In last weekend’s issue of Barron’s, the “The Striking Price” column headlined “VIX Signals Many 4% Daily Moves” certainly caught my eye.

In the column, Steven Sears begins:

It's the best of all possible worlds for long-term investors—even as options on the market's "fear gauge" are priced as if the S&P 500 will move about 4% each day into November.

I think that’s just plain wrong. Even if we take last week’s highest VIX reading of 43.87, a daily move in the S&P 500 of 4% would not be uncommon, but I don’t think anyone really expects that to happen every single day.

## The VIX: Implied standard deviation

Every so often you read or hear that the VIX “implies” a move of some specific percentage, but it’s rarely put in context of what the VIX represents.

The VIX measures implied volatility, of course, but that’s pretty much the same thing as saying it represents an implied standard deviation.

Here’s how it works: To calculate volatility you simply find the standard deviation of a set of daily price changes. Then multiply it by the square root of the number of trading days in a year (~15.87) to get “annualized volatility.”

But that’s for actual historical data. What the VIX is supposed to represent is a consensus on what that same calculation might look like one month from today. So just work backwards. Take the VIX and divide it by 15.87 and you get the expected standard deviation.

So a VIX of 43.87 divided by 15.87 gives us a standard deviation of 2.76%. If returns fit a normal distribution, we can expect daily moves of 2.76% or less 68% of the days and moves of twice that level about 95% of the days in the time period.

Here’s what that looks like for a VIX of 43.87 as compared to three months ago when the VIX was at 19.05.

But there are a few caveats. First, market returns usually don’t fit into a neat little bell curve – at least in the short term. Plus, any one month contains only 21 or 22 trading days. That’s a not a very large sample size. Plot a histogram of most one-month time periods and you’ll rarely see anything that looks like a bell curve.

Still, the move that’s predicted by implied volatility of any stock or index is based on expected standard deviation. If that standard deviation is 4%, that only means such a move would not be unusual, not that it will happen most days.

## The VIX of the VIX

What I think Steven Sears could have been referring to was *not* the implied move of S&P 500 option prices, but the implied volatility of options on the VIX itself.

Could the VIX move 4% every day. Now *that’s* certainly possible (although I wouldn’t say highly likely). Over the past year the VIX has moved up or down more than 4% per day more than half of the time. Since August 1, it’s gone up or down more than 4% on 64% of the trading days.

The implied volatility of options on the VIX (a “VIX of the VIX” so to speak) on a 60-day basis is roughly 95% as of Friday. Divide that by 15.87 and you get a standard deviation of 6% or so – or a curve like this.

With that kind of expected standard deviation, sure, I could see a chance the VIX could move by 4% a majority of the days into November. But the S&P 500 itself? That’s unlikely. Even in late 2008 when the market collapsed, those 4%+ moves were common, but they still occurred on less than one out of three trading days.

Look, I think you could see the S&P 500 moving far more than 4% on any *one* given day, but that’s far different than expecting that move *every* day.

Besides, the “VIX of the VIX” can often be more than 100%, and rarely dips below 50% as this chart shows:

Everyone will interpret the VIX and the implied volatility of the VIX itself in a different way -- and that's fair. But I disagree with Steven as I predict 4% moves in the S&P 500 will be the exception, not the rule.

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