追蹤指數與控管CVaR之投資組合規劃模型

Abstract

指數型基金透過追蹤指數來提供投資人被動管理的投資策略，因而成為保守投資人的熱門投資工具。本論文的目的在於建立一個追蹤指數的同時也能有效控管損失的指數型基金。在此目標下，該基金面臨到的不單是追蹤指數的績效，還有降低資產配置風險的問題。有鑑於此，本論文融合兩種下方風險的概念：指數追蹤的下方偏差(downside absolute deviation)以及條件風險值(conditional value-at-risk, CVaR)。針對兩者間的規避程度分別分配其權重，並以該基金之平均報酬大於指數的平均報酬作為限制條件，經由改寫下方偏差與離散化CVaR後得到一個新的線性規劃模型。本論文以台灣50指數與恆生指數的歷史資料做為實證探討的對象，驗證使用本線性規劃模型所建立之指數型基金的效能。

Index fund has become popular in these days among the conservative investors since it provides a passive investment strategy. The main purpose of this paper is to create an index fund which can replicate the performance of a broad-based index of stocks and has the ability to control the loss efficiently at the same time. For this purpose, the index fund we build confronts with not only the performance of index tracking, but also lowering the level of the risk of assets allocation. In order to accomplish the goal, we combine two concepts of downside risk: downside absolute deviation and conditional value-at-risk (CVaR). Under the constraint of average portfolio return being greater than average index return, and assign weights according to the degree of evasion to each of the risks, a linear programming model is formulated by rewriting downside absolute deviation and discretizing CVaR. The results obtained from the computational experience on Taiwan 50 index and Hang Seng index are provided for testing the efficiency of this model.

誌 謝 IV\r\n摘 要 ....................................................................................................................V\r\nABSTRACT ...............................................................................................................VI\r\n表 目 錄 ...............................................................................................................VIII\r\n圖 目 錄 ..............................................................................................................IX\r\n\r\n第一章 緒論 .............................................................................................................1\r\n1.1 前言 ..............................................................................................................1\r\n1.2 研究目的與架構 .........................................................................................3\r\n\r\n第二章 文獻回顧 ......................................................................................................5\r\n2.1 資產配置文獻之回顧............ .......................................................................6\r\n2.2 指數追蹤文獻之回顧...................................................................................8\r\n2.3 VaR與CVaR文獻之回顧….....................................................................12\r\n\r\n第三章 相關模型探討 ...........................................................................................14\r\n3.1 資產配置模型之探討.................................................................................14\r\n3.2 指數追蹤模型之探討.................................................................................20\r\n3.3 CVaR模型之探討......................................................................................32\r\n\r\n第四章 考量CVAR及追蹤誤差之規劃模型 ......................................................40\r\n4.1 考量追蹤誤差之數學模型 .......................................................................40\r\n4.2 考量CVaR之數學模型 ….........................................................................44\r\n4.3 同步考量追蹤誤差及CVaR之數學模型 .................................................48\r\n\r\n第五章 實證研究 ....................................................................................................50\r\n第六章 結論與建議 ................................................................................................78\r\n參考文獻 ....................................................................................................................79