Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks

2025-07-05

AI Summary

Traditional mean–variance portfolio optimization struggles to capture nonlinear dependencies among assets and incurs high turnover, escalating transaction costs. Method: We propose a quantum stochastic walk (QSW)-based portfolio optimization framework: assets are modeled as nodes in a weighted graph, edge weights are encoded via a covariance kernel, and nonlinear asset weights are derived from the stationary distribution of the QSW, yielding a hybrid quantum–classical optimization model. Contribution/Results: Our approach explicitly models higher-order dependencies by relaxing the quadratic-form assumption inherent in classical models, while endogenously suppressing turnover. Empirical evaluation on S&P 500 constituents demonstrates a 15% improvement in annualized Sharpe ratio, a reduction in median turnover from 351% to 36% (a 90% decline), and strict compliance with UCITS regulatory constraints.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Financial markets are noisy yet contain a latent graph-theoretic structure that can be exploited for superior risk-adjusted returns. We propose a quantum stochastic walk (QSW) optimizer that embeds assets in a weighted graph: nodes represent securities while edges encode the return-covariance kernel. Portfolio weights are derived from the walk's stationary distribution. Three empirical studies support the approach. (i) For the top 100 S&P 500 constituents over 2016-2024, six scenario portfolios calibrated on 1- and 2-year windows lift the out-of-sample Sharpe ratio by up to 27% while cutting annual turnover from 480% (mean-variance) to 2-90%. (ii) A $5^{4}=625$-point grid search identifies a robust sweet spot, $α,λlesssim0.5$ and $ωin[0.2,0.4]$, that delivers Sharpe $approx0.97$ at $le 5%$ turnover and Herfindahl-Hirschman index $sim0.01$. (iii) Repeating the full grid on 50 random 100-stock subsets of the S&P 500 adds 31,350 back-tests: the best-per-draw QSW beats re-optimised mean-variance on Sharpe in 54% of cases and always wins on trading efficiency, with median turnover 36% versus 351%. Overall, QSW raises the annualized Sharpe ratio by 15% and cuts turnover by 90% relative to classical optimisation, all while respecting the UCITS 5/10/40 rule. These results show that hybrid quantum-classical dynamics can uncover non-linear dependencies overlooked by quadratic models and offer a practical, low-cost weighting engine for themed ETFs and other systematic mandates.

Problem

• Optimizing portfolios using quantum stochastic walks on financial networks
• Improving risk-adjusted returns by exploiting latent graph structures
• Reducing turnover and enhancing Sharpe ratio compared to classical methods

Innovation

• Quantum stochastic walk optimizes portfolio weights
• Graph nodes represent securities, edges encode covariance
• Hybrid quantum-classical dynamics improve Sharpe ratio