The VIX is low...

This is relevant to my MBA students who currently have an assignment on implied volatility:

The VIX has declined steadily over the past few months, and at the same time, stocks have rebounded.  

From the graph it appears that the VIX is quite negatively correlated with the S&P 500.  Something that is pointed out here and here.  

I decided to grab some data from yahoo finance and look at the correlations.  First of all if you just look at the raw correlation of the VIX and the S&P 500 from 1990 you get a small positive correlation of about 0.14.  However, if you look at the daily change in the VIX and the change in the level of the index, the correlation is -0.57.  That's a pretty large negative correlation.   

What is unclear, of course, is what is causing what?  Is higher volatility hurting prices or is that falling prices increases volatility?  An obvious thing to look at is the correlation between the prior day change in the VIX and the current day change in the index.  Not surprisingly, this correlation is close to zero indicating that there isn't a simple trading rule.  (If there was, do you think I'd blog it?)

Still, the VIX is a pretty interesting index.