臺灣博碩士論文加值系統

共同基金是投資人熱愛的商品之一，乃因對於一般投資人，藉由專業經理人可降低其風險，且省去研究選股與擇時的心力。然而研究顯示，大部分的主動式基金績效難以超越市場指標，而指數化投資受到越來越多投資人的青睞。指數化投資工具例如指數型基金及ETFs，皆以複製或貼近市場績效為目的。然而指數追蹤投資組合因受限於實務上追隨指數變動調整成分股需付出手續費的成本，另外仍需維持一定的現金部位供投資人贖回，因此將產生較大的追蹤誤差。所以除了盡可能地最小化追蹤誤差，仍須追求適度的超額報酬以達到真正的複製或貼近市場績效的目的。追求低追蹤誤差與追求超額報酬為兩相衝突的目標。目標規劃適合處理兩互相衝突目標之問題，但目標規劃的基本精神乃為預先設定明確目標，然而現實金融市場環境，決策者的期望目標往往不明確。｢極小化追蹤誤差｣ 及 ｢極大化超額報酬｣ 此兩相衝突目標在本研究將以模糊理論中的歸屬函數表示其滿意程度，以模糊目標規劃方式建立一指數追蹤模型，標竿指數為台灣五十指數。結果顯示透過適當的歸屬函數與模型，可建構出追蹤誤差比台灣五十指數基金低但超額報酬近似的投資組合。

Mutual fund is one of favorite tools of the investors. Individual investors need no efforts on stock-picking and market-timing because the investing risk can be lowered through the professional management. But the researches indicate that most actively managed mutual fund’ performance is difficult to beat the market, and index investing is more and more popular among the investors. Index investing instruments, such as index funds and ETFs, aim to track the market performance. In practical, an index tracking portfolio has to pay the transaction cost due to following the change of benchmark index and also has to remain certain cash position. This result in the higher tracking error, therefore we want to pursuit both tracking error minimization and excess return maximization to attain the real performance tracking. Both are conflicting objectives. Goal programming is suitable for handling multiple conflicting objectives, but the basic goal programming concept is first to set up the crisp goals. In the real financial environment, the desired/expected level of the decision maker is usually imprecise. Minimizing the tracking error and maximizing the excess return are both represented as “fuzzy goals” in this research. Results show that through certain membership function and tracking model, an index tracking portfolio whose tracking error is lower than 0050 index fund but excess return is similar to 0050 index fund can be constructed.

Section 1. Introduction 1
Section 2. Literature Review 4
2.1 Index tracking 4
2.2 Fuzzy theory and goal programming 11
2.3 Different types of fuzzy goal programming 19
Section 3. Data and Methodology 23
3.1 Data 23
3.2 Performance measurement 25
3.3 Fuzzy goal programming models for index tracking portfolio 29
Section 4. Empirical Results 31
Section 5. Conclusion 37
References 39
Appendix 44

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