結合量子隨機走路與 Black-Litterman 模型之量子啟發式投資組合配置方法

Abstract

隨著金融市場日益複雜，傳統的投資組合配置方法如現代投資組合理論及黑李特曼模型廣泛應用於資產配置領域。然而，這些方法大多仰賴明確的數值最適化程序，對輸入的精確性高度敏感，缺乏對資訊結構的深入表達能力。因此，本研究並非旨在解決既有方法的缺陷，而是嘗試結合量子啟發式演算法與圖論方法，探索投資組合配置的全新可能性。我們首先透過黑李特曼模型計算每支資產的後驗期望報酬與後驗相關性矩陣，並基於該資訊建構一張加權有向圖，將每支股票視為圖上的節點。接著應用基於量子隨機行走的量子 pagerank 方法，將資產的重要性視為其穩態機率分佈，並據此分配投資權重。為評估本方法的效果，本研究利用 S&P 100 指數成分股從 2016 年至 2024 年的歷史資料進行滾動視窗回測，並與傳統的現代投資組合理論模型與黑李特曼模型進行比較。實驗結果顯示，本研究提出的量子隨機行走方法在累計收益、夏普比率等指標上均優於基準模型。透過調整量子隨機行走中用以平衡量子同調演化與古典隨機過程的混合參數 ω，我們發現模型在 ω = 0.9 與 ω = 0.7 的設定下表現最為穩健。此外，我們亦針對不同觀點輸入、再平衡頻率與隨機資產選樣進行穩健性測試，結果顯示量子隨機行走模型在多種市場假設下皆能維持優越的表現。本研究展示了量子啟發方法於投資組合理論之應用潛力，並為未來結合量子演算法與金融決策提供實證依據。

As financial markets become increasingly complex, traditional portfolio allocation methods such as modern portfolio theory (MPT) and the Black-Litterman (BL) model have been widely applied in asset allocation. However, these methods strongly rely on explicit numerical optimization procedures and are highly sensitive to input precision, lacking the ability to express the structural information embedded in the data. Therefore, this study does not aim to address the limitations of existing methods, but instead explores a new possibility for portfolio construction by integrating quantum-inspired algorithms with graph-based approaches. We first calculate the posterior expected returns and correlations for each asset using the Black-Litterman model, and construct a weighted directed graph based on this information, treating each asset as a node in the graph. We then apply the quantum pagerank (QPR) method based on quantum stochastic walks (QSW), interpreting the asset's importance as its stationary probability distribution, which is then used to assign portfolio weights. To evaluate the performance of the proposed methods, we perform rolling window backtesting using historical data of S&P 100 index constituents from 2016 to 2024, and compare the results with those of traditional MPT and BL models. Experimental results show that the QSW method proposed in this study outperforms the benchmark models in terms of cumulative return, Sharpe ratio, and other metrics. By adjusting the mixing parameter ω, which interpolates between quantum coherent evolution and classical stochastic processes in the QSW framework, we find that the model exhibits its most robust performance under the settings of ω = 0.9 and ω = 0.7. In addition, we conduct robustness tests under different market view settings, asset reallocation frequencies, and randomly selected asset subsets. The results indicate that the QSW-based model maintains superior performance under various market assumptions. This study demonstrates the potential of quantum-inspired methods in portfolio theory and provides empirical evidence for future integration of quantum algorithms in financial decision-making.