美股指數變化與台股指數波動之關聯性研究－GARCH族模型之應用

A Study of the Relationship between Changes in US Stock Indices and the Volatility of the Taiwan Stock Index-An Application of GARCH Family Models

薛舜仁(Shun-Jen Hsueh)

《立德學報》 6卷2期 (2009/06) Pp. 6-17

https://doi.org/10.7080/JLU.200906.0006

摘要

本研究之貢獻主要在探討台灣加權股價指數報酬率波動是否會受到前一日美股道瓊工業指數變化量及那斯達克指數變化量的影響，研究發現，在我們的研究期間美股變化對台股指數波動性是具顯著性，且每當任一指數之變化量達一個標凖差時，透過條件變異數產生對報酬方程式之風險溢酬，換算出今日之股價指數對於昨日來說會約有2%左右之變化量，顯示此二種美股指數變化量對台股指數報酬率影響程度相當具有指標的參考價值。
此外，我們利用GARCH族之六種模型來加以討論，發現以GJR-GARCH-M(1.1)及EGARCH-M(1.1)模型對我國股市解釋能力最佳，且我國股市報酬率變動具有顯著的「貢桿效應」(leverage effect)，壞消息對指數波動性的衝擊遠大於好消息。

關鍵字

指數波動性 ； 風險溢酬 ； GJR-GARCH ； EGARCH ； 槓桿效應

並列摘要

This study examines whether the volatility of the return of Taiwan Stock Index will be affected by the changes of the preceding day's American Dow Jones Industry Index and Nasdaq Index. We find that in the data period the changes of the above two US stock indices impact significantly on the volatility of the Taiwan Stock Index, and when any above US index has a change of one standard deviation, via the contribution of the risk premium of conditional volatility, it will produce about a 2% change in the Taiwan Stock Index. This indicates that keeping track of these two US stock's indices is very valuable while making short-term investment decisions in Taiwan's stock market.
In addition, we use the following GARCH family models to explain the performance of Taiwan Stock Index, including GARCH(1,1), GARCH-M(1,1), GJR-GARCH(1,1), GJR-GARCH-M(1,1), EGARCH(1,1), EGARCH-M(1,1). The results suggest that GJR-GARCH-M(1,1) and EGARCH -M(1,1) can explain well the performance of the Taiwan Stock Index. We also find the volatility of the Taiwan Stock Index exhibits the ”leverage effect”, which means the impact of bad news is heavier than that of good news.

並列關鍵字

Volatility ； Risk Premium ； GJR-GARCH ； EGARCH ； Leverage Effect