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

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.

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

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.
Paper Structure (47 sections, 15 equations, 3 figures, 5 tables, 1 algorithm)

This paper contains 47 sections, 15 equations, 3 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Classical Portfolio Optimisation
  4. Evolutionary and Machine Learning Approaches
  5. Quantum Portfolio Optimisation
  6. Methodology
  7. Problem Statement
  8. Data and Universe Construction
  9. Asset Selection via Hierarchical Clustering
  10. Ledoit-Wolf Shrinkage Covariance.
  11. Angular Distance and Hierarchical Clustering.
  12. Cluster Representative Selection.
  13. Weight Optimisation
  14. Entropy-Regularised Genetic Algorithm.
  15. Minimum Variance Weights.
  16. ...and 32 more sections

Figures (3)

  • Figure 1: Asset selection results. Left: Ledoit-Wolf shrinkage correlation matrix of the 10 selected stocks. Off-diagonal values range from 0.07 (CHD--TPL) to 0.62 (CTAS--AMP), confirming low inter-asset correlation. Right: Annualised Sharpe ratios (log returns) on the training period (2010--2024). All selected stocks achieve Sharpe $> 0.6$.
  • Figure 2: Backtest results (test period: Jan--Dec 2025). Top left: Cumulative portfolio value. Classical strategies (blue dashed) vs. QAOA strategies (orange solid) vs. S&P 500 (black). GA + QAOA (bright orange) achieves the highest terminal value among all quantum and classical strategies. Top right: Drawdown profiles. QAOA strategies maintain tighter drawdown control than periodic rebalancing. Bottom left: Sharpe ratio comparison (horizontal bar chart). GA + QAOA achieves the highest Sharpe (0.588), highlighted in gold. Bottom right: Normalised QUBO matrix (GA weights, walk-forward window 1), illustrating the structured cost landscape solved by QAOA.
  • Figure 3: Left: QAOA measurement bitstring distribution for GA + QAOA (top 20 bitstrings, 4,096 shots). The top bitstring 11000010 accounts for $>7\%$ of shots, indicating successful QAOA convergence. Right: Weight comparison across all four portfolio methods. GA concentrates on LLY and COST; MinVar distributes more evenly; Ensemble averages all three.

Theorems & Definitions (1)

  • Definition 1: Rebalancing Schedule Problem