Classical mean-variance optimization is powerful in theory but fragile in practice, often producing highly concentrated, high-turnover portfolios. Naive equal-weight (1/N) portfolios are more robust but largely ignore cross-sectional information. We propose a quantum stochastic walk (QSW) framework that embeds assets in a weighted graph and derives portfolio weights from the stationary distribution of a hybrid quantum-classical walk. The resulting allocations behave as a “smart 1/N” portfolio: structurally close to equal-weight, but with small, data-driven tilts and a controllable level of trading. On recent S&P 500 universes, QSW portfolios match the diversification and stability of 1/N while delivering higher risk-adjusted returns than both mean-variance and naive benchmarks. A comprehensive hyper-parameter grid search shows that this behavior is structural rather than the result of fine-tuning and yields simple design rules for practitioners. A 34-year, multi-universe robustness study with rolling re-optimization further demonstrates that the QSW optimizer preserves these advantages across market regimes. Overall, the QSW framework improves risk-adjusted performance while maintaining strong diversification and moderate turnover.
Classical mean-variance optimization is powerful in theory but fragile in practice, often producing highly concentrated, high-turnover portfolios. Naive equal-weight (1/N) portfolios are more robust but largely ignore cross-sectional information. We propose a quantum stochastic walk (QSW) framework that embeds assets in a weighted graph and derives portfolio weights from the stationary distribution of a hybrid quantum-classical walk. The resulting allocations behave as a “smart 1/N” portfolio: structurally close to equal-weight, but with small, data-driven tilts and a controllable level of trading. On recent S&P 500 universes, QSW portfolios match the diversification and stability of 1/N while delivering higher risk-adjusted returns than both mean-variance and naive benchmarks. A comprehensive hyper-parameter grid search shows that this behavior is structural rather than the result of fine-tuning and yields simple design rules for practitioners. A 34-year, multi-universe robustness study with rolling re-optimization further demonstrates that the QSW optimizer preserves these advantages across market regimes. Overall, the QSW framework improves risk-adjusted performance while maintaining strong diversification and moderate turnover.
Abstract Financial markets are noisy yet contain a latent graph–theoretic structure that can be exploited for superior risk-adjusted returns. We propose a \emph{quantum-stochastic-walk} (QSW) optimizer that embeds assets in a weighted graph—nodes are securities, edges encode the return–covariance kernel—and derives portfolio weights from the stationary distribution of the walk. Three empirical studies support the method. (i)~On the \textbf{Top-100 S\&P constituents} (2016–2024) six scenario portfolios fitted on 1- and 2-year windows lift the out-of-sample Sharpe ratio by up to \textbf{+27\,\%} while slashing annual turnover from 480% (mean–variance) to 2–90%. (ii)~A \mbox{625} grid search isolates a robust sweet-spot—α,λ≲0.5, ω∈[0.2,0.4]—that delivers Sharpe ≈0.97 at ≤5% turnover and Herfindahl–Hirschman index(HHI) ∼0.01. (iii)~Repeating the full grid on \textbf{50 random 100-stock subsets} of the S\&P\,500 generates 31,350 additional back-tests: the best-per-draw QSW beats re-optimized mean–variance on Sharpe in 54\,\% of samples and \emph{always} wins on trading efficiency, with median turnover \textbf{36\,\%} versus \textbf{351\,\%}. Overall, QSW raises the annualized Sharpe ratio by \textbf{15\,\%} and cuts average turnover by \textbf{90\,\%} relative to classical optimization, all while remaining comfortably within UCITS 5/10/40 rule. The findings demonstrate that hybrid quantum–classical dynamics can uncover non-linear dependencies overlooked by quadratic models, offering a practical low-cost weighting engine for themed ETFs and other systematic mandates.
Large-scale portfolio optimization is hard because investors must balance risk, return, diversification, and liquidity across many assets with complex constraints. Classical methods, such as quadratic programming or metaheuristics, often become slow or less effective as the number of assets and factors grows. In this project, I explore the use of the Quantum Approximate Optimization Algorithm (QAOA) as a hybrid quantum–classical approach to portfolio selection. The framework encodes portfolio decisions as qubits and represents financial objectives—such as mean–variance trade-offs or risk-adjusted return—inside a parameterized quantum circuit. Classical optimization is then used to tune the circuit parameters so that the quantum system converges toward low-risk, high-return portfolios. Multi-factor constraints, including sector limits, liquidity rules, ESG scores, and macroeconomic risk factors, are integrated into the Hamiltonian as penalty terms. A qualitative comparison with classical solvers (e.g., mixed-integer programming and simulated annealing) suggests that QAOA can scale more gracefully in high-dimensional settings and handle complex constraint structures. Overall, the project shows how quantum hybrid optimization could support future portfolio management, linking theoretical quantum algorithms with practical, sustainability-aware investment strategies.
Portfolio optimization under conditions of risk and market uncertainty remains a foundational challenge in financial economics and investment management. Classical optimization frameworks, including mean–variance models and stochastic programming approaches, often struggle with high-dimensional asset universes, nonlinear correlations, and dynamic market regimes. This paper examines quantum computing approaches to portfolio optimization under risk and market uncertainty, focusing on hybrid quantum–classical algorithms designed to enhance combinatorial optimization and probabilistic modeling. By integrating quantum annealing, variational quantum circuits, and quantum-enhanced sampling techniques with classical financial analytics, the study evaluates their potential to improve computational efficiency and scenario sensitivity. The analysis considers both theoretical advantages and practical limitations within the Noisy Intermediate-Scale Quantum (NISQ) era. The findings suggest that quantum-assisted optimization may complement traditional portfolio models by expanding feasible solution spaces and improving robustness under uncertainty, thereby contributing to more adaptive and resilient investment strategies.
The increasing complexity of financial markets has heightened the demand for advanced computational methods capable of optimizing portfolios under multi-dimensional constraints involving risk, return, diversification, and liquidity. Traditional optimization frameworks, such as mean-variance analysis and heuristic meta-optimization, are limited by their scalability and sensitivity to non-convex, high-dimensional data structures. This study explores the application of quantum algorithms to portfolio optimization, demonstrating how Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing, and Variational Quantum Eigensolver (VQE) can address computational bottlenecks inherent in classical approaches. Quantum computation offers the potential to encode complex financial systems as Hamiltonian functions, allowing parallel exploration of vast solution spaces through superposition and entanglement. This enables faster convergence toward optimal portfolio allocations while simultaneously accounting for multi-factor correlations and dynamic market conditions. The research further investigates the role of hybrid quantum–classical optimization pipelines, in which quantum solvers perform core optimization tasks while classical systems manage data preprocessing and constraint validation. Empirical modeling and simulation indicate that quantum-based approaches can outperform conventional methods in risk-adjusted return optimization, efficient frontier computation, and real-time portfolio rebalancing. By bridging the gap between quantum computing and financial engineering, this study contributes to the development of next-generation financial analytics systems, aligning with the broader goal of achieving more adaptive, transparent, and data-resilient financial decision-making.
Portfolio diversification is one of the most effective ways to minimize investment risk. Individuals and fund managers aim to create a portfolio of assets that not only have high returns but are also uncorrelated. This goal can be achieved by comparing the historical performance, fundamentals, predictions, news sentiment, and many other parameters that can affect the portfolio's value. One of the most well-known approaches to manage/optimize portfolios is the well-known mean-variance (Markowitz) portfolio. The algorithm's inputs are the expected returns and risks (volatility), and its output is the optimized weights for each asset in the target portfolio. Simplified unrealistic assumptions and constraints were used in its original version preventing its use in practical cases. One solution to improve its usability is by altering the parameters and constraints to match investment goals and requirements. This paper introduces PortFawn, an open-source Python library to create and backtest mean-variance portfolios. PortFawn provides simple-to-use APIs to create and evaluate mean-variance optimization algorithms using classical computing (real-valued asset weights) as well as quantum annealing computing (binary asset weights). This tool has many parameters to customize the target portfolios according to the investment goals. The paper introduces the background and limitations of the mean-variance portfolio optimization algorithm, its architecture, and a description of the functionalities of PortFawn. We also show how one can use this tool in practice using a simple investment scenario.
This paper investigates and compares quantum and classical investment strategies for portfolio construction under realistic trading and allocation constraints. The study considers a multi-period portfolio re-balancing setting in which asset weights are subject to lower and upper bounds, class-level exposure restrictions, and turnover limitations. On the quantum side, the portfolio selection problem is reformulated as a quadratic unconstrained binary optimization (QUBO) model through a finite binary encoding of asset weights, and subsequently embedded into a constrained quadratic model (CQM) solved by a hybrid quantum-classical optimization workflow. On the classical side, benchmark allocation strategies are introduced to provide an economically meaningful reference for performance assessment. The proposed framework jointly evaluates portfolio efficiency from two complementary perspectives: business performance, measured through return, volatility, and a measure of the trade-off between them, the Sharpe ratio; and computational performance, assessed through solver structure, constraint handling, and hardware execution characteristics. The resulting comparison provides a rigorous basis for understanding the practical role of quantum annealing in constrained portfolio optimization, while clarifying both its modeling advantages and its current implementation limitations relative to established classical approaches.