臺灣博碩士論文加值系統

國內已有許多學者以偏態係數或常態檢定，來驗證金融資產之報酬分配是否為常態分配。極值理論主要是用來探討尾部分配的型態，藉此了解金融資產極值分配的型態和極端行為，近年來在財務領域上之應用，十分廣泛。本文旨在利用極值理論以驗證國內台股指數是否為厚尾分配（Fat-Tailed Distributions）；亦即本文以高斯-牛頓法（Gauss-Newton Method）求算非線性迴歸模型中，所需估計極值理論之三種參數，並且檢定左右尾部指數是否符合常態或厚尾分配；為了克服樣本可能過少的問題，本文採取1996年至2006年共11年之台股指數日報酬率作為樣本，以克服樣本數不足將會降低極值分配的近似效果與模型中各種參數估計的精確度之問題。此外本文利用估計所得之尾部指數來建構投資組合，並與大盤之投資績效作一比較。實證結果發現利用極值理論所估算出之尾部指數，指出國內股價指數為非常態分配，其符合厚尾的Frèchet分配。此外利用兩種尾部指數估計法所建構之投資組合績效，均能擊敗股價指數。

The assumption that financial asset’s return follows the non-normal distribution is confirmed by many studies. However, there is no direct evidence pointing to a (Fat-Tailed Distributions) in Taiwan market index. In this study, the extreme value theory is employed to calculate the tail index of Taiwan weighted stock index. The left and right tail indices were examined to determine the distribution type and then to check whether they follow normal or Frèchet distribution. Additionally, Gauss-Newton method is used to obtain the three parameters required in estimating the extreme value theory in a non-linear regression. It is known that a low sample number would cause a decrease in the reliability of extreme distribution as well as a decrease in the precision of the estimation of parameters. To overcome this problem, a total of eleven years (1996-2006) of data were analyzed. Finally, we examine the issue whether the performance for investment portfolio based on tail indices has better performance than the market index.
The empirical results indicate that both extreme value theories (BMM and POT) have confirmed the Taiwan market index has a non-normal distribution. Additional tests also indicate that it follows the Frèchet distribution. It also shows that the investment portfolios based on either type of tail index can provide better investment performance than the market index.

目錄

摘要 i
Abstract ii
誌謝 iii
表目錄 v
圖目錄 vi
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 4
第三節 研究架構 4
第二章 文獻回顧與探討 6
第一節 風險值模型介紹 6
第二節 極值理論相關文獻 7
第三節 尾部指數介紹 12
第四節 傳統投資組合 15
第五節 考慮風險值後之投資組合 15
第三章 研究方法與模型 17
第一節 極值理論模型 17
第二節 參數求解 24
第三節 檢定估計法 26
第四節 建構投資組合 28
第四章 實證結果分析 30
第一節 資料描述與基本統計分析 30
第二節 尾部指數估計與檢定 34
第三節 建構投資組合 37
第五章 結論與建議 42
參考文獻（References） 44
附錄 高斯-牛頓法 49

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