用量子算法优化股票组合再平衡，降低交易成本同时保持收益。
Quantum-Assisted Optimal Rebalancing with Uncorrelated Asset Selection for Algorithmic Trading Walk-Forward QUBO Scheduling via QAOA
- 将再平衡调度建模为量子可解的QUBO问题，结合经典遗传算法加速优化。
- 实测年化夏普比0.588，交易次数减少44.5%，成本显著降低。
- 适合关注量子计算金融应用、低频高精度交易策略的研究者。
我们提出一种混合经典-量子框架用于投资组合构建与再平衡。通过Ledoit-Wolf收缩协方差估计结合层级相关性聚类，从标普500中无幸存者偏差地选出n=10个不相关的股票。投资组合权重由熵正则化遗传算法（GA）在GPU上加速优化，并对比闭式最小方差与等权基准。核心贡献是将再平衡调度建模为无约束二次二值优化（QUBO）问题，采用量子近似优化算法（QAOA）在行走前向框架下求解，消除前瞻偏差。基于标普500数据回测（训练：2010–2024；样本外测试：2025，n=249个交易日），该方法实现夏普比0.588，总收益10.1%，略优于最强经典基线（10天周期再平衡，夏普比0.575），且仅执行8次再平衡，较24次减少44.5%交易成本。多重启QAOA（每轮4096次测量）显示高质量解的概率集中，表明变分过程稳定收敛。结果表明，混合架构可在维持风险调整后收益的同时降低换手率，为近期量子优化在金融领域的应用提供结构化验证平台。
原文摘要 · Abstract (English)
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.
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