臺灣博碩士論文加值系統

投資組合的觀念在馬可維茲1952 年提出後，成為投資人用以避險的最佳工具
之一，而投資組合資產配置問題乃是其中令人十分困擾的議題。只是投資組合資
產配置問題為一NP-Hard 問題使得傳統的線性方程式所能達到的最佳化效果受到
限制。因此，近年來遺傳演算法技術大量地被應用在投資組合資產配置的問題上。
然而，在傳統的遺傳演算法中通常是透過字串編碼並利用正規化的方式去表示一
組資產配置的解，但正規化的過程中容易使收斂過程震盪過於激烈，以致於無法
找出全域的最佳解。為解決上述問題，本研究提出可延展實數遺傳演算法讓使用
者可以利用遺傳演算法配置適當的投資組合資產權重。在可延展實數遺傳演算法
中每條染色體代表一個投資組合中資產權重分配的可行解，而各基因以實數表
示，每個基因代表一個資產所得到的資產權重。由於現實環境中資產配置總有許
多條件限制，因此在本編碼機制中允許投資人對每個資產設定不同的投資上下
限，使得染色體所表示的資產權重服從投資人所希望的投資限制。在這個編碼機
制中基因與基因之間彼此互相獨立，不會因為彼此的關聯性而導致劇烈的震盪，
所以交配方法不會影響整體收斂速度或導致發散。我們配合上述編碼機制設計了
一套交配方法，以基因值與投資上下限重新定義交配權重的範圍，隨著收斂過程
交配權重的範圍會逐漸擴大，使得染色體再度發散，如此一來遺傳演算法可以更
有效地避免陷入區域最佳解。實證研究中我們使用可延展實數遺傳演算法去萃取
最佳的投資組合並最佳化投資組合中的資產配置，從實驗結果可以看出，可延展
實數遺傳演算法成功地打敗簡單遺傳演算法與傳統的實數遺傳演算法，並且所獲
得的效用函數值與期望報酬率均較簡單遺傳演算法、傳統的均異分析法與以市值
比例為投資權重所獲得的投資組合報酬率來得優異。

The Portfolio is best tool for avoid investment risk was proposed by Markowitz in
1952. The asset allocation problem is one of the portfolio topics to making people
perplex very much among them. The asset allocation optimization problem is complex
and NP-hard problem. It is nonlinear with many local optima. Thus, the genetic
algorithm is applied to the asset allocation optimization generously in recent years.
However, most of GA-based portfolio assets allocation uses normalization method to
allocate investment asset’s weight. The normalization process will cause unease
converging and even diverging characteristics, because it changes the gene’s relativity
of address in chromosome. In order to solve above-mentioned problems, our research
proposes an Extendable Real number Genetic Algorithm (ERGA) to allocate suitable
assets in portfolio. Each gene encoded as a real number not a bit string in a
chromosome is denoted as the weighted number of assets in our approach. We allow
investors to set up different investment upper and lower limits to each asset in this
encoding scheme. Due to no specific relationship assumed in our encoding scheme, the
crossover process would not influence overall converging speed or even lead to diverse.
In addition, in order to avoid losing optimal asset allocations through quicker
converging, we also allow enlarging the possible range of crossover weight with gene
value and investment upper and lower limits during the evolutionary process. This
study introduces an evolutionary portfolio asset allocation model to optimize portfolios
under their maximum expected returns subject to a risk constraint. We use a GA to
extract the best portfolio set and optimal asset allocation in portfolio in order to gain
excess profit of investment.

摘要................................................................................................................................ iv
Abstract ........................................................................................................................... v
致謝................................................................................................................................ vi
目錄................................................................................................................................ vii
圖目錄............................................................................................................................. ix
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 論文架構...................................................................................................... 4
第二章 文獻回顧...................................................................................................... 6
2.1 投資組合...................................................................................................... 6
2.1.1 投資組合概念.................................................................................. 6
2.1.2 均異分析法...................................................................................... 9
2.1.3 投資組合績效之衡量.................................................................... 10
2.2 投資組合相關文獻.................................................................................... 13
2.3 遺傳演算法................................................................................................ 17
2.3.1 簡單遺傳演算法............................................................................ 17
2.3.2 編碼................................................................................................ 18
2.3.3 演算法設計.................................................................................... 19
2.3.4 實數型遺傳演算法........................................................................ 23
2.4 遺傳演算法應用在有限資源配置最佳化之相關文獻............................ 25
2.5 遺傳演算法應用在投資組合之相關文獻................................................ 26
2.6 正規化表示法應用在投資組合之問題討論............................................ 29
第三章 研究設計.................................................................................................... 34
3.1 研究架構.................................................................................................... 34
3.2 演算法流程................................................................................................ 35
3.2.1 編碼機制........................................................................................ 35
3.2.2 初始化............................................................................................ 36
3.2.3 交配方法論.................................................................................... 37
3.3 適應函數.................................................................................................... 41
第四章 實驗環境與系統介面................................................................................ 43
4.1 系統簡介.................................................................................................... 43
4.2 系統環境.................................................................................................... 44
4.2.1 硬體環境........................................................................................ 44
4.2.2 軟體環境........................................................................................ 44
4.3 參數設定.................................................................................................... 44
4.4 投資標的設定............................................................................................ 46
4.5 執行視窗.................................................................................................... 47
第五章 實證分析.................................................................................................... 48
5.1 資料來源和研究期間................................................................................ 48
5.2 實驗設計.................................................................................................... 52
5.3 實驗結果分析............................................................................................ 53
第六章 結論與建議................................................................................................ 77
參考文獻........................................................................................................................ 79

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