensional systems described by low-rank deformations of Wishart ensembles, where incorporating eigenvector information enables the detection of multiscale and hierarchical structure that is inaccessible to purely eigenvalue-based methods. ...

Robust Optimization in Causal Models and G-Causal Normalizing Flows ArXiv ID: 2510.15458 “View on arXiv” Authors: Gabriele Visentin, Patrick Cheridito Abstract In this paper, we show that interventionally robust optimization problems in causal models are continuous under the $G$-causal Wasserstein distance, but may be discontinuous under the standard Wasserstein distance. This highlights the importance of using generative models that respect the causal structure when augmenting data for such tasks. To this end, we propose a new normalizing flow architecture that satisfies a universal approximation property for causal structural models and can be efficiently trained to minimize the $G$-causal Wasserstein distance. Empirically, we demonstrate that our model outperforms standard (non-causal) generative models in data augmentation for causal regression and mean-variance portfolio optimization in causal factor models. ...

(Non-Parametric) Bootstrap Robust Optimization for Portfolios and Trading Strategies ArXiv ID: 2510.12725 “View on arXiv” Authors: Daniel Cunha Oliveira, Grover Guzman, Nick Firoozye Abstract Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances demands methods that mitigate estimation error, parameter instability, and model misspecification. Traditional approaches, including parametric, bootstrap-based, and Bayesian methods, enhance stability by relying on confidence intervals or probabilistic priors but often impose restrictive assumptions. This study introduces a non-parametric bootstrap framework for robust optimization in financial decision-making. By resampling empirical data, the framework constructs flexible, data-driven confidence intervals without assuming specific distributional forms, thus capturing uncertainty in statistical estimates, model parameters, and utility functions. Treating utility as a random variable enables percentile-based optimization, naturally suited for risk-sensitive and worst-case decision-making. The approach aligns with recent advances in robust optimization, reinforcement learning, and risk-aware control, offering a unified perspective on robustness and generalization. Empirically, the framework mitigates overfitting and selection bias in trading strategy optimization and improves generalization in portfolio allocation. Results across portfolio and time-series momentum experiments demonstrate that the proposed method delivers smoother, more stable out-of-sample performance, offering a practical, distribution-free alternative to traditional robust optimization methods. ...

Evaluating Investment Performance: The p-index and Empirical Efficient Frontier ArXiv ID: 2510.11074 “View on arXiv” Authors: Jing Li, Bowei Guo, Xinqi Xie, Kuo-Ping Chang Abstract The empirical results have shown that firstly, with one-week holding period and reinvesting, for SSE Composite Index stocks, the highest p-ratio investment strategy produces the largest annualized rate of return; and for NYSE Composite Index stocks, all the three strategies with both one-week and one-month periods generate negative returns. Secondly, with non-reinvesting, for SSE Composite Index stocks, the highest p-ratio strategy with one-week holding period yields the largest annualized rate of return; and for NYSE Composite stocks, the one-week EEF strategy produces a medium annualized return. Thirdly, under the one-week EEF investment strategy, for NYSE Composite Index stocks, the right frontier yields a higher annualized return, but for SSE Composite Index stocks, the left frontier (stocks on the empirical efficient frontier) yields a higher annualized return than the right frontier. Fourthly, for NYSE Composite Index stocks, there is a positive linear relationship between monthly return and the p-index, but no such relationship is evident for SSE Composite Index stocks. Fifthly, for NYSE Composite Index stocks, the traditional five-factor model performs poorly, and adding the p-index as a sixth factor provides incremental information. ...

Multi-Agent Regime-Conditioned Diffusion (MARCD) for CVaR-Constrained Portfolio Decisions ArXiv ID: 2510.10807 “View on arXiv” Authors: Ali Atiah Alzahrani Abstract We examine whether regime-conditioned generative scenarios combined with a convex CVaR allocator improve portfolio decisions under regime shifts. We present MARCD, a generative-to-decision framework with: (i) a Gaussian HMM to infer latent regimes; (ii) a diffusion generator that produces regime-conditioned scenarios; (iii) signal extraction via blended, shrunk moments; and (iv) a governed CVaR epigraph quadratic program. Contributions: Within the Scenario stage we introduce a tail-weighted diffusion objective that up-weights low-quantile outcomes relevant for drawdowns and a regime-expert (MoE) denoiser whose gate increases with crisis posteriors; both are evaluated end-to-end through the allocator. Under strict walk-forward on liquid multi-asset ETFs (2005-2025), MARCD exhibits stronger scenario calibration and materially smaller drawdowns: MaxDD 9.3% versus 14.1% for BL (a 34% reduction) over 2020-2025 out-of-sample. The framework provides an auditable pipeline with explicit budget, box, and turnover constraints, demonstrating the value of decision-aware generative modeling in finance. ...

Bayesian Portfolio Optimization by Predictive Synthesis ArXiv ID: 2510.07180 “View on arXiv” Authors: Masahiro Kato, Kentaro Baba, Hibiki Kaibuchi, Ryo Inokuchi Abstract Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is usually unknown to investors. Various methods have been proposed to estimate distribution information, but their accuracy greatly depends on the uncertainty of the financial markets. Due to this uncertainty, a model that could well predict the distribution information at one point in time may perform less accurately compared to another model at a different time. To solve this problem, we investigate a method for portfolio optimization based on Bayesian predictive synthesis (BPS), one of the Bayesian ensemble methods for meta-learning. We assume that investors have access to multiple asset return prediction models. By using BPS with dynamic linear models to combine these predictions, we can obtain a Bayesian predictive posterior about the mean rewards of assets that accommodate the uncertainty of the financial markets. In this study, we examine how to construct mean-variance portfolios and quantile-based portfolios based on the predicted distribution information. ...

Signed network models for portfolio optimization ArXiv ID: 2510.05377 “View on arXiv” Authors: Bibhas Adhikari Abstract In this work, we consider weighted signed network representations of financial markets derived from raw or denoised correlation matrices, and examine how negative edges can be exploited to reduce portfolio risk. We then propose a discrete optimization scheme that reduces the asset selection problem to a desired size by building a time series of signed networks based on asset returns. To benchmark our approach, we consider two standard allocation strategies: Markowitz’s mean-variance optimization and the 1/N equally weighted portfolio. Both methods are applied on the reduced universe as well as on the full universe, using two datasets: (i) the Market Champions dataset, consisting of 21 major S&P500 companies over the 2020-2024 period, and (ii) a dataset of 199 assets comprising all S&P500 constituents with stock prices available and aligned with Google’s data. Empirical results show that portfolios constructed via our signed network selection perform as good as those from classical Markowitz model and the equal-weight benchmark in most occasions. ...

Signature-Informed Transformer for Asset Allocation ArXiv ID: 2510.03129 “View on arXiv” Authors: Yoontae Hwang, Stefan Zohren Abstract Robust asset allocation is a key challenge in quantitative finance, where deep-learning forecasters often fail due to objective mismatch and error amplification. We introduce the Signature-Informed Transformer (SIT), a novel framework that learns end-to-end allocation policies by directly optimizing a risk-aware financial objective. SIT’s core innovations include path signatures for a rich geometric representation of asset dynamics and a signature-augmented attention mechanism embedding financial inductive biases, like lead-lag effects, into the model. Evaluated on daily S&P 100 equity data, SIT decisively outperforms traditional and deep-learning baselines, especially when compared to predict-then-optimize models. These results indicate that portfolio-aware objectives and geometry-aware inductive biases are essential for risk-aware capital allocation in machine-learning systems. The code is available at: https://github.com/Yoontae6719/Signature-Informed-Transformer-For-Asset-Allocation ...

From Headlines to Holdings: Deep Learning for Smarter Portfolio Decisions ArXiv ID: 2509.24144 “View on arXiv” Authors: Yun Lin, Jiawei Lou, Jinghe Zhang Abstract Deep learning offers new tools for portfolio optimization. We present an end-to-end framework that directly learns portfolio weights by combining Long Short-Term Memory (LSTM) networks to model temporal patterns, Graph Attention Networks (GAT) to capture evolving inter-stock relationships, and sentiment analysis of financial news to reflect market psychology. Unlike prior approaches, our model unifies these elements in a single pipeline that produces daily allocations. It avoids the traditional two-step process of forecasting asset returns and then applying mean–variance optimization (MVO), a sequence that can introduce instability. We evaluate the framework on nine U.S. stocks spanning six sectors, chosen to balance sector diversity and news coverage. In this setting, the model delivers higher cumulative returns and Sharpe ratios than equal-weighted and CAPM-based MVO benchmarks. Although the stock universe is limited, the results underscore the value of integrating price, relational, and sentiment signals for portfolio management and suggest promising directions for scaling the approach to larger, more diverse asset sets. ...

Conditional Risk Minimization with Side Information: A Tractable, Universal Optimal Transport Framework ArXiv ID: 2509.23128 “View on arXiv” Authors: Xinqiao Xie, Jonathan Yu-Meng Li Abstract Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable conditional distributions from limited data is notoriously difficult, motivating a series of optimal-transport-based proposals that address this uncertainty in a distributionally robust manner. Yet these approaches remain fragmented, each constrained by its own limitations: some rely on point estimates or restrictive structural assumptions, others apply only to narrow classes of risk measures, and their structural connections are unclear. We introduce a universal framework for distributionally robust conditional risk minimization, built on a novel union-ball formulation in optimal transport. This framework offers three key advantages: interpretability, by subsuming existing methods as special cases and revealing their deep structural links; tractability, by yielding convex reformulations for virtually all major risk functionals studied in the literature; and scalability, by supporting cutting-plane algorithms for large-scale conditional risk problems. Applications to portfolio optimization with rank-dependent expected utility highlight the practical effectiveness of the framework, with conditional models converging to optimal solutions where unconditional ones clearly do not. ...