The VIX tends to spike when equity markets take a downturn. Is this just because of the way participants in the options markets think? Perhaps it is because increases in equity volatility empirically tend to be associated with increases in downside volatility.
Here is a chart that shows the S&P 500, a measure of volatility, and a measure of upside vs. downside volatility. The two lines tend to move in opposite directions.
Update: Eyeballing a chart of the covariance shows up instances where equity volatility and upside volatility look to have risen together: Oct 08, Oct 02, Apr 01, Mar 00 (and Feb 91, when I don’t think there was a VIX). I don’t have VIX data — can anyone see what it did in those periods?