近十年來，共同基金的投資觀念逐漸為國人所接受，但對於如何評估基金績效，則較沒有統一的看法，這樣的需求便引發本文研究動機，本文旨在建構一個全面性的基金績效綜合指標，不僅是對歷史績效做一綜合考核，也能幫助投資人挑選出「未來」績效好的基金。

　　本文挑選一些績效指標做為合成綜合指標之內容，共分七類，十四種指標，又每種指標皆計算一個月、三個月、六個月、一年，共四種時間長度，便形成五十六項原始指標。

　　本文研究期間分為兩個時期，在估計期利用因素分析法做為將一個個單一指標群組化的工具，得出三個指標群命名為長期績效指標、短期績效指標、風險加擇時能力指標，再依各指標群重要性，依0.5、0.3、0.2之權重形成綜合指標；在回測期時利用分群法，以綜合指標將基金分為Ａ∼Ｅ五群，且每月更新一次投組內容，最後計算各群之累績報酬率及重要統計量。

　　應用投資組合經由適當選擇形成投資群組來降低風險的概念，本文的核心方法採用「綜合」與「群組」的想法，以綜合指標整合各指標特性，採用分群法觀察基金群體的表現，而本文實證結果顯示Ａ群基金報酬率顯著優於Ｅ群，p-value值為0.12%，表示本綜合指標確有良好的基金鑑別力；在2001/01至2005/12這段期間共累績了74.47%之報酬率，年化報酬率為11.99%，Sharpe值為1.41，操作績效良好，除了可做為投資人選擇基金時之參考依據之外，此操作方式更適合組合式基金經理人做為操作策略之參考。

　　本篇論文獲國科會中小企業產學合作計劃獎助，預計將研究結果成果落實於富盈財務科技公司之PRISS系統中，預期形成程式化、系統化、彈性化之操作介面之後，將有助於未來相關研究更迅速地發展。

　　The motivation of this research is to construct a Composite Index of funds which can help investors to choose funds with better “future” performance.
　　The Composite Index in this thesis includes 14 kinds of indexes, such as Sharpe, Treynor, Sortino, and etc. Each kind of index is calculated by 4 different time lengths, they are 1 month, 3 months, 6 months, and 1 year. Therefore, there are 56 indexes in the Composite Index (CI).
　　Factor analysis method was used to analyze fund performance from 1998/01 to 2000/12, and the perfect weight combination to make 56 indexes become one CI was found out. In order to prove the performance of the CI in selecting funds, funds were distributed into 5 groups by their Composite Index scores every month. Therefore, we had group A to E from high CI score to low CI score. We calculated these funds’ returns in the next month, and cumulated them by group from 2001/01 to 2005/12. After calculating, the cumulative returns of group A are 74.47% higher than group E, annual returns are 11.99%, and Sharpe index is 1.41. It shows that Composite Index can really distinguish the future, at least in one month, performance of stock funds. Investors are recommended to change their fund portfolios by latest CI scores once a month. Therefore, the Composite Index is more suitable for fund-of-fund manager, because their transaction costs are lower.
　　This thesis was awarded by “Industry-University Cooperative Research Project” of National Science Council, and is going to be developed in PRISS system, a financial analysis software of Folion Financial Technology Co., Ltd. Therefore, a more systemized, programmed, and efficient environment for this kind of research is expectable.

目 錄

第一章 緒論 1
1.1 研究動機與現況 1
1.2 研究目的 2
1.3 研究限制 3
1.4 章節結構 3

第二章 文獻探討 5
2.1 共同基金績效指標 5
2.1.1 報酬率績效指標 5
2.1.2 風險指標 6
2.1.3 風險調整(Return-Adjusted Return)指標 7
2.1.4 進階風險調整指標 8
2.1.5 Value-Added Model(附加價值指標) 10
2.1.6 擇時選股能力指標 10
2.2 股票型基金之多因子模型 12
2.3 多變量分析法於綜合指標之應用 14

第三章 研究方法 16
3.1 研究架構 16
3.2 研究資料範圍 18
3.2.1 研究對象 18
3.2.2 樣本期間 18
3.3 研究方法 19
3.3.1 績效指標選擇 20
3.3.2 因素分析法 21
3.3.3 因素命名 24
3.3.4 綜合指標 26
3.3.5 回測法 29

第四章 實證分析 30
4.1 因素分析結果 30
4.1.1 因子個數選擇 30
4.2 群聚關係分析及綜合指標 32
4.2.1 群聚關係命名及分析 32
4.2.2 群聚關係檢視 34
4.3 基金分群回測結果 37
4.3.1 綜合指標分群結果 37
4.3.2 其他研究結果探討 38

第五章 結論與建議 47
5.1 研究發現 48
5.2 研究貢獻 49
5.2.1 策略涵意 49
5.2.2 基金市場發展 50
5.2.3 學術價值 50
5.3 後續研究方向建議 50

參考文獻 52
英文部分 52
中文部分 53

英文部分
1.Chang, E. C. and W. G Lewellen. (1984). “Market Timing and Mutual Fund Investment Performance.” Journal of Business, 57, 57-72.

2.Hotelling, H. (1933). “Analysis 0f a Complex of Statistical Variables into Principal Components.” Journal of Educational Psychology, 24:417-520.

3.Gower, J. C.. (1966). “Some Distance Properties of Latent Root and Vector Methods Used in Multivariate Analysis.” Biometrika, 53:325-38.

4.Jeffers, J.N.R. (1967). “Two Case Studies in the Application of Principal Components Analysis.” Appl. Statist. 16, 225–236.

5.Jensen, M. C., (1968). “The Performance of Mutual Funds in the Period 1945-1964.” Journal of Finance, Vol. 23, 389-416。

6.Korkie, Robert M. and Turtle, Harry J.. (Winter2002). “What a portfolio Manager Worth?” Journal of Portfolio Management, Vol. 28 Issue 2, 65-73.

7.Moses, E.A., J.M. Cheyney, , and E.T. Viet. (1987). “A New and More Complete Performance Measure.” Journal of Portfolio Management, 24-33.

8.Pearson, K. (1901). “On Lines and Planes of Closest Fit to Systems of Points in Space.” Phil. Mag., 6:559--572. Ser. 2.

9.Prather L, Bertin WJ, Henker T. (2004). “Mutual Fund Characteristics, Managerial Attributes, and Fund Performance.” Rev Financ Econ., 13(4):305-326.

10.Rao, C.R.. (1964). “The Use and Interpretation of Principal Component Analysis in Applied Research.” Sankhya A 26, 329-358.

11.Sharpe, W. F.. (1966). “Mutual Fund Performance.” Journal of Business 39, 119-138.

12.Treynor, J.L.. (1965). “How to Rate Management Investment Fund.” Harvard Business Review, Jan/Feb, Vol. 43, 63-75.

13.Treynor, J., And K. Mazuy. (1966). “Can Mutual Funds Outguess the Market?” Harvard Business Review 44, 131-136.


中文部分

1.王郁仁，「股票型基金綜合指標與基金績效動態監控」，國立中山大學財務管理研究所碩士論文，民國94年。

2.林郁翎，「銀行危機預警綜合指標之建立」，東吳大學經濟學研究所碩士論文，民國91年。

3.胡忠琳，「主成份分析在各種多元統計方法上的應用」，國立政治大學統計研究所碩士論文，民國77年。

4.胡崇銘，「以主成分分析評估基金績效與風險」，國立臺灣大學商學研究所，民國89年。

5.周文賢，多變量統計分析，初版，2002年，智勝出版。

6.陳順宇，多變量分析，四版，2005年，華泰出版。