結合流形學習與 Graphical Lasso 之投資組合與風險分散策略

Abstract

隨著可投資資產的種類與數量大幅增加，傳統投資組合理論在面對高維度資料時，逐漸暴露出共變異數矩陣估計不穩定及線性假設過於簡化等限制。為解決ㄇ此一問題，本研究提出並實作一個創新的交集網絡框架，以建構更穩健且具解釋力的量化投資組合策略。

本研究以台灣股市上市櫃公司為研究樣本，核心方法為結合兩種異質性網絡以擷取資產間之強關聯性：結合非線性技術特徵相似性及稀疏精度矩陣。僅保留在上述兩種網絡中皆存在之連結，交集後即構成本研究所定義之交集網絡。基於此網絡結構，設計選股策略，並搭配權重配置方式，進行序時回測與穩健性檢驗。

實證結果顯示，多數策略在風險調整後報酬上均明顯優於大盤基準。其中，融合網絡拓樸結構與傳統量化因子相結合的策略，能有效提升超額報酬潛力。分期測試亦證明，核心策略於熊市期間具備優異的抗跌性與防禦力；此外，敏感度分析指出，模型績效對核心超參數之設定不具高度敏感性，進一步強化其應用上的穩健性。綜合而言，本研究提出之交集網絡不僅能有效降低金融網絡建構過程中的雜訊干擾，更成功應用於具實務潛力之資產配置策略設計，為現代投資組合理論與資產管理實務提供一項具創新性的可行路徑。

As the variety and volume of investable assets continue to expand, traditional portfolio theories increasingly reveal their limitations when dealing with high-dimensional data—specifically, the instability of covariance matrix estimation and the oversimplification of linear assumptions. To address these challenges, this study proposes and implements an innovative intersection network framework to construct more robust and interpretable quantitative investment strategies.

Using listed companies in the Taiwan stock market as the research sample, the proposed method integrates two types of heterogeneous networks to capture strong asset relationships: one based on nonlinear technical feature similarity, and the other derived from sparse precision matrices. Only the links simultaneously present in both networks are retained, forming what this study defines as the intersection network. Based on this structure, a series of stock selection strategies are developed and combined with various weighting schemes for sequential backtesting and robustness testing.

Empirical results show that most strategies achieve significantly better risk-adjusted returns than the market benchmark. In particular, strategies that combine network topology with traditional quantitative factors demonstrate strong potential for generating excess returns. Period-based evaluations also confirm that the core strategies exhibit superior defensive performance during bear markets. Moreover, sensitivity analysis indicates that model performance is not overly dependent on specific hyperparameter settings, further reinforcing the robustness of the framework. Overall, the proposed high-conviction network effectively reduces noise in financial network construction and is successfully applied to practical portfolio design, offering an innovative and feasible approach to modern portfolio theory and asset management.