I have always wanted to use the word "mysterious" in an essay title, and this week it finally roughly fits!

A fascinating and mysterious daily anomaly occasionally occurs in the celebrated VIX Implied Volatility Index. It is always quite odd to witness in real-time as it occurs, and it never ceases to leave me puzzled when I see it. I am not alone either, as even though these anomalies are rare whenever one spawns I inevitably receive e-mails from other speculators around the world sharing my curiosity at the event.

With several of these odd VIX anomalies transpiring in recent months, an amount that kind of intuitively just felt like a high frequency, this week I would like to take a look at this strange phenomenon, which I call VIX Divergences.

Anomalies are always interesting in the financial markets. The entire art of speculation rests on the idea, which sometimes works and sometimes doesnt, that past market performance can yield valuable clues about future market direction. Whenever apparent anomalies arise, speculators have to decide whether they may have predictive power or not.

An anomaly with apparent predictive power can be extremely valuable to speculators. If the markets generally usually do one particular thing after an anomaly transpires, speculators can trade accordingly in the future whenever that particular anomaly spawns again. On the other hand, the vast majority of market anomalies generally lack any predictive power. They are probably the product of essentially random market factors that simply do not grant a speculation edge to those who observe them.

Are these mysterious VIX Divergences the precious predictive kind of anomaly, valuable to speculators, or the random kind, essentially useless to all but the fanatical market nerds like me interested in arcane market trivia? In order to gain an idea of which way the VIX Divergences would slide on the grand predictive/random scale, we allocated some research time this week to investigating this curious phenomenon.

In order to understand the VIX Divergences, you first have to understand the VIX itself.

For over a decade now, the celebrated and widely followed VIX has been the implied volatility index for the elite S&P 100. Implied volatility refers to the index's calculation methodology, which is rather complex and involves computing what the volatility would be on a hypothetical 30-calendar-day at-the-money OEX (S&P 100) index-options contract. The math behind the VIX is pretty intimidating, but fortunately speculators don't need to understand the calculations in order to actually use the VIX in their own trading.

At a practical level, the VIX is in effect the de facto "fear gauge" for the US equity markets. When investors and speculators are scared, they tend to get frightened into trading more and volatility, along with the VIX, soars. When investors and speculators grow complacent and content, they tend to trade less and volatility, and the VIX, withers.

Therefore the VIX is extremely useful to contrarian speculators looking to trade opposite of the thundering herd, as I have documented in many past essays including "Trading the NASDAQ Bust 2" and "Trading the Relative VIX 2". A really low VIX often signals a major interim top in the markets, the very time to sell long positions and throw short. Conversely a very high VIX virtually always signals a major interim bottom in the markets, the ideal moment to close short positions and throw long.

On an interesting side note, I would be remiss to fail to mention that just this past Monday, September 22nd, the VIX calculation methodology was changed substantially by its custodian, the venerable Chicago Board Options Exchange. This is big news for index speculators!

Now instead of being based off of the S&P 100 (OEX), going forward the VIX is now the implied volatility index for the entire S&P 500 (SPX), of which the S&P 100 is a massive subset. In addition, the range of options strike prices included in the actual VIX formula has been broadened, and individual options used as formula ingredients will now be weighted based on their distance from true at-the-money options. Options closer to being at-the-money will have a higher weight than those farther out-of-the-money.

It all sounds complicated, and it is, but at this stage in the game I suspect the changes will not materially affect the usefulness of the VIX for speculators. The S&P 100 stocks, the index for the original VIX, currently run about 70% of the market-cap of the entire S&P 500, the subject of the new VIX, so the original VIX already reflected the most important 70% of the new VIX. The benchmark SPX is a more relevant index for speculators than the OEX anyway, and the new VIX ought to better reflect its prospects.

That being said, only time and research will tell if the new VIX proves to be as useful to speculators in real-time as the original VIX has been. We are going to be watching the new VIX closely at Zeal, along with the original VIX which will now be calculated going forward under the symbol VXO. All speculators who use the VIX in their trading really need to go read the CBOE's original announcement in order to gain a basic understanding of what the new VIX just introduced this week truly entails.

Back to the task at hand, thankfully the anomalous VIX divergences are far easier to understand than the VIX calculation methodology.

Because the VIX is effectively a proxy for general sentiment in the markets, it tends to move in lockstep opposition to the major indices. Whenever the stock markets are up, people grow complacent and fear wanes. This leads to a lower VIX. So the vast majority of the time, if the Big Three US stock indices are up, then the VIX will close lower on that particular trading day.

Conversely when the major stock indices slide lower, fear gradually begins to grow and fester within investors and speculators. Folks start getting scared and increase their trading, which vaults up volatility and leads to a higher VIX. Once again in the vast majority of the time, if the Big Three US indices close down odds are the VIX will head higher on that particular trading day.

This usual inverse relationship between the stock markets and the VIX is well known and heavily studied. The anomaly of the VIX Divergences arises when this relationship breaks on a material change in the stock indices. For example, what if the US stock markets and VIX are both up or both down by material amounts on the same trading day? These rare days do indeed occur and are the perplexing VIX Divergences!

In order to research these VIX Divergences, we used the S&P 500 as a proxy for the US stock markets as a whole. The S&P 500 is the flagship US index as well as the most important one on Earth, and its massive market cap encompasses the majority of the entire US equity-market capitalization.

Next we had to decide on what kind of move we would consider to be relevant in the S&P 500 on a daily basis, a threshold for uncovering VIX Divergences. Certified Public Accountants use a concept called materiality, the idea of ignoring small variations unless they reach a certain threshold that would make them meaningful to a financial statement as a whole. Since I originally hail from that strange CPA world, the many esoteric teachings of accountancy still ricochet around my skull.

As active speculators, my team at Zeal and I generally consider any single-day change of under 1% in the equity markets to be immaterial, not important. Internally, if the markets are either up less than 1% or down less than 1% on any given trading day, we call them unchanged. A sub-1% move most often seems to be purely random, attributable to general market noise, without much bearing on major trends in progress.

I decided to carry our practical 1% daily materiality threshold from speculating into our research this week. As such, for the purposes of this essay a VIX Divergence only occurs when both the S&P 500 and the VIX move by 1% or more in the same direction on the same trading day. If either the S&P 500 or VIX moved by less than 1% on any trading day, or they moved in different directions, that day could not be considered an official VIX Divergence.

We sub-divided these divergences into two categories, positive and negative. A positive VIX Divergence occurs when both the S&P 500 and VIX close more than 1% higher on the same trading day. A negative VIX Divergence is witnessed when both the S&P 500 and VIX close more than 1% lower on the same trading day.

How often do these VIX Divergences occur? We chose to initially limit our focus to the Great Bear market period since 2000 in this essay. The graph below shows positive VIX Divergence dates in green and negative VIX Divergence dates in red. These VIX Divergences are indeed rare events and it is no wonder that they leave speculators in awe and amazement when they transpire.

As you can see above, there have been exactly 13 VIX Divergence days since 2000, 6 positive and 7 negative. For reference there are 935 trading days shown in this chart, so a VIX Divergence day has only been witnessed 1.4% of the time in our Great Bear market to date! I don't know about you, but a 1%ish occurrence of these odd anomalies is pretty darned rare in my book!

Of these 935 trading days since 2000, there were 403 days when the S&P 500 moved by more than 1% in either direction, 776 days when the VIX moved by more than 1% in either direction, and 380 days when both the SPX and VIX had absolute daily moves greater than 1%. Of the SPX absolute 1% move days, 53% were down. Regarding the VIX absolute 1% move days, 52% were down.

Of course in a Great Bear market we would expect the majority of 1% absolute move days in the SPX to be down, since there is a prevailing bearish downtrend, but then the majority of the VIX 1% absolute move days should probably be up due to the usual SPX/VIX inverse relationship. This wasn't the case in the actual data though. VIX 1% down days were slightly more common than VIX 1% up days, kind of strange in a Great Bear market.

I suspect this is due to the asymmetric nature of the VIX. While it generally falls towards complacency slowly over time, fear often ignites rapidly as a stock-market waterfall decline accelerates. On the graph above the massive VIX spikes showing widespread popular fear soar into the heavens from nothing, towering spires on the chart. This rapidly ignited fear bleeds off slowly though, leading to more material VIX down days than up days.

Now if all these numbers haven't put you to sleep yet, you are probably noticing a pattern. If these VIX Divergences are truly random, meaningless market noise that lacks a predictable future-activity quality, the distribution should be about equal. After all, markets can either go up or down and a random distribution of days would yield about 50/50 up days and down days, right?

On our grand predictive/random scale I mentioned in opening, the raw stats seem to lean towards the pure random side. Out of 13 VIX Divergences since 2000, roughly half are positive and half are negative. In addition, also about half of the SPX and VIX absolute 1% days are up and half down, farther exacerbating the sense of randomness. An even distribution of positive/negative VIX Divergences does not look hopeful in terms of speculators being able to actually successfully deploy future trades based on these rare days alone.

So can we throw these VIX Divergences out as meaningless trivia? Maybe, but upon closer visual examination they offer even more insight than their underlying statistical distribution would suggest.

For example, if you examine the 13 VIX Divergence dots on the chart above, all but 2 are above the S&P 500 line. They tend to occur at higher points in the SPX, or observed another way, they generally tend to occur when the index is poised for a pullback or outright waterfall decline. The 8/13/2002 red negative divergence dot, by the way, really should appear above the SPX line as it happened when the index was trading near 885, far above the July 2002 interim lows under 800.

So out of these 13 VIX Divergences, 12 occurred near higher points or times preceding a significant decline in the S&P 500. The only outlier that truly occurred on an interim low was the negative VIX Divergence of 9/21/2001, which transpired on the V-bounce low only weeks after the 9/11 attacks. On that peculiar day of market history the S&P 500 fell by 1.9% to carve a new interim low but the VIX also fell 1.6% to a still very high level of 48.27.

So with the exception of the strange post-9/11 action, 12 of the 13 VIX Divergences tended to occur anywhere from a few days to a few weeks before minor pullbacks or even major downlegs. Both positive and negative divergences occurred, on average, at relatively low VIX levels marking complacency. The average positive VIX Divergence occurred at 23.5 on the VIX, while the average negative VIX Divergence happened around 33.1 or so, which is still not super high in VIX terms. Average negative VIX Divergences ran at VIX levels 41% higher than average positive VIX Divergences.

As you can see above, our latest three VIX Divergences were all positive, with the most recent happening in early September. Even during a strong bear-market rally, these VIX Divergences seemed to herald minor pullbacks in the S&P 500. Our most recent VIX Divergence of September 2nd happened when the SPX closed at 1022, only about 1.7% below its latest interim high of 1040 or so achieved last week. Perhaps this particular VIX Divergence heralds a pullback or outright major decline too. Only time will tell!

For another perspective on these VIX Divergences, we graphed the same 13 shown above against the Relative VIX, a hybrid measure of the VIX relative to its 200-day moving average. This helps us gain a better sense of where the VIX was trading in relation to its current 200-day baseline when these VIX Divergences arose out of the market mists to captivate speculators.

Once again, both positive and negative VIX Divergences tended to occur when the VIX was relatively low. The average positive VIX Divergence day occurred at a Relative VIX around 0.81, while the average negative VIX Divergence day was seen around a Relative VIX of 1.26, about 56% higher. Even the negative VIX Divergences were fairly low though, as an extremely high Relative VIX reading will challenge 1.80, lofty levels that have never witnessed a VIX Divergence day with the notable exception of the post 9/11 V-bounce 9/21 negative VIX Divergence at a Relative VIX level of 1.72.

So apparent statistical randomness aside, is there a pattern emerging here? Perhaps. These VIX Divergence days, with the exception of 9/21/2001, seem to tend to occur around complacent moments in market time. It is almost as if traders are indecisive near high points so they are trading in a method unconventional enough to drive both the S&P 500 and VIX 1% or more in the same direction on the same trading day.

While the markets don't immediately slide right after a VIX Divergence day by default, they certainly appear to slide more often than not within days or weeks of this rare indecision and decoupling of the VIX and its usual relationship with the S&P 500. If I had to make an interpretation of these VIX Divergence days, I would have to say that the odds are slightly bearish after they occur, either for a temporary short-term pullback or a serious Great Bear downleg.

Nevertheless though, since these odd VIX Divergences are not overwhelmingly mapped right at major interim tops or major interim bottoms, at this stage in the game I don't think there is enough evidence to lean heavily on VIX Divergence days for trading cues. While the visual distribution of these anomalous days is provocative and leans towards a bearish interpretation, the statistical data underneath is running close enough to 50/50 across the board to tilt the scales away from predictability and towards randomness.

VIX Divergences aside, the VIX and Relative VIX themselves are offering a great deal of insight for speculators today. This weekend I will be working hard on the upcoming October issue of our monthly Zeal Intelligence newsletter, to be published in the middle of next week for our subscribers, which will discuss the current index-speculation scene and outline our current strategy and tactics for playing it. Naturally the volatility indices will factor into this discussion on index-options trading strategy moving forward for the remainder of 2003 and beyond.

The bottom line is the mysterious VIX Divergences quite a few speculators have observed in recent months are certainly intriguing, but at first glance the evidence is not compelling enough to trade directly upon. Naturally there are countless variations of this line of inquiry which could affect the results, including defining materiality at different levels, but at 1% absolute moves the VIX Divergence day distribution remains tantalizing but not conclusive enough to speculate upon.

While these mysterious VIX Divergences may indeed wield some predictive power, the element of randomness in their statistical underpinnings is too powerful to ignore. Nevertheless, we will continue noting these odd days when they occur in the future and perhaps some useful and actionable trading information will yet emerge out of the VIX Divergences.