Optimal rebalancing with uncorrelated asset selection for algorithmic trading: Walk-forward QUBO scheduling via QAOA

We propose an algorithmic trading framework that addresses two core portfolio management problems simultaneously: principled asset selection and optimal rebalancing scheduling. Asset selection is performed using Ledoit–Wolf shrinkage covariance estimation with hierarchical correlation clustering to select maximally uncorrelated 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 baselines and a three-way ensemble. The central contribution is the formulation of the portfolio rebalancing schedule as a Quadratic Unconstrained Binary Optimisation (QUBO) problem, solved using the Quantum Approximate Optimisation Algorithm (QAOA) — a classical variational circuit simulation — within a walk-forward framework that eliminates lookahead bias. This recasts dynamic rebalancing as a combinatorial optimisation problem amenable to variational methods. We note that the QAOA implementation used here runs on a classical statevector simulator; no quantum hardware is employed, and the formulation is intended to demonstrate the viability of the QUBO structure and walk-forward scheduling methodology as a stepping stone toward future quantum hardware deployment. Backtests on S&P 500 data (training: 2010–2024; test: 2025, trading days) show that the GA + QAOA strategy achieves a Sharpe ratio of 0.588 and total return of 10.1%, compared with 0.575 for the strongest classical baseline (GA with 10-day periodic rebalancing). The QAOA-scheduled approach executes 8 rebalances versus 24 for the classical benchmark, corresponding to a 44.5% reduction in transaction costs. Multi-restart QAOA with 4,096 measurement shots demonstrates concentrated probability mass on high-quality rebalancing schedules, indicating stable convergence of the variational optimisation procedure. These results provide preliminary evidence that QUBO-based rebalancing scheduling can reduce turnover while maintaining competitive risk-adjusted performance relative to classical rules applied to the same portfolio. We acknowledge that a single-year out-of-sample test is an exploratory result, and multi-year rolling evaluation is identified as a primary direction for future work.