VIX指數之動態相關性與預測能力研究

Abstract

本文主要是應用Engle（2002）提出的動態條件相關係數（dynamic conditional correlation, DCC）模型，探討S&P 500股價指數與波動率指數（VIX）之間的關係。實證結果顯示S&P 500股價指數與VIX指數之間具有明顯的動態負向關係，處於波動率高的期間，兩者之間的負向相關係更為明顯。另外，結果也證實兩者之間具有不對稱性關係，也就是說VIX指數在S&P 500指數下跌時的變化量大於S&P500指數上漲時的變化量，且在低波動率時期，不對稱效果更為明顯。接著，探討波動性指數是否能夠做為股票市場的買進及賣出訊息，我們發現波動率為相對低點時（波動率低於5%與10%個樣本值時），持有股票的報酬率大致為正的，只有在極端的情況下（波動率在低於1%時），投資人短期持有才為負報酬；而在波動率為相對高點時（波動率高於90%、95%及99%個樣本值時），在持有短期至中期的報酬率均為正的，顯示高波動率時期對投資人而言，應採取買進持有的策略；相反的，在波動率較低的時期，只有在極端的情況下，投資人應該進行賣空股票的策略。

This study provides dynamic time-varying viewpoint by using the Dynamic Conditional Correlation (DCC) model of Engle (2002) to estimate the time-varying correlation between volatility index and stock index and we also investigate the relationship during four distinct sub-periods which pertain to different trading environments. The empirical analysis shows that there is a strong negative relationship between the returns of VIX and S&P 500 index and the negative correlation is stronger in high-volatility trading environments than in low-volatility markets. In addition, we demonstrate that there exists an asymmetric relationship between returns of VIX and S&P 500 index, and the VIX returns’ response to negative S&P 500 index returns is sharper in low-volatility periods. Subsequently, we examine whether VIX can identify buying or selling opportunities in stock market. A “sell signal” just occurred when the VIX level is extremely low. On the other hand, high or very high VIX levels indeed over-sold markets and hence can be viewed as short-term to middle-term “buy signals”.