It’s all about Symmetry

Posted on: by .

It looks for now that the short-term supports have held and while we could see some volatility in the weeks ahead, I believe that the Fed will come to the rescue. However, probably not until the September or perhaps in the 11th hour at their October FOMC meeting. I don’t see any major shifts of accommodations come this July meeting as I suspect that we will have an “initial” positive GDP that will bring forth a sigh of relief and allow the Fed to keep on their current course.

It’s all about Symmetry

Courtesy of wikipedia

Lost in averages…
Most of us, including the Federal Reserve, get caught in averages as if it is the end-all be-all of determinations. Chartists look at all kinds of moving averages, weighted, non-weighted, etc. The Fed looks at 12 month averages in the economic data, like the GDP. Even I review the VIX and averages. Investors and economists talk about “reverting to the mean”, but when it comes to math we are very myopic and it all is about averages.

I would argue that what is sometimes far better to grasp, understand, and visualize is the skew, slope, and the curvature. Collectively they show both expectations of change as well as rate of change. Visually they can show trends and rate of changes of those trends. An average is just an average and has really no predictive abilities, but add in the skew, slope, and curvature and we begin to see and understand symmetry.

Random Ignorance

I am of the rare camp that does not believe in a market of “pure random walk” for numerous reasons including, but not limited to: market rules, market bias, gapping markets, liquidity factors, insider trading, etc. I certainly do not wish to spend this morning writing a debate for/against “pure random walk”, but suffice to say that there are some GENERAL market predictive elements that can help give us insight on how to position ourselves in the market.

Courtesy of wikipedia

There are two general predictive market stances one can take; directional and volatility. The vast majority of market participants are laser focused on trying to pick direction, it is a simple and binary prediction and one would think because of its basic binary outcome that we should be able to easily predict the market. The vast majority of financial engineering and applications to market predictive analysis is on direction.

However, the study of volatility, while generally more complex in the initial math is far more easy to predict in my very humble opinion (very humble because I am a layman when compared to my brethren in the financial engineering field). Understanding volatility, it’s components, and mathematical measures gives us a far better understanding to directional predictive analysis. I would go as far to say that those that ONLY focus on average predictive directional analysis without including volatility and the symmetry of slope, skew, and curvature are half blind.

Reason, the most formidable of weapons.

Thomas Paine said, “The most formidable weapon against errors of every kind is Reason. I have never used any other, and I trust I never shall.” So let’s apply reason and logic for now, as I don’t have the time nor do I want to turn this into a technical paper on math equations on slope, skew, and curvature.

Courtesy of wikipedia

One reason we know the market is not merely a “pure random walk” is by applying reason and logic to understanding volatile events. I can predict accurately to the day several times a year in which a stock or even the market as a whole will make an abnormally large move (volatility), far beyond the mean. Some would say, “Wow, how can you do this?” There is no secret or magic, just apply some deductive reasoning and the answer is so simple you may feel embarrassed. For example earnings, we know on that date the stock will report results on how it DID over the last quarter and also a forecast on what to expect for the next. By paying some attention over the quarter to the company news and expectations, one can make a reasonable prediction that on that day there will be volatility, simply saying the stock will make a rather large move (up or down). The point is there are many events in which one can make volatile predictions fairly accurately by just applying reason and logic.

So how can we apply some math to understand the possible directions of stocks and expectations of those directions? This is where we must focus on Skew, Slope, and Curvature, all of which are pieces of the puzzle that give us a far better picture of the stock and the market.

Slope and Curvature

Let’s start with Slope and Curvature first, these work in conjunction with one another and can help to determine direction and rate of change (the gamma function) of that direction. When one looks at averages, weighted or not, we are looking at a single number that defines a value based on a string of historical numbers. However it doesn’t tell us HOW we got to that number or where we came from. Knowing the history of how we derived that average is sometimes far more important than knowing the average.

What do I mean by this? Simply if I had a set of numbers to determine an average I could put them in any order and the average would always be the same. Some will certainly argue for using weighted averages, which I agree give us a better result, but it STILL does not give us an accurate indication of where exactly we came from and how we got here. Understanding both the slope and curvature will give us a better resolution as to how we got here. Some more astute technical analyst will forward the idea of “momentum” and I would agree that too brings some more insight, but what I am always curious about is what is happening to the slope and the curvature at this time and how is it helping me forecast a trend going forward. Essentially is it giving me any predictive (educated guesses) on future trends?

I know of one trader who wouldn’t know the math of slope or curvature, yet he could SEE in his mind’s eye the slope and curvature which helps him in determining supports and resistances. I use to watch him with fascination on the trading floor as he would be actually practicing Tai-Chi while making decisions on his Deltas based on this Zen like vision he had. He would swing a big soft delta bat, as they say and did exceedingly well. The fact is, what he saw in his mind’s eye can be easily explained with math, which he understood but was far more comfortable with his Zen like ways.

Hey, don’t change what works for you. The point being is that we are all getting to the same answer and some people only need to apply reason and logic, some can “see” it, and others need to do the hard math. If the reasoning and logic is sound, then how it is explained is immaterial. Some see poetry and music as math, others experience it.

Courtesy of wikipedia


That leaves me with SKEW, which I find as one of the more interesting factors to understanding and “seeing” market anticipation and risk. While I frequently refer to the VIX as an important market gauge, it is an average. In my own mind’s eye I see the VIX as where the action is currently pricing market volatility and many times it is fairly ignorant to REAL world factors (even the skew) and thus is not pricing risk correctly. First, to see the VIX as I do, you must understand that the VIX is never right or wrong, it is just a value at which the forces of Supply and Demand price risk (or options premium). The VIX is frequently wrong and once again one only has to apply reason and logic to see that, especially at the extremes. Did we actually believe, when the VIX was at 80, that the S&P 500 had a one standard deviation of 80%? Of course not, panic and fear had investors far over paying for options premium. Sort of like when a hurricane is reported in the Gulf and NOW you want to buy hurricane insurance, the insurance company is going to over-charge you on premiums.

Courtesy of wikipedia

A simple review on how the VIX is calculated is important before we further talk about the Skew. The VIX is a weighted average of option premiums with the AT-THE-MONEY ‘ATM’ (option strike prices that are priced closely to the stock price) the most weighted. As I previously mentioned, while weighted averages are certainly better, it is still an average. It doesn’t tell us the SLOPE or CURVATURE of how the options are priced as we move away from (higher or lower) the ATM strike. In fact looking at the VIX alone we can get some erroneous information by not understanding how the Slope and Curvature of the options premiums (volatility) as we move away from the ATM strike. For instance we could easily have a VIX priced at 12 with the ATM options at 9 and with a very steep slope and curvature, just as easily we could have a VIX price at 12 with that ATM options at 12 and a very flat slope and curvature. This difference, known as SKEW, is very important. Without it we do NOT understand how the market is pricing risk beyond the mean reversion factor of that ATM strikes vs. the S&P historical. It is important because the steeper the slope and curvature (Skew) regardless of the VIX value, the market is expecting (pricing) the probability of a larger move, beyond 1 standard deviation. This is known as “fat tails”.

Hidden Volatility

I have mentioned “hidden volatility” in previous previews, the basic definition is volatility that is not mathematically visible, but is there none the less. Sort of like a coiled spring, we SEE a spring but we can NOT see the energy that is IN the spring. The Skew, which is the slope and curvature of the option’s premium, helps us SEE that potential hidden volatility. It is a warning sign that hidden volatility in the underlying is building, even if the AVERAGE is not pricing it in the market.

The Chicago Board Options Exchange (CBOE) actually tracks the SKEW of their VIX index. It is worth a look and I think you will find it interesting that while the VIX is at some very low levels, the SKEW is relatively very high. This creates a conundrum for those that don’t apply any sound reason and logic, yet the answer is fairly clear. The majority of supply/demand (“action”) is ATM money, around where the index is trading. The actual volatility (frequently referred to as historical volatility) of the underlying, in this case S&P 500, is fairly low. One only has to look at a graph of the S&P 500 to see that, as we have been moving up in a steady manner. I won’t even get into the math of declining volatility as price rises, but suffice to say actual volatility is low and the VIX AVERAGE is reflecting that. However, there is hidden concern and trepidation in this rising market and that can easily be seen in the SKEW. The cost of hedging downside risk is on the rise and if measured relative to the ATM options premiums is becoming exceedingly expensive. I believe the longer we go without a significant correction the steeper the slope and curve of the SKEW, despite the value of the VIX average. In fact we could possibly have a lower VIX (weighted average). To see the VIX in the single digits and the SKEW starting to look like Mt. Everest is a RED ALERT, we are getting to serious correction levels.

Courtesy of CBOE

Whether you are charting direction of assets, take the time to learn about curvature and slope to help give you better resolution than just relying on averages. But to get a far more complete picture of the market, understand how volatility works and don’t just look at the VIX, get your mind around the SKEW as well.

Kobayashi Maru Moment

Remember your Quadratic Formula in high school? I didn’t, so I had it printed UPSIDE DOWN and BACKWARD on the front of my t-shirt so when I looked down I could read it. I guess you could call that my Kobayashi Maru moment, my teacher appreciated the ingenuity and let me wear it during my finals, which I passed. The point is, you need not memorize and be an expert in math, but you sure better appreciate it and figure it out – even if it means you have to cheat to get the right answer! Do the math!

Support & Resistance

INDU 16,700
Looks like we may still be consolidating up in the 16,800 range with a low short-term support at 16,700. I stand pat on a small correction down to the 16,600 area with a low of 16,400. With upside to the 17,000 level at resistance.

NDX 3800
The tech heavy index is holding up well, but this index can be extremely volatile with some of the overweights. Look at 3700 as broad support with the 3600 as low support in a short-term correction environment.

SPX 1950
The S&P 500 looks very much like the Dow Jones – consolidating waiting for a big move. VIX is in that 11-13 range, but the SKEW is rising. So in general it is pricing a moderately bullish market, but is very concern about a big correction.

RUT 1150
I continue to look at the Russell to gauge general market order flow. It has bounced well, but I see a revisit to the 1130-1140 in the cards in a short-term correction, perhaps before the July FOMC meeting. However, I don’t expect any panic sell-offs.

Fed Factor

The market has a savior or a drug dealer, depending on how you look at it. The Fed is a force in the market; fixing interest rates at zero, flattening the yield curve, and printing money. I guess you could say another example why I am not a believer in the “pure random walk” theory. The Fed’s participation can certainly exacerbate the VIX and the Skew.

The one factor we are not measuring the FAITH in our currency, it is faith and faith alone that is allowing the Fed to continue. Personally I believe that faith should be left to our spiritual beliefs and endeavors and should never be applied to the mathematics of economics and certainly not on man and man’s inability to govern. Yet since 1971 we have been using a FIAT currency, which is no longer backed by any intrinsic value and is literally based on the Good CREDIT and Good FAITH of the issuing government. Reasonable people will agree we ran out of credit a few years ago, hence the need for QE. So now we are running purely on FAITH.

No doubt Faith is very powerful, can move mountains and has. Yet when Faith is applied purely to the realm of man, it will always lose when it tries to oppose math. It’s time we start paying closer attention to the math if we are to protect and hedge against our future, rather than place our faith in the “hope and change” of man, even if those men have the best of intentions.

One Response to “It’s all about Symmetry”

  1. [...] SPX 1950 The range will most likely be in the 1930 – 1990 range. Bad news will drive the index to a support area of 1920. As long as the VIX is in the 11-13 range I suspect we will consolidate with a slight up move trend in the market. The Labor Report could bring more volatility. Also read my report on Skew/Slope/Curvature. [...]