SPX vs. VIX: When Indices Attack

By Adam Warner Mar 13, 2009 9:05 am

Steering clear of an unusually volatile relationship.



So let's say, hypothetically, that we have a down day in the market. I know, I know - sounds far-fetched. But remember back, oh, last week? It happened quite often.

Now, let's go all Vantage Point. One observer, sitting at home, looks at the VIX and sees it lift all day, close high, and last. His conclusion? Fear has increased.

The other observer -- a guy standing in the SPX options crowd -- trades all day. He notes that, despite the decline in the market, the volatility on the board hasn't budged.

Now how can that be? The VIX is an index that measures volatility on the SPX. One of them must hit happy hour a bit earlier than announced.

But guess what? They're both correct. And it all ties into the months-old question we get asked every day: Why the so-so VIX in the midst of what was, until recently, an incredibly ugly market?

Edward K. Tom, a Credit Suisse derivatives strategist, has a report out this week, covered nicely by Stephen Sears in Barron's, and it brings this to light, among other salient points.

The inverse relationship between VIX and SPX has much to do with the skew of the options board and the formula used in any volatility calculation. What I mean is, in normal skew, the lower the strike, the higher the volatility. And the closer to the money, the more weight that strike has in the volatility calculation.

Ergo, a decline of the SPX, in and of itself, will, in the very short term, produce a higher VIX reading, even if the volatility of each and every series remains unchanged, as the trader observed above. It's simply a function of lower strike/higher volatility options now closer to the money, and greater weight in the volatility calculation.

Over time -- perhaps as soon as that afternoon, perhaps not -- the board will often adjust, and the "new" ATM strikes will trade at the same volatility the old ones did yesterday.

Now, the SPX has obviously declined an awful lot this year, but there hasn't been much move in the VIX. Why? As per Tom, the VIX will adjust over the course of a month or so, via the process laid out above. What that implies, is that over the course of time, an SPX of a given value won't couple with a specific VIX. Or, in his words "...the S&P 500 can be at 700, and VIX could be at 50, 100, or 20, without any sense of incongruity whatsoever."

That's kind of what we've seen. A walk-down and gradual readjustment of the options board to the new absolute price levels.

And you know how I've said endlessly that the VIX has simply reflected "realized" (historical) volatility, which is just not as high now as it was in the fall? Well, guess what: His report agrees. 94% of the decline in the VIX (from the fall highs) can be explained by the drop in realized volatility.
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