臺灣博碩士論文加值系統

摘要
投資組合的發展中，熵值 (Entropy) 被引入投資理論分別用來處理投資組合過度集中投資的問題與作為風險衡量指標用來取代傳統均異投資組合模型 (Mean-variance, MV)中的變異數。此外，為描述投資標的未來報酬的不確定性 (模糊報酬) 與投資者可接受之報酬之範圍，模糊理論被運用在建構在模糊環境下的投資組合，Huang (2008) 提出模糊均熵 (Fuzzy-Mean-Entropy, FME) 投資組合模型，同時考量報酬、風險、模糊變數與熵值風險衡量指標等要素。模糊熵投資組合模型與MV模型一樣，存在過度集中投資於少數標的問題。因此，本研究在模糊報酬的環境下，藉著使用熵來處理分散化與不確定性的兩大問題，以達到高報酬與規避風險的目的。本研究整合Yager (1995) 的熵作為分散化的機制，建構雙目標的Fuzzy Mean_Yager- entropy (FM_Y) 投資組合模型同時處理模糊報酬與風險分散化，接著再以模糊熵 (FME) 投資組合模型為基礎，加入Yager的熵作為分散化的機制，建構三目標的Fuzzy Mean- Entropy_Yager-entropy (FME_Y) 投資組合模型，同時分析比較MV、FME、平均分配投資組合 (1/N) 模型，觀察各投資組合的效益。利用投資組合的衡量指標如市場價值 (Market value)、夏普指數 (Sharpe ratio)、Omega指數 (Omega ratio) 等比較各模型的績效，觀察到：(1) 考量模糊報酬與最小化報酬不確定性的FME比MV模型能更準確衡量未來不確定的報酬與風險。(2) 同時考量模糊熵 (Fuzzy entropy) 與風險分散的投資組合FME_Y在景氣循環谷底時可以維持較小的損失與較高的效益。

Abstract
On the development of portfolio selection, Entropy is not only dealt with the issue of non-diversification but used as the measurement of risk to replace the variance in Mean-Variance portfolio selection model. Besides, to describe the uncertainty of future return (fuzzy return) and the range of the return that the investors can accept, Fuzzy theory is used to construct portfolio selections under the fuzzy environment. Huang (2008) proposed Fuzzy-Mean-Entropy model (FME) and considered the elements of returns, risk, fuzzy variables and the entropy risk measurement. Due to FME model still have the issue with MV model of non-diversification, we use Entropy to handle two kinds of issue of diversification and the uncertainty of future return, to construct the portfolio for maximal returns and minimal risk. Under the fuzzy environment we consider the Entropy model proposed by Yager (1995) and construct the two objectives Fuzzy Mean_Yager-entropy model (FM_Y) to deal with fuzzy return and risk diversified. On the basis of FME model, we integrate Yager’s Entropy model to construct the three objectives Fuzzy Mean-Entropy_Yager-entropy (FME_Y) afterwards. And compare with the 1/N (Buy and Hold) model, MV model and FME model, we use the performance measures of portfolio such as Market value, Sharpe ratio, Omega ratio etc. to analyze each model. The research shows that (1) FME model with fuzzy returns and minimal uncertain returns can measure the uncertain returns and risk more accurate than MV model. (2) The FME_Y model considers Fuzzy entropy and risk diversified at the same time can maintain less loss and higher benefit during the down turns of economy cycles.

目次
致謝 i
摘要 ii
Abstract iii
目次 v
圖目次 vi
表目次 vii
第一章 序論 1
1.1 研究背景與動機 1
1.2 論文組織與架構 3
第二章 文獻探討 5
2.1 傳統均異模型 5
2.2 模糊投資組合模型 6
2.3 可信性理論 6
2.4 模糊熵值及模糊熵值投資組合模型 7
2.5 傳統熵值理論 8
第三章 模糊熵投資組合模型介紹 11
3.1 多目標的投資組合再調整模型 12
3.2 加入考量放空機制的投資組合模型 14
3.3 簡單權重法 16
3.4 投資組合效益評估指標 16
第四章 長期資料測試 (2002-2012) 19
4.1. 資料來源與蒐集 19
4.2. 移動視窗及考量交易成本的再調整模型 19
4.3. 資料內測試與分析 20
4.4. 資料外測試與分析 23
第五章 景氣衰退時期資料測試 27
5.1 次級房貸風暴時期實驗 (2008-2009) 27
5.2 阿根廷通貨危機時期實驗 (2001) 28
第六章 結論與未來研究 30
參考文獻 31
附錄 34
附錄1 投資標的之對照表 34
附錄2 各投資組合覆蓋率指數 35
附錄3 各投資組合模型之相似指數 38

 
圖目次
圖一 論文整體架構 4
圖二 三角模糊數的隸屬函數形式 6
圖三 各投資組合期望報酬 20
圖四 投資組合投資標的數 21
圖五 投資組合相似指數 22
圖六 投資組合標準差 22
圖七 夏普指數變化 23
圖八 各投資組合模型市場價值比較圖 24
圖九 各投資組合模型市場價值比較圖 25
圖十 2008-2009年市場價值圖 27
圖十一 需求報酬0.01%之2001年市場價值圖 29
圖十二 需求報酬0.05%之2001年市場價值圖 29
圖十三 需求報酬0.1%之2001年市場價值圖 29

 
表目次
表一 各投資組合模型所考慮的目標 11
表二 各投資組合模型市場投資組合績效指標比較表 24
表三 各投資組合模型市場投資組合績效指標比較表 25
表四 2008-2009投資組合指標 28

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