隨著指數型基金投資蔚為風潮, 主動式管理是否仍具價值已成為學術界與實務界之核心辯證。雖然共同基金的持股明細隱含經理人的私有訊息, 但在台灣股票市場中, 研究者面臨兩大結構性挑戰: 一是「股票數量遠多於基金數量」所導致的維度災難(Dimensionality Curse); 二是季報公告遞延所引發的資訊落後 (Information Lag) 問題。

為解決上述挑戰, 本研究引入廣義逆矩陣 Alpha (Generalized Inverse Alpha, GIA) 模型, 利用奇異值分解 (SVD) 技術與頻譜過濾機制, 旨在從高度稀疏且充滿雜訊的機構持股矩陣中, 逆向萃取出個股的預期超額報酬。本研究以 2006 年至 2025 年為樣本期間, 針對台灣股票市場進行實證分析, 並特別針對持股動能、回報缺口等關鍵因子進行參數敏感度校準。

研究結果顯示, 不同屬性的基金特徵因子呈現相異的頻譜結構。值得注意的是, 具備隱含能力性質的「回報缺口 (Return Gap)」在台灣市場呈現顯著的負向預測力 (t = −2.51)。此結果顯示, 在資訊揭露遞延的環境下, 模型對經理人績效產生了「歸因錯置 (Attribution Error)」: 高 Return Gap 往往隱含經理人已進行獲利了結, 導致基於舊持股的跟單訊號指向了已被拋棄的標的; 本研究透過訊號方向校準, 證實了此反向指標在修正後仍能提供顯著的超額報酬資訊。

在投資組合績效方面, 經 GIA 模型篩選之贏家組合 (Decile 10) 年化報酬率達 19.72%, 顯著優於市場標竿 0050 ETF 的 12.18%。此外多空對沖策略 (Long-Short) 創造了高度顯著的風險調整後 Alpha (t = 4.57), 且最大回撤控制在 −17.39%。實證結果顯示, GIA 贏家組的高波動主要源自於對市場系統性風險 (Beta) 的曝險, 而非選股因子的失效; 透過 GIA 模型的頻譜過濾技術, 投資人能有效剝離羊群效應雜訊, 在台灣淺碟市場中提煉出穩健的主動選股超額報酬。

Amid the growing popularity of index fund investing, whether active management still creates value has become a central debate in both academia and industry. Although mutual fund portfolio holdings embed managers’ private information, researchers studying the Taiwanese equity market face two structural challenges: first, the Dimensionality Curse arising from the fact that the number of stocks far exceeds the number of funds; and second, the Information Lag caused by the delayed disclosure of quarterly holdings reports.

To address these challenges, this study introduces the Generalized Inverse Alpha (GIA) model, which employs Singular Value Decomposition (SVD) and a spectral filtering mechanism to reverse-engineer the expected excess returns of individual stocks from a highly sparse and noisy institutional holdings matrix. Using a sample period from 2006 to 2025, this study conducts an empirical analysis of the Taiwanese equity market, with particular attention to parameter sensitivity calibration for key factors such as holding-based momentum and Return Gap.

The results reveal that fund characteristic factors with different economic properties exhibit distinct spectral structures. Notably, Return Gap—an indicator that captures managers’ implicit skill—exhibits significantly negative predictive power in the Taiwanese market (t=−2.51). This finding suggests that, under delayed information disclosure, the model suffers from an Attribution Error: a high Return Gap typically implies that the manager has already realized profits, so copycat signals derived from stale holdings point toward stocks that have already been divested. Through signal-direction calibration, this study confirms that this contrarian indicator, once redirected, still conveys significant excess-return information.

In terms of portfolio performance, the winner portfolio (Decile 10) selected by the GIA model achieves an annualized return of 19.72%, significantly outperforming the market benchmark Yuanta Taiwan 50 ETF (0050) at 12.18%. The long-short hedging strategy generates a highly significant risk-adjusted alpha (t = 4.57), with the maximum drawdown contained at −17.39%. The empirical results indicate that the high volatility of the GIA winner portfolio stems primarily from exposure to systematic market risk (beta) rather than from the failure of stock-selection factors. Through the spectral filtering mechanism of the GIA model, investors can effectively strip away herding noise and extract robust active stock-selection alpha in Taiwan’s shallow equity market.

一、中文部分
1. 李春安、賴藝文 (2005)。股市劇烈變動區間台灣股票市場與本國機構投資人從眾行為之研究。台灣管理學刊,5(2),231-267。
2. 盧秋玲、張清發、沈仰斌 (2017)。積極比例是否解釋台灣共同基金績效?證券市場發展季刊,29(3),1-38。

二、英文部分
1. Amihud, Y., & Goyenko, R. (2013). Mutual fund's R² as predictor of performance. The Review of Financial Studies, 26(3), 667-694.
2. Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57-82.
3. Chen, H. L., Jegadeesh, N., & Wermers, R. (2000). The value of active mutual fund management: An examination of the stockholdings and trades of fund managers. Journal of Financial and Quantitative Analysis, 35(3), 343-368.
4. Cohen, R. B., Coval, J. D., & Pástor, Ľ. (2005). Judging fund managers by the company they keep. The Journal of Finance, 60(3), 1057-1096.
5. Cremers, K. J. M., & Petajisto, A. (2009). How active is your fund manager? A new measure that predicts performance. The Review of Financial Studies, 22(9), 3329-3365.
6. DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 22(5), 1915-1953.
7. Elton, E. J., Gruber, M. J., & Blake, C. R. (2011). Holdings data, security returns, and the selection of superior mutual funds. Journal of Financial and Quantitative Analysis, 46(2), 341-367.
8. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
9. Grinblatt, M., Titman, S., & Wermers, R. (1995). Momentum investment strategies, portfolio performance, and herding: A study of mutual fund behavior. The American Economic Review, 85(5), 1088-1105.
10. Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65-91.
11. Jensen, M. C. (1968). The performance of mutual funds in the period 1945–1964. The Journal of Finance, 23(2), 389-416.
12. Jones, C. S., & Mo, H. (2021). Out-of-sample performance of mutual fund predictors. The Review of Financial Studies, 34(1), 149-193.
13. Kacperczyk, M., Sialm, C., & Zheng, L. (2005). On the industry concentration of actively managed equity mutual funds. The Journal of Finance, 60(4), 1983-2011.
14. Kacperczyk, M., Sialm, C., & Zheng, L. (2008). Unobserved actions of mutual funds. The Review of Financial Studies, 21(6), 2379-2416.
15. Li, Z., & Rao, X. (2023). Exploring the zoo of predictors for mutual fund performance in China. Pacific-Basin Finance Journal, 77, 101930.
16. Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703-708.
17. Pollet, J. M., & Wilson, M. (2008). How does size affect mutual fund behavior? The Journal of Finance, 63(6), 2941-2969.
18. Wermers, R. (2000). Mutual fund performance: An empirical decomposition into stock-picking talent, style, transaction costs, and expenses. The Journal of Finance, 55(4), 1655-1695.
19. Wermers, R., Yao, T., & Zhao, J. (2012). Forecasting stock returns through an efficient aggregation of mutual fund holdings. The Review of Financial Studies, 25(12), 3490-3529.