在多維常態、自我迴歸、自我迴歸-廣義自我迴歸條件異質變異模型下幾種貝氏最佳投資組合之探討

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林琬真(Wan-chen Lin) 查詢紙本館藏

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統計研究所

論文名稱

在多維常態、自我迴歸、自我迴歸-廣義自我迴歸條件異質變異模型下幾種貝氏最佳投資組合之探討

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摘要(中)

近年來，由於經濟市場的快速成長以及各國經濟趨向穩定，投資變成是越來越多人的理財工具，因此「如何對各種產業進行搭配以賺取更多的利益」越來越受到人民的重視。本篇論文乃是探討如何應用預測分配之期望值與共變異矩陣、期望效用函數的最大值以及風險值找出最佳投資比例。%由三個法則探討如何找出最佳投資組合並加以比較，分別是由 Markowitz (1952) 所提出的利用預測分配之期望值與變異數 (MV)dd 利用期望效用函數的最大值 (DU) 以及由風險值 (VaR) 來找出其最佳的投資組合並以真實資料去加以模擬。
本文考慮不同產業的報酬率分別為獨立且同分配的多維常態模型，自我迴歸 (Autoregressiveff 簡稱 AR) 模型及廣義自我迴歸條件異質變異 (Generalized Autoregressive Conditional Heteroskedastical；簡稱 GARCH) 模型，以貝氏方法求各資產在 Markowitz 所提出的均值-變異數法則、期望效用函數法則以及風險值法則下個別之最佳投資組合，並以模擬資料對各模型的預測結果加以比較，結果顯示在 AR(1)-GARCH(1,1) 模型配適資料的情況下，會得到最多的獲利。
另外並以實例分析各模型下由各法則所得之最佳報酬，文中所述之 AR(1)-GARCH(1,1) 模型較多維常態模型及 AR(1) 模型更能表現各期資產報酬率的關聯性及波動性，因此由 AR(1)-GARCH(1,1) 模型進行配適可獲得最大的利益。

摘要(英)

Recently, the rapid growth of economic markets and the stability of economic tendency make investment become a more and more common tool of personal financial management.
Therefore, it is important to think of how to work with an allocation of properties so as to earn more return. In this article, we consider three models for returns of investments, namely, identically independent normal model, autoregressive (AR) model, and generalized autoregressive conditional heteroskedastical (GARCH) model. We estimate
the parameters of each models through a Bayesian perspective, and then derive the best portfolio selection under the mean-variance, the direct-ultility, and the value-at-risk(VaR) criteria. A simulation study is done for comparing the prediction result of each models, and an empirical example is analyzed for the maximum return of each criteria under each model. As a result, the proposed AR(1)-GARCH(1,1) model can exhibit better correlation and volatility of property return of each period than the normal and AR(1) model.

關鍵字(中)

★ GARCH
★ 風險值
★ 效用函數
★ 均值-共變異數
★ 投資組合

關鍵字(英)

★ GARCH
★ value-at-risk
★ utility
★ mean-variance
★ portfolio

論文目次

Abstract...................................................i
摘要.......................................................ii
目錄......................................................iii
表目次...................................................v
誌謝......................................................vi
第一章緒論...........................................1
1.1 研究背景及動機..............................1
1.2 研究目的及方法..............................3
1.3 研究架構..........................................7
第二章統計模型與參數估計...............8
2.1 常態分配..........................................8
2.1.1 主觀貝氏.......................................9
2.1.2 經驗貝氏......................................10
2.1.3 James-Stein估計量........................12
2.1.4 階層式貝氏...................................12
2.2 AR模型.............................................14
2.3多維 AR-GARCH模型......................17
第三章最佳投資組合...........................22
3.1 MV法則............................................22
3.1.1 M維常態模型................................24
3.1.2 M維AR(1)模型..............................24
3.1.3 M維AR(1)-GARCH(1,1)模型........25
3.2 DU法則............................................26
3.3 VaR法則...........................................29
第四章統計模擬與實際資料分析.......32
4.1 模擬範例..........................................32
4.1.1模型配適與參數估計....................32
4.1.2 配適不同模型之預測結果...........36
4.1.3 投資組合.......................................38
4.2 實際資料分析與預測......................40
第五章結論...........................................42
參考文獻................................................43
附錄 A. Metropolis-Hastings 演算法......49

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2009-6-25

推文