Glitches, Statistics, Volatilties, and the VIX

Warning: This post has math, including Greek letters representing variables.  Known side effects range from dizziness, nausea, and vomiting to cranial explosions.  In extremely rare cases these are accompanied by a feeling of achieving the oft-talked about state of Nirvana and immortality.

As Vincent Vega would say, “that’s a bold statement.”  And thus opens a good read that Adam Warner penned at OptionsZone (emphasis is mine):

If there’s one point I’ve tried to make more than any other, it’s that the CBOE Volatility Index (VIX) is a statistic, not a stock and, as such, it behaves differently than a stock.

via A Glitch in the VIX.

Funny thing is, he’s right.  The VIX is actually calculated using some inputs and a fancy equation, which I found courtesy of the CBOE’s VIX whitepaper:

There’s a lot of stuff in the equation, and there’s a lot needed to explain and understand the variables.  But at the end of the day, the VIX is really like any other derivative security: it’s value/level is a function of expected moves in the underlying asset (or in this case, a metric) and time. Since the VIX is calculated off of near and next-near term SPX options (both puts and calls), it measures volatility by measuring the strike price range of options which have non zero bids.  So more volatile months have more active SPX puts and calls across a wider range of strike prices and quieter months have less.  So levels of put/call activity only tell you part of the story.  Dispersion among strike prices is probably just as important.

It’s important to understand because as Adam points out, you have to deal with time decay in options.  Time decay, normally referred to as theta, refers to the tendency of options to get cheaper as time elapses so theta tends to be negative.  Look at the VIX formula again and you’ll see time to expiration (T) will naturally drive the index’s value lower, because SPX options tend to have negative theta as well.  In fact, I think it’s a safe bet you could track the price of an option reasonably well using theta alone if you had low levels of volatility in the price of the underlying stock or in this case, SPX options.

One other thing: volatility isn’t one-sided.  Is a series of daily 2% moves to the upside over 5 days any less volatile than if you saw the same 2% moves down given the average daily move was +/- 0.33%?  Of course not, but we’re conditioned to fear the downside more than the upside.  It’s natural and reasonable, but we need to understand fear is an emotion – a psychological phenomenon.  In either case, volatility would show an increase.  But I bet most folks would be much more inclined to take a position on the VIX if those moves were downward rather than upward.

So now take a step back and see the bigger picture for a second.  What does all of this mean?  Well, two things come to mind.  First, when you’re talking about going long on the VIX, you’re making a broad-based directional trade on the market’s tenor/mood.  Because as an option, the natural progression in its price is to grind lower due to theta.  A stock can theoretically stay at the same price for a given timeframe, but an option can’t.  Its value is constantly being eroded by the sands of time.  So if you want to establish a long position, you’re assuming volatility in the underlying stocks is going to be high enough that you’ll want to hedge it and it will also be high enough to offset the negative theta.  Second, as a coincidental metric, it only conveys the current state of the world.  It’s not backward-looking nor is it forward-looking.  So rising VIX levels are not so much predictive as they are reflective.

That’s all for now.

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2 Comments

Filed under finance, Markets

2 responses to “Glitches, Statistics, Volatilties, and the VIX

  1. Pingback: Taking Stock of Wall Street 2008-10-13

  2. Pingback: Tweets that mention Glitches, Statistics, Volatilties, and the VIX « Deep Thoughts by Professor Pinch -- Topsy.com

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