Monday, November 10, 2008

The Spread Between the VIX and 20 Day Historical Volatility in the SPX

In the last few weeks I have received a lot of positive feedback on my posts about the VIX and historical volatility in the SPX. For those who may have missed it, you may wish to start with The VIX in the Context of Historical Volatility in the SPX and The VIX – SPX 30 Day Historical Volatility Spread and Performance.

Today Todd Salamone of SchaeffersResearch.com has a Monday Morning Outlook post in which he observes:

“We are also closely watching the behavior of the CBOE Market Volatility Index (VIX – 56.10) from 2 perspectives. First, the VIX continues to trade at a steep discount to the SPX's 20-day historical volatility, which has begun to level off just above 80% during the past few weeks. Our interpretation of this development is that there is little fear of another major setback in the market. Typically, such fear leads to major market bottoms. If fear and panic were elevated, the VIX would be trading above the actual volatility of the SPX.

Second, we are keeping an eye on the 44-45 area in regard to the VIX. We think this area is important, as it marked last week's low, and represents the VIX's "half-high" achieved on October 24. Moreover, this area is currently home to the VIX's rising 50-day moving average.”

While both points are interesting ones, it is the historical volatility piece that I wish to comment on here. Starting with some history, since 1990 the VIX has traded above the 20 day historical volatility of the SPX over 90.6% of the time, often in an uninterrupted fashion for months on end. The fact that the VIX is above 20 day historical volatility, therefore, says very little about elevated levels of fear and panic.

In the chart below, I have plotted the VIX minus the 20 day historical volatility in the SPX (expressed as a percentage of the VIX) from 2007 through Friday. In the chart, it is evident that when the VIX-HV is high, this generally tends to coincide with short-term bottoms in the SPX. The low levels of VIX-HV are not as easy to decipher. The two most dramatic VIX-HV lows on the chart both occurred after a low in the SPX and coincided with a several month uptrend in the SPX.

In the current environment, I would consider Tuesday’s record low in the VIX-HV ratio to be a signal that a near-term bottom is in the process of forming. I do not, however, see the need for the VIX to trade above the SPX’s 20 day historical volatility, as it did for one day on October 27th for instance, to provide any confirmation signal.

[source: VIX and More]

6 comments:

Anonymous said...

Bill,

some statistics makes it evident that SchaeffersResearch.com's interpretation concerning fear and gread based on the delta between the VIX (index) and the SPX's 20-day historical volatility is going the right direction.

Since 02/01/1990 the average delta between the VIX and the respective SPX's 20-day historical volatility is +4.27%. During the last 252 trading days it was only 0.10% with a 7.35% one standard deviation.

What I looked for was the following:

Is there any (statistical relevant) difference and trading edge for a respective trading day on which the delta betweeen the VIX (index) and the SPX's 20-day historical volatility is at least one standard deviation below or one standard deviation above the last year's average in comparison to the any time odds that for any given trading day the SPX will close below that day's close during the next 5 trading sessions ?

I determined the number of trading days (since 02/01/1990) on which the delta betweeen the VIX (index) and the SPX's 20-day historical volatility was at least one standard deviation (7.35%) below (little fear, very low expectation concerning a further major setback) and one standard deviation above (fear of increasing volatility and a major setback) the last year's average (0.10%).

Whenever that was the case then I looked foward the next 5 trading days and checked if the SPX closed (on any of these 5 trading days) below the close of the respective's trading day (on which the delta betweeen the VIX and the SPX's 20-day historical volatility as one standard deviation below or one standard deviation above the last year's average).


Here are the results (since 02/01/1990):
delta between the VIX (index) and the SPX's 20-day historical volatility 1 standard deviation (7.35%) below/above the last year's average (0.10%):
1 SD below: 52 occurrences (trading days), thereof closing lower on at least one trading day during the next 5 trading sessions on 48 occurrences (92.31%)
1 SD above: 711 occurrences (trading days), thereof closing lower during the next 5 trading sessions on 507 occurrences (71.31%)
any time odds: 4.503 trading days, thereof closing lower during the next 5 trading sessions on 3.260 occurrences (72.40%)

1.5 standard deviation (11.02%) below/above the last year's average (0.10%):
1.5 SD below: 22 occurrences (trading days), thereof closing lower during the next 5 trading sessions on 19 occurrences (86.36%)
1.5 SD above: 126 occurrences (trading days), thereof closing lower during the next 5 trading sessions on 79 occurrences (62.70%)
any time odds: 4.503 trading days, thereof closing lower during the next 5 trading sessions on 3.260 occurrences (72.40%)

2 standard deviation (14.70%) below/above the last year's average (0.10%):
2 SD below: 17 occurrences (trading days), thereof closing lower during the next 5 trading sessions on 15 occurrences (88.24%)
2 SD above: 28 occurrences (trading days), thereof closing lower during the next 5 trading sessions on 14 occurrences (50.00%)
any time odds: 4.503 trading days, thereof closing lower during the next 5 trading sessions on 3.260 occurrences (72.40%)

That means whenever the delta between the VIX (index) and the SPX's 20-day historical volatility is at least 1 standard deviation below the last year's average the probability for a lower close during the next 5 trading sessions is much higher than the any time odds (currently at 92.31%), while for a trading day on which the delta between the VIX (index) and the SPX's 20-day historical volatility is at least 1 standard deviation above the last year's average the probability is either comparable to the any time odds or (much) lower for those occurences with 1.5 or 2 SD above (more fear).

Best regards
Frank
(it is a bit difficult to explain such a complex topic not being a native speaker)

Bill Luby said...

Well done Frank, in any language. Thanks for chiming in.

I actually have similar data and similar conclusions, but wasn't even going to try to shoehorn everything in to one post.

I will follow up with some additional data, charts and analysis tomorrow.

Cheers,

-Bill

valeriobrl said...

Great Job Frank, I really appreciate your comment.
Great Blog and Great comment

David Smith said...

Hi, I was just trying to re-create this study of yours and I'm wondering when you say you take the VIX minus the HV, is it simply just that? If the VIX were 45 on a day and the standard deviation of SPX for the last 20 days was 40 points, is it 45 minus 40 equals 5? Then divide that by 45 and multiply by 100 to create a percentage?

Thanks, David

Bill Luby said...

Hi David,

Yes, your assumptions about the calculations are correct.

The formula I use here is (VIX-SPXhv20)/VIX -- with the result expressed as a percent.

I should add that in calculating the historical volatility, I choose the "ditching the mean" approach. This approach assumes the mean is 0 over the long term and drops the mean from the calculations. For an index or stock that is in a strong trending mode, this provides, in my opinion, more accurate historical volatility numbers.

If it helps, this will be the subject of a post in the near future.

Cheers,

-Bill

David Smith said...

Thanks. I like the idea of using 0 as the mean to de-trend things.

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