以目標規劃模型建立成長型投資組合

Abstract

本論文使用大中取小原則及目標規劃技術，提出建構投資組合的數學規劃模型。要求此投資組合面對於不確定的股市，能夠在控制風險最小的情況下穩定且具有成長性的獲利。論文內探討如何透過數學的限制式來控制風險，而又能兼顧穩定且具有成長性的獲利，同時模型也可針對不同投資者的需求設定其數學規劃模型。最後以台灣股票市場做為實證分析的對象，給予不同的參數設定來驗證投資組合的表現。實證發現若以期初的配置比重持有到投資期間結束，此投資方式的績效欠佳。因此論文中進一步探討最佳的調整週期，實證顯示每經過8週，根據最新的資訊，重新調整建立新的投資組合，投資績效最好。

This thesis proposed a mathematic programming model to construct a growth portfolio by using the mini-max principle and goal programming technique. The constructed portfolio is required to minimize the risk and to earn a stable profit under uncertain market. In the thesis, we discussed how to control the risk and maintain the growth of the portfolio by using the linear constraints. The proposed model also provides several parameters setting to meet the different investors` requirement. Finally, an empirical study will be provided by using the data from Taiwan’s stock market. The portfolios are constructed by giving different parameters and the performances are reported. The empirical study showed that holding a portfolio through the entire investment period without rebalance yield the performances that are not good. Therefore, the rebalance timing is investigated and the empirical study showed that a portfolio with rebalance strategy by every 8 weeks yield the best performance.

摘要............................................v\r\n\r\n第一章 緒論……………........……………………………………………………………..1\r\n1.1 研究動機…………..........………………………………………………………….1\r\n1.2 研究目的與架構… ………………………………………………………….3\r\n\r\n第二章 非線性轉變為線性的數學模型之文獻回顧………………………………..4\r\n2.1 Markowitz的貢獻與數學模型…………………………………………..…..5\r\n2.2 線性化的風險函數……………………………………………………...…..8\r\n2.3 其他投資組合的選取方法…………………………………………….......15\r\n\r\n第三章 數學規劃模型………………………………………………………………18\r\n3.1以利潤為考量所建立的限制式……………………………………………19\r\n3.2以風險為考量所建立的限制式……………………………………………21\r\n3.3建立數學規劃模型…………………………………………………………23\r\n\r\n第四章 實證研究……………………………………………………………………26\r\n4.1 檢測模型在不同時間段的有效性………………………………………...28\r\n4.2檢測單一投資標的投資金額比重不同上限的表現………………………32\r\n4.3檢測定期調整投資組合的必要性……………….…………….…………..40\r\n\r\n第五章 結論與建議…………………………………………………………………47\r\n5.1 結論……………………………………………………….………………..47\r\n5.2 建議................…………………………………………………...…………48\r\n參考文獻……………………………………………………………………………..49