Measuring Abnormal Volatility
Implied volatility reflects systematic and idiosyncratic risk. The VIX Index captures the total risk of a portfolio containing approximately 80% of the U.S. public equity capitalization. Thus, it is a popular proxy market risk. We expect a strong relationship between the level of the VIX Index and the implied volatility of individual stocks. For an example, see the implied volatility of Valero Energy Corporation’s implied volatility in relation to the VIX Index over 100 days.
There are several applications for the identification of events that cause individual stocks’ implied volatilities to break from their relationship to the VIX Index. Forecasting events that shift implied volatility may lead to profitable options trading strategies. And the identification of corporate events that shock implied volatility can shed light on the risk implications of managerial decisions.
I start with real-world implied volatilities from over 2,800 stocks. To simulate a single event study, I randomly choose a sample of implied volatilities. Then I induce several levels of artificial shocks in terms of increasing or decreasing each annualized implied volatility in the sample. Since under normal conditions the model residuals are zero on average, we would expect a random sample of residuals to have an average of zero if there were no volatility shocking event. To test if the mean is zero I use a two-tailed T-test with a 5% tolerance level.
I repeat the random sampling and testing for 10,000 event studies and report the size-adjusted rejection rates. These rejection rates tell us how likely this event study method is to detect events that shock volatility given a certain size shock (in basis points of annualized volatility) and a certain sample size of historical observations of similar events. The plot below shows a visualization of the statistical power of this methodology.
Using this methodology with a sample size of 250, the size-adjusted power was 95.76% when there was a 1% increase in implied volatility. In other words, 9,576 of the 10,000 randomly sampled event studies resulted in rejecting the null hypothesis of volatility model residuals equal to zero. The high power of detecting volatility events with relatively small samples illustrates the potential value of the model’s standardized residuals.