臺灣博碩士論文加值系統

投資組合策略在考量期望報酬時，也必須衡量其帶來的風險，此類型問題在學術界被視為多目標問題（Multi-Objective Optimization Problem），屬於 NP-Hard 類型問題。在過去研究中，此類問題幾乎是考量在同類型資產下的投資組合策略，鮮少針對不同資產來進行研究，然而實務上在面對資產配置的議題時，投資人通常會運用不同類型的投資工具來進行投資理財規劃，此類型決策模式則視為多準則決策問題 (Multiple Criteria Decision-Making；MCDM) 。根據本研究調查，台灣的投資人最常使用的前三大投資理財工具分別是銀行存款、股票與共同基金，但是要如何將資金以適當比例配置到各種投資工具之中，且在繁雜的投資標的中決定最佳的投資組合則顯得格外重要。

而本研究提出一套整合投資決策模式，透過網路層級分析法 (Analytic Network Process，ANP) 來評估此三種投資工具之最適資金配置比例，再針對股票、共同基金以變動鄰域搜尋法 (Variable Neighborhood Search；VNS) 替投資者搜尋最佳投資組合，同時評估投資效益。此外，多目標問題往往因為所求之目標函數相互衝突，因此無法精準定義出單一最佳解，必須藉由效率前緣（Efficient Frontier）或柏拉圖前緣（Pareto Front）來提供給決策者做出最適決策。而研究結果顯示，利用 ANP 法能提供不同風險屬性投資者之資金配重比例，並搭配 VNS 能夠在短時間內求解出良好的投資組合結果。

When optimizing a portfolio, an investor not only considers the expected return, but also cares about the risk coming with the investment. This optimization problem has been classified as a multi-objective optimization problem which also falls into the class of NP-Hard problems. Most of past studies focused on the optimization of a portfolio from one type of asset such as stocks or mutual funds alone. However, lots of investors nowadays allocate their money to different investment tools to reduce their risk while hopefully enhance the profit. How to distribute money properly to these three tools among all possible asset options is indeed a complex and important topic in practice.

This study proposes an integrated decision model that combines the Analytic Network Process (ANP) and a metaheuristic algorithm Variable Neighborhood Search (VNS). ANP is used to identify the target asset types and then determine the corresponding percentage of each asset. This study finds that the top three investment tools favored by Taiwanese investors are term deposit, stock, and mutual fund, respectively. Afterward, a VNS algorithm is constructed to optimize the portfolio of stocks and mutual funds using the information obtained from Taiwan financial market separately. Since the property of the multi-objective problem, an efficient frontier that consists of multiple portfolios is built to offer investors more alternatives. This study provides suggestions for different types of investors, i.e., for both risk-aversion and risk-lover, and also recommends portfolio choices under different number of asset selection.

中文摘要i
ABSTRACTii
致謝 iv
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究範圍 5
1.4 研究架構與流程 5
第二章 文獻探討 7
2.1 投資組合與配置最佳化問題 7
2.1.1 資產配置最佳化與其相關研究 8
2.1.2 投資組合與其相關研究 10
2.2 多準則決策分析之理論與發展 14
2.2.1 網路層級分析法 17
2.2.2 網路層級分析法之相關研究 18
2.3 變動鄰域搜尋法之介紹 21
2.3.1 變動鄰域搜尋法之相關研究 21
第三章 研究方法 25
3.1 投資組合問題 26
3.1.1 非受限投資組合最佳化問題 26
3.1.2 受限投資組合最佳化問題權重模型 27
3.2 網路層級分析法 28
3.2.1 網路層級分析法及其執行步驟 29
3.3 變動鄰域搜尋法 36
3.4 績效衡量指標 41
第四章 研究結果與分析 44
4.1 受訪者特性分析 44
4.2 ANP 之結果分析 46
4.2.1 ANP 結果分析─不針對特定投資屬性之投資人探討 50
4.2.2 ANP 結果分析─針對不同投資屬性之投資人探討 54
4.3 VNS 驗證資料來源 58
4.4 VNS 參數設定 59
4.5 VNS 實驗結果 60
4.5.1 測試資料─台灣股市 60
4.5.2 測試資料─台灣可投資之共同基金 64
4.5.3 參考效率前緣與演算法效效率前緣之圖形比較 68
4.6 最佳資產配置與投資組合之投資決策模式建立 72
4.7 結論與未來研究方向 78
4.7.1結論 78
4.7.2 未來研究方向 79
參考文獻 80
附表一 (準則之相關係數檢定表) 87
附表二 (台灣股票標的編號對照表) 88
附表三 (共同基金標的編號對照表) 98
附表四 (建議之最佳投資組合編號對照表) 103
附表四 (建議之最佳投資組合權重對照表) 125

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