穩定分配與幾何穩定分配在財務金融之運用

Stable Distributions and Geometric Stable Distributions in Financial Applications

姚任鴻(Ren-Hong Yao)

指導教授 ： 葉小蓁

國立臺灣大學/管理學院/財務金融學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201701173

摘要

對於金融資產的報酬，我們常假設其為常態分配。然而，許多文獻指出，多數金融資產報酬率之分配具有厚尾的特性，也就是極端事件發生的頻率和大小比常態分配所描述的現象更高。此外，文獻亦指出資產之報酬率有可能受到重大消息影響，而產生結構改變。因此，穩定分配和幾何穩定分配可用於替代傳統上使用常態分配的假設。本篇論文的研究分為兩部分，第一部分比較以常態分配，穩定分配與幾何穩定分配來配置台股指數，三大權值股，及三外匯之報酬率的情形；第二部分則建立以三大權值股報酬率為因變數，台股指數報酬率為自變數之迴歸模型，比較以常態分配與拉普拉斯分配來配置誤差項的情形。本篇論文主要的發現是對於這些資產的報酬率，比起常態分配和穩定分配，幾何穩定分配的確更適合描述它們的行為，代表台灣股市及外匯之報酬率如文獻所提，不但具有厚尾之現象，更會出現結構的改變。而對於市場模型及資本資產定價模型，雖然迴歸模型誤差項的假設並不影響貝他值的估計，但進行統計推論時可能因為常態誤差的假設而低估了它們的標準差，因此讓投資人低估了持有金融資產的風險。

關鍵字

穩定分配 ； 幾何穩定分配 ； 拉普拉斯分配 ； 相關係數 ； 科摩哥洛夫-史密洛夫檢定

並列摘要

For the returns of financial assets, we used to specify that they follow normal distributions.However, researches indicate that most of them possess fat tail properties, say both the frequency and size of extreme events are greater than normal ones. Furthermore, studies shows that their return may be affected by big news in the market; that is, there may be structural changes.Hence, the stable distributions and the geometric stable distributions may be used to replace the normal distributions. The paper is devided into two parts. First, we compare the goodness-of-fit of the normal distribution, stable distribution, and the geometric stable distribution to the TWSE index, top three individual stocks in Taiwan and three foreign exchanges. In the second part, we regress the return of top three individual stocks in Taiwan on the return of TWSE index and compare the performance of Normal errors and Laplace errors. Our main finding is that among all the assets, the geometric stable distribution best describes their behaviors, which implies there are fat tails and structural changes in the market. As of the market model or the CAPM, the distribution of the error term does not affect the estimation of beta coefficient; however, when we are making statistical inferences, the normality assumption may underestimate the standard deviation and thus underestimate the risk investors bore.

並列關鍵字

stable distribution ； geometric stable distribution ； Laplace distribution ； correlation coefficient ； Kolmogorov- Smirnov test

參考文獻

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