馬克維茲於1952年提出的平均-變異數模型十分容易受到市場雜訊影響，導致其模型的穩健性不高，為了改善馬克維茲的平均-變異數模型，於1952年之後，樣本共變異數矩陣和縮減法相繼問世，更甚者，有2022年最新推出的Gerber統計法和修改的Gerber統計法，為了研究最新推出的兩種Gerber統計法是否適用於台灣股市，故本研究以台灣50檔股票為主要標的，代入樣本共變異數矩陣、縮減法、Gerber統計法和修改的Gerber統計法這四種方法，並對其進行投資組合配置，計算出投資組合的年化報酬率，並與0050的年化報酬率進行比較。最終，實證結果發現以上四種方法之績效於50檔時不優，但若從50檔股票中透過限制產業再篩選出10檔股票，其績效可超越0050，但是，本研究尚未考慮手續費，故若要再進一步探詢Gerber統計法和修改的Gerber統計法是否在台灣股市具有效性，可再進一步分析其他台灣的資產。

Markowitz's mean-variance model, proposed in 1952, is highly susceptible to market noise, leading to its lack of robustness. In order to improve Markowitz's mean-variance model, subsequent to 1952, the sample covariance matrix and shrinkage methods were introduced. Moreover, the latest Gerber statistics and modified Gerber statistics were introduced in 2022. To investigate the applicability of these two new Gerber statistics in the Taiwanese stock market, this study focuses on the top 50 stocks in Taiwan and applies the sample covariance matrix, shrinkage methods, Gerber statistics, and modified Gerber statistics. The study then constructs investment portfolios and calculates their annualized returns, comparing them with the annualized return of the benchmark index 0050. The empirical results indicate that the performance of the four methods on the 50-stock portfolio is not favorable. However, if the 50 stocks are further screened to select 10 stocks with industry restrictions, the performance is expected to outperform 0050. Nevertheless, to further investigate the effectiveness of Gerber statistics and modified Gerber statistics in the Taiwanese stock market, it is suggested to conduct further analysis on other Taiwanese assets.

一、中文參考文獻

陳岐穎(2011)。「不同估計方法對資產配置的影響」，國立交通大學財務金融研究所碩士論文。

何家祐(2012)。「可調式馬可維茲模型的績效驗證-以台灣50指數與產業研究報告為例」，國立台北科技大學資訊與運籌管理研究所碩士論文。

張翔、廖崇智(2019)。「提綱挈領學統計」，大碩教育股份有限公司，頁598。

張翔、廖崇智(2020)「運籌帷幄學財管」，大碩教育股份有限公司，頁182-212。

二、英文參考文獻

Blackwell,B.(1959). Portfolio Selection: Efficient Diversification of Investments. Cambridge, MA.

Brianton.G.,(1998). Portfolio Optimization, Risk Management and Financial Derivatives: A Guide to the Mathematics.1st edition, Palgrave(trade).

Campbell.R, Magnus and Harvey (2001). Global Tactical Asset Allocation. Emerging Market Quarterly, Spring, 6-14.

Cheng, E., Struck, C.C.,(2021). Antinoise in US equity markets. Quantitative Finance, Vol.21, No 12, 2069–2087.

Chopra.V.K, Ziemba.W.T (1993).The effect of errors in means, variance, and covariances on optimal portfolio choice.The Journal of Portfolio Management, 19(2), 6-11.

Eichhorn,D. Gupta.F, and Stubbs,E(1998). Using Constraints to Improve the Robustness of Asset Allocation, The Journal of Portfolio Management, 24(3), 41-48.

Frost, P.A., Savarino, J.E(1986). An empirical Bayes approach to portfolio selection. Journal of Financial and Quantitative Analysis, 21(3),293 – 305.

Gerber, S., Markowitz, H.M., Ernst, P.A., Miao, Y., Javid, B., Sargen, P.,.(2022) The Gerber statistic: a robust co-movement measure for portfolio optimization. The Journal of Portfolio Management, 48(3), 87-102.

Hampel, F.R. (1968). Contributions to the Theory of Robust Estimation. Ph. D.
Thesis, University of California, Berkeley.

Jobson. J. D. and Korkie.B(1980). Estimation for Markowitz Efficient Portfolios. Journal of the American Statistical Association, 75(371), 544–554.

Jorion, P.(1985). International portfolio diversification with estimation risk. The Journal of Business, 58(3), 259–278.

Kendall .M. G.(1938).A New Measure of Rank Correlation. Biometrika, 30(1), 81-93.

Ledoit, O. and M. Wolf. (2003).Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5), 603-621.

Ledoit, O. and M. Wolf.(2004). Honey, I Shrunk the Sample Covariance Matrix. The Journal of Portfolio Management, 30(4), 110–119.

Markowitz,H.(1952). Portfolio Selection. The Journal of Finance, 7(1),77-91.

Michaud, R. O. (1989). The Markowitz Optimization Enigma: Is Optimized Optimal? Financial Analysts Journal, 45(1), 31-42.

Pástor, L. (2000). Portfolio selection and asset pricing models. The Journal of Finance, 55(1), 179–223.

Rodrigo.Z, Michael.S, Camille.M, Matthew J. Smith(2022). The Delta-Method and Influence Function in Medical Statistics: a Reproducible Tutorial. RESEARCH ARTICLE.

Sharpe, W.F. (1963). A Simplified Model for Portfolio Analysis. Management Science, 9(2), 277-293.

Smyth,W and Broody,D (2022). An enhanced Gerber statistic for portfolio optimization . Finance Research Letters 49,103229.