A Glitch in the VIX

by Adam Warner | March 24, 2010 9:05 pm

If there’s one point I’ve tried to make more than any other, it’s that the CBOE Volatility Index (VIX[1]) is a statistic, not a stock and, as such, it behaves differently than a stock. This being the case, it has quirks, one of which I call the “day of the week quirk.”

This is the tendency of the VIX to look weaker on Fridays and stronger on Mondays, even when there has been no real change in the market’s assessment of volatility.

This happens because traders tend to lower their bids ahead of weekends and/or holidays to avoid needlessly paying for time decay. This gives the illusion of a drop in volatility, but a better description would be a forwarding of the calendar.

Likewise, when traders return from a weekend and/or holiday, the calendar has caught up to the dollar price of the option, giving the illusion of a lift in volatility that is especially pronounced near the open. In reality, though, volatility assumptions stayed the same.

Confused? OK, let me explain by walking you through a hypothetical VIX calculation.

The VIX is an estimation of the 30-day volatility of a hypothetical at-the-money (ATM) S&P 500 (SPX[2]) index option. The formula is based on the volatility of options in the nearest one or two expiration cycles depending on where we are in the cycle.

For ease of illustration, let’s say we concoct the VIX number based on the volatility of one option, the closest to the money strike, with 30 days until expiration. To simplify things, we’ll continue to use just this one option to create our hypothetical VIX, even as we approach expiration. And to make things really easy, we’ll say this ATM call option trades for $30.

Now, an option is a decaying asset that decays in exponential fashion, i.e., the daily decay will grow each day as it gets closer to expiration. So perhaps it’s worth 40 cents less tomorrow than it is today, then 50 cents less than that the next day, and so on. But again, since we’re trying to make this easy on ourselves, we’ll say the option will lose $1 every day, for 30 days.

So tomorrow, if SPX has not moved, and volatility remains exactly the same, the ATM option now has a value of $29. So our concocted VIX in this example stays the same. Let’s say it’s at 20.

To recap: Today is Wednesday, there are 30 days to go until expiration, the call opens the day at $30, and volatility as measured by our pretend VIX sits at 20.

If nothing happens, and volatility stays the same, the option will have less value on the close than it does at the open, as it now has one less trading day until it expires. At tomorrow’s open, all things being equal, it’s worth $29.

Of course, there’s some risk of an overnight gap, so it will trade somewhere between $30 and $29, but for argument’s sake, let’s say there’s not much fear of an overnight move, so it’s very close to $29.

Our concocted VIX calculation still thinks there are 30 days to go until expiration, though, so when it calculates the volatility of the option, it will think it’s something less than 20 (we’ll call it 19.5). But have volatility assumptions really declined that much?

Nope. It’s just a quirk. Options buyers see one fewer day until expiration and lower their bids accordingly so as to not pay more for overnight decay than they need to. (One thing to note: The real VIX calculates volatility based on minutes until expiration, not days, so its clock has forwarded about one-quarter of a day at this point, so I’m overstating the error in this example.)

The following day, the SPX is exactly the same price, but the option opens at $29. so the volatility that “closed” the night before at 19.5 has “re-opened” at 20. But, again, there’s no real change in volatility assumptions. I would strongly suggest that real volatility never moved, yet to the untrained eye, it dipped .5, then rallied back to 20.

That’s just an overnight glitch. What if instead of Wednesday, it’s Friday? On Fridays, a trader faces not one overnight, but three, before the SPX trades again. Instead of the option dropping from $30 to almost $29, it might drop from $30 to near $27. But the calendar still says Friday. If on Friday, the concocted VIX calculator sees 30 days until expiration, and a price of about $27, it will think volatility has dropped maybe 1.5 points, to 18.5.

When you return on Monday, the option is at $27, and there are only 27 calendar days until expiration. Our concocted VIX has “rallied” back to 20, but, again, real volatility assumptions never budged. The notion of a volatility rally is an illusion.

Now, this is a simplistic and extreme example. I’ve basically zeroed out every variable except for calendar time. And the real VIX adjusts for this quirk modestly by using minutes instead of days to measure the time an actual option has until expiration.

But the dynamic I laid out here is quite real, and this is why there is the illusion of a drop in volatility on Fridays and a lift in volatility on Mondays.

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Endnotes:
  1. VIX: http://optionszone.com/getaquote/?STOCK_VAR=vix
  2. SPX: http://optionszone.com/getaquote/?STOCK_VAR=spx
  3. download his FREE trading guide here.: http://investorplace.com/order/?sid=OT3248

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