The purpose of this paper is to examine what happens to the variance of individual stocks forming the Dow Jones Industrial Average (DJIA) allowing for aggregate uncertainty measured by VIX, the “fear gauge index” of US options contracts. In examining each individual stock belonging to DJIA in 2011, the authors reconsider aggregate market uncertainty (VIX) as the mixing variable. In contrast to studies on the effects of VIX on the aggregate equity market, the data set used in this paper allow a further look at the proposition that market aggregate uncertainty should have varying impact on individual stock variance.
GARCH-M models estimate individual stock returns belonging to the DJIA in 2011 on its lags and on the ARCH-M term in the mean equation linking stock returns to the variance equation. The longest time span has 5,738 observations for most stocks under daily frequency from January 3, 1990 to December 30, 2011. The authors use one lag for the VIX2 term to address simultaneity problems in the variance equation. In order to allow for interactions between volatility and business cycles, the authors include a dummy variable for the three recessions identified by the NBER over the period.
Adding the “fear gauge” VIX index and a dummy variable for recessions to the variance equation in GARCH-M models, the VIX coefficient always increases variance and the recession dummy has mixed effects. Overall, VIX acts as expected as mixing variable. Supporting the mixture of distribution hypothesis, the impact of VIX is always positive (1.039 on market variance) and GARCH effects vanish completely for the index and almost as much for 24 stocks.
In theory, the effects of VIX on stock variance should be positive and statistically significant, together with reductions of GARCH persistence. The authors find this to be the case for the aggregate stock market and for 24 out of its 29 DJIA stocks. The authors leave for further work extensions to estimating the variance equation for companies very exposed to idiosyncratic changes, such as oil price fluctuations or stock buybacks. The implication of this research for the academic or financial community relies on the estimation of VIX effects on individual stock variance, controlling for business cycles.
Due to its benchmark in equities, stocks in the Dow Jones Industrials make it a very interesting case study. This paper reconsiders the aggregate uncertainty hypothesis for two main reasons. First, the financial press and traders keep a very close track on the daily evolution of VIX. Second, recent research emphasizes the formal predictive power of VIX in US stock markets. For the variance equation, existing works report positive values for the VIX-coefficient on the S&P 500 index but they have not examined individual stocks as the authors do in this paper.
JEL Classification – G12, G14
The author acknowledges very helpful comments from two anonymous referees of this journal, Don Johnson (the editor), JaeHan Koh, and Thanh Ngo. Javeria Farooqi and Khoa Nguyen provided able research assistance in different stages of this research project. The usual disclaimer applies.
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