Treynor Ratio、Sharpe Ratio、Jensen's Alpha和Information Ratio為一般常用的基金績效評估指標，但每一指標考量的風險不盡相同，且投資者也不清楚哪一個指標較合適，故難以單一指標作為選購基金的參考，本研究除了比較這四個單一準則績效評估指標外，再透過多屬性決策分析方法將這四個指標綜合考量以評估共同基金績效，主要採用的多屬性決策分析方法為理想解類似度偏好順序評估方法（Technique for Order Preference by Similarity to the Ideal Solution），以13種加權距離法建立13個多準則績效評估指標，研究2002年9月到2005年6月的82支台灣開放式股票型（投資國內）共同基金發現，在單一準則績效評估指標中以Jensen's Alpha較佳，多準則績效評估指標中則以CRITIC權重下的城市街道加權距離法最好，13個多準則績效評估指標雖然沒有顯著優於單一績效評估指標，但由於多準則績效評估指標能同時將更多的風險和資訊納入考量，所以本研究提出的多準則績效評估指標能作為投資共同基金另一參考的指標。

The purpose of this study is to evaluate the performance of mutual funds. "Treynor Ratio", "Sharpe Ratio", "Jensen's Alpha" and "Information Ratio" are four commonly used indices for evaluating the competing mutual funds. However, it is not clear which measure is the most robust. This study has a different focus not only on investigating the four criteria separately but also combining all the indices at the same time in making a final ranking of the mutual funds. This study found that Jensen's Alpha outperforms the rest indices of both uni-criterion and multi-criteria. Although multi-criteria indices are not noticeably better than uni-criteria indices, the index using CRITIC weight method under City block distance measure is recommended if the correlation between the rankings is concerned. Even though the new indices are not noticeably more accurate than uni-criterion indices in ranking the mutual funds. But a good and informative index should be able to chart aggregate changes in market levels. Those uni-criterion indices only justify the risk or a mutual fund manager's ability partially. Multi-criteria indices are another choices which can be used to evaluate the mutual funds and can take all the criteria into consideration simultaneously. That's the main contribution of this research.

List of Figures	IV
List of Tables	V
Acronyms	VII
Notations	X
Chapter 1  Introduction	1
1.1  Preliminaries	1
1.2  The Research Purposes and Problems	2
1.3  The Research Scope	4
1.4  The Research Structure	4
Chapter 2  Literature Review	7
2.1  Performance Evaluation of Mutual Funds	7
2.2  Multi-Criteria Decision Making	10
2.2.1  Decision Problems	10
2.2.2  Categories of Multi-Criteria Decision Making	11
2.2.3  Multi-Attribute Decision Analysis	11
Chapter 3  Research Method	18
3.1  Performance Evaluating Measures of Mutual Funds	18
3.2  TOPSIS Method	21
3.3  The TOPSIS Method with Different Objective Weights and Distances Approach	24
3.3.1  Problem Setup	24
3.3.2  Objective Weights	26
3.3.3  Weighted Distances	28
3.3.4  Overall Index	33
3.4  Methods Evaluation	35
3.4.1  Spearman's Rank Correlation Coefficient r_s	35
3.4.2  Proportion of Rankings Matched with Rankings of AR	36
Chapter 4  Empirical Results	38
4.1  Uni-criterion	39
4.2  Multi-criteria	40
4.2.1  An Illustrative Example	44
4.2.2  Distance Measures Effect	51
4.2.3  Weight Methods Effect	62
4.2.4  13 Indices of TOPSIS Method	68
4.3  Comparison of Uni-criterion and Multi-criteria	71
Chapter 5  Conclusion and Suggestion	73
Bibliography	74
Appendices
Appendix A  Derivation of the Result that s_{j/prop}^2 Is Proportional to (CV_j)^2	79
Appendix B  List of the Mutual Funds in the Sample	81
Appendix C  Results of the Illustrative Example	84

List of Figures
Figure 1.1 	Flow Chart for the Research	6
Figure 2.1 	A Taxonomy of MADM (Yoon and Hwang (1995))	12
Figure 2.2 	A Taxonomy of Weights	14
Figure 3.1 	The Idea of TOPSIS Method	23
Figure 3.2 	Distance Curves: EU, CB and MI	31
Figure 3.3 	Distances of the Positively Correlated Criteria	34
Figure 3.4 	Distances of the Negatively Correlated Criteria	34
Figure 4.1 	Histograms of r_s for Uni-criterion Cases, 2002.09-2005.06	41
Figure 4.2 	Time Series Plot of r_s for Uni-criterion Cases, 2002.09-2005.06	42
Figure 4.3 	Histograms of r_s under MW, 2002.09-2005.06	59
Figure 4.4 	Histograms of r_s under EW, 2002.09-2005.06	60
Figure 4.5 	Histograms of r_s under CV, 2002.09-2005.06	61
Figure 4.6 	Histograms of r_s under CR, 2002.09-2005.06	62

List of Tables
Table 4.1	Methods Evaluation for Uni-criterion Cases	43
Table 4.2	Original Data (September, 2002) for 82 Mutual Funds Studied	46
Table 4.3	Transformed Data by Location Shift	47
Table 4.4	IDR, ANIDR and Objective Weights for 4 Criteria	48
Table 4.5	WDIDR, WDANIDR, INDEX and Rankings under Euclidean for MW Method	49
Table 4.6	Methods Evaluation for the Period in September, 2002	50
Table 4.7	Weights of Each Criterion under Four Objective Weight Methods	54
Table 4.8	Spearman's Rank Correlation Coefficients r_s under Fixed Weight	56
Table 4.9	Methods Evaluation for Fixed Weight Methods for 34 Periods	58
Table 4.10	Spearman's Rank Correlation Coefficients r_s under Fixed Distance	65
Table 4.11	Methods Evaluation for Fixed Distance Measures for 34 Periods	67
Table 4.12	Methods Evaluation for 13 Indices for 34 Periods	70
Table 4.13	Methods Evaluation for Uni-criterion and Multi-criteria Cases for 34 Periods	72
Table B.1	List of the Mutual Funds Studied	81
Table C.1	WDIDR, WDANIDR, INDEX and Rankings under City Block for MW	85
Table C.2	WDIDR, WDANIDR, INDEX and Rankings under Minkowski for MW	86
Table C.3	WDIDR, WDANIDR, INDEX and Rankings under Euclidean for EW	87
Table C.4	WDIDR, WDANIDR, INDEX and Rankings under City Block for EW	88
Table C.5	WDIDR, WDANIDR, INDEX and Rankings under Minkowski for EW	89
Table C.6	WDIDR, WDANIDR, INDEX and Rankings under Euclidean for CV	90
Table C.7	WDIDR, WDANIDR, INDEX and Rankings under City Block for CV	91
Table C.8	WDIDR, WDANIDR, INDEX and Rankings under Minkowski for CV	92
Table C.9	WDIDR, WDANIDR, INDEX and Rankings under Euclidean for CR	93
Table C.10	WDIDR, WDANIDR, INDEX and Rankings under City Block for CR	94
Table C.11	WDIDR, WDANIDR, INDEX and Rankings under Minkowski for CR	95
Table C.12	WDIDR, WDANIDR, INDEX and Rankings under Mahalanobis	96
Table C.13	The Yearly Rate of Actual Return and the Corresponding Rankings	97

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