Quantum-Assisted Optimal Rebalancing with Uncorrelated Asset Selection for Algorithmic Trading Walk-Forward QUBO Scheduling via QAOA

Paper: arXiv 2603.16904

Authors: Abraham Itzhak Weinberg

Abstract

We present a hybrid classical-quantum framework for portfolio construction and rebalancing. Asset selection is performed using Ledoit-Wolf shrinkage covariance estimation combined with hierarchical correlation clustering to extract n = 10 decorrelated stocks from the S&P 500 universe without survivorship bias. Portfolio weights are optimised via an entropy-regularised Genetic Algorithm (GA) accelerated on GPU, alongside closed-form minimum-variance and equal-weight benchmarks. Our primary contribution is the formulation of the portfolio rebalancing schedule as a Quadratic Unconstrained Binary Optimisation (QUBO) problem. The resulting combinatorial optimisation task is solved using the Quantum Approximate Optimisation Algorithm (QAOA) within a walk-forward framework designed to eliminate lookahead bias. This approach recasts dynamic rebalancing as a structured binary scheduling problem amenable to variational quantum methods. Backtests on S&P 500 data (training: 2010-2024; out-of-sample test: 2025, n = 249 trading days) show that the GA + QAOA strategy attains a Sharpe ratio of 0.588 and total return of 10.1%, modestly outperforming the strongest classical baseline (GA with 10-day periodic rebalancing, Sharpe 0.575) while executing 8 rebalances versus 24, corresponding to a 44.5% reduction in transaction costs. Multi-restart QAOA (4096 measurement shots per run) exhibits concentrated probability mass on high-quality schedules, indicating stable convergence of the variational procedure. These findings suggest that hybrid classical-quantum architectures can reduce turnover in portfolio rebalancing while preserving competitive risk-adjusted performance, providing a structured testbed for near-term quantum optimisation in financial applications.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a highly novel integration of variational quantum optimization (QAOA) for portfolio rebalancing scheduling, backed by solid classical baselines. Empirical evaluation is rigorous, using a walk-forward structure on S&P 500 data and explicit transaction cost accounting.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimize portfolio rebalancing using hybrid classical-quantum algorithms to reduce turnover"] --> B["Data Input: S&P 500 Equity Universe<br/>(Train: 2010-2024, Test: 2025)"]
    
    B --> C["Asset Selection: Ledoit-Wolf Covariance & Hierarchical Clustering<br/>(Selects n = 10 decorrelated stocks)"]
    
    C --> D["Weight Optimization: GPU-Accelerated Entropy-Regularized Genetic Algorithm"]
    
    D --> E["Rebalancing Schedule Formulation: QUBO Problem solved via Multi-Restart QAOA<br/>(Walk-Forward Framework)"]
    
    E --> F["Outcomes & Key Findings:<br/>• Sharpe Ratio: 0.588 (vs 0.575 classical baseline)<br/>• 44.5% Reduction in Transaction Costs (8 vs 24 rebalances)<br/>• Total Out-of-Sample Return: 10.1%"]

Cited References (24)

1. Markowitz’s" portfolio selection": A fifty-year retrospective (2002)
2. Portfolio selection: efficient diversification of investments (2008)
3. Mutual fund performance (1966)
4. Dynamic strategies for asset allocation (1988)
5. A well-conditioned estimator for large-dimensional covariance matrices (2004)
6. A quantum approximate optimization algorithm (2014) — link
7. Quantum computing in the NISQ era and beyond (2018)
8. Dynamic portfolio optimization with real datasets using quantum processors and quantum-inspired tensor networks (2022)

0 of 24 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.