Yesterday I offered up some numbers to help describe the relationship between daily moves in the SPX and the VIX. I hear quite a few observers comment along the lines of “the SPX was up(down) X% and yet the VIX was only down(up) Y%.” Typically, the next action is to wonder aloud whether the corresponding VIX movement is ‘normal’ and whether any divergences might provide clues about the future direction of the markets.
Naturally, I’ll take the easy part of that equation first and offer the reader two ways to look at this. The graph below plots daily percentage changes in the VIX against daily percentage changes in the SPX. From the graphic, you can see that the relationship between the two is fairly linear for a SPX moving +/- 1.5% in a day. Once the SPX moves outside of those bounds, however, the equations get a little messier. Part of this, of course, is the accelerating fear factor that comes with extreme market moves.
The next graph ignores the absolute numbers and focuses on the magnitude of the typical VIX movement versus the SPX movement. Readers are encouraged to ignore the valley around the zero (where strange things happen when you try to divide by zero) and focus instead on the fairly predictable ratio of the VIX to SPX that varies from about -2.5x to about -5.0x, depending upon the daily change in the SPX.
As for the remaining question about whether divergences from the normal relationship provide reliable clues about the future direction of the market, I am going to address this more difficult question over the course of the lifetime of this blog. I will offer this though: if I think I can simplify the answer in one concise post, I will do the best I can to communicate my thinking here.