台灣50ETF與臺灣加權股價指數關係之研究

Abstract

如果能掌握股市先機，洞悉台灣50ETF與台灣加權股價指數間的互動關係，將有助於市場上台灣50ETF的投資者，找到停利點，或減少損失。 本文主要應用ADF單根檢定、向量自我迴歸（VAR）模型，研究台灣50ETF與台灣加權股價指數的關係，資料期間區分為兩段：第一段為2007年1月2日至2007年9月29日，共計182筆，第二段為2009年1月5日至2009年9月30日，共計185筆。本研究除使用股市每日收盤價資料外，亦採取市場上常用的短期五日均線，以彌補資料過於短期的缺失。經過實證研究，可以得到以下三點結論： （一）經由預測誤差變異數分解得知，台灣50ETF及台灣50ETF五日均值外生性較強，台灣50ETF領先台灣加權股價指數，而台灣50ETF五日均值亦領先台灣加權股價指數五日均值。 （二）由衝擊反應分析中得知，台灣50ETF或台灣加權股價指數變動一標準差時，台灣50ETF在第一期時的衝擊反應最大，之後反應隨即減緩，可以發現台灣50ETF日資料，在極短期內深受自身及台灣加權股價指數的影響，也就是說若欲從中套利，投資者須眼明手快，否則將可能反遭套牢。 （三）從衝擊反應分析中得知，台灣50ETF五日均值、台灣加權股價指數五日均值變動一標準差時，台灣50ETF五日均值在第五期時衝擊反應最劇烈，故當台灣50ETF五日均線或台灣加權股價指數五日均線，在趨勢上有所變動時，投資台灣50ETF者，須留意短期投資方向的正確性，以減少損失；值得注意的是，在金融海嘯發生後，台灣50ETF五日均值在第二至第四期時，衝擊反應變動較在金融海嘯發生前大，意味著金融海嘯發生後，台灣50ETF五日均值與台灣加權股價指數五日均值的結構關係有所變化。

It is helpful for those who invest Taiwan 50ETF in the stock market to find the Stops the Favorable Spot or decrease the losses if they can predict the development of the stock market and understand the interactions between Taiwan 50ETF and the Stock Index. The main purpose of the present study is to apply Augmented Dickey-Fuller Test and Vector Autoregression Model (VAR) to investigate the relationships between Taiwan 50ETF and the Stock Index. The processes of data collection were divided into two periods: (1) the first was 182 in total from January, 2nd to September 29th, 2007; (2) the second was 185 in total from January, 5th to September 30th, 2009. To complement the flaw of the short-term data collection, the present study analyzed the data of daily closing price as well as short-term five daily average lines often used in the stock market. Results are shown as follows: First, by forecasting Error Variance Decomposition, the exogenous of Taiwan 50ETF was as strong as that of Taiwan 50ETF five daily average value, Taiwan 50ETF exceeded Taiwan Stock Index, and Taiwan 50ETF five daily average value was also higher than the five daily average value of Taiwan Stock Index. Second, by Impulse Response Analysis, when the figures of Taiwan 50ETF and the Stock Index changed up to one standard error, Taiwan 50ETF in the first period was influenced the most. After that, the impact gradually decreased. It was found that the data of Taiwan 50ETF was deeply impacted by itself and the Stock Index. That is, if investors want to get profits from it, they have to make decisions quickly; otherwise, their investment might be locked up. Finally, from the results of Impulse Response Analysis, as five daily average values of Taiwan 50ETF and the Stock Index changed up to one standard error, five daily average values of Taiwan 50ETF in the fifth period reacted the most violently. Thus, when five daily average values of Taiwan 50ETF and the Stock Index alter, the investors should pay attention to correct short-term investment to avoid losses. It is worthwhile to know that after the economic decline, five daily average value of Taiwan 50ETF in the second and fourth periods made changes a lot before it. It implies that the structure of the five daily average values of Taiwan 50ETF and the Stock Index varied in the wake of the economic depression.