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From Macro to Micro Volatility Trading | Released: July, 2010
When you think of standard deviations in a distribution, what do you think of?
For most, we think of static points away from the mean. In other words, we think of standard deviations as the "wingspan" of the distribution. Here's the problem, we are conventionally taught these points are "static" as well, meaning that they do not compress and expand, as prices dynamically move up and down.
Figure 4.1 | Plot of Normal
Distribution
Figure 4.1 shows the 2nd and 3rd standard deviations as the width, or
wingspan of a distribution.
Please read the following very closely... To show just how horribly broken even statistical information is presented to markets; take a moment to read the following explanation of standard deviation from the mass-accepted open source Website Wikipedia.com.
(By the way, I'm not faulting Wikipedia, as it is a great source for general information... However, for those seeking information about markets though, common resources can sometimes do more damage than good.)
Wikipedia states:
"In probability theory and statistics, the standard deviation of a
statistical population, a data set, or a probability distribution is
the square root of its variance. Standard deviation is a widely used
measure of the variability or dispersion, being algebraically more
tractable though practically less robust than the expected deviation
or average absolute deviation.
It shows how much variation there is from the 'average' (mean). A low
standard deviation indicates that the data points tend to be very close
to the mean, whereas high standard deviation indicates that the data are
spread out over a large range of values.
For example, the average height for adult men in the United States is
about 70 inches (178 cm), with a standard deviation of around 3 in (8
cm). This means that most men (about 68 percent, assuming a normal
distribution) have a height within 3 in (8 cm) of the mean (67–73 in
(170–185 cm)) – one standard deviation, whereas almost all men (about
95%) have a height within 6 in (15 cm) of the mean (64–76 in (163–193
cm)) – 2 standard deviations. If the standard deviation were zero, then
all men would be exactly 70 in (178 cm) high. If the standard deviation
were 20 in (51 cm), then men would have much more variable heights, with
a typical range of about 50 to 90 in (127 to 229 cm). Three standard
deviations account for 99.7% of the sample population being studied,
assuming the distribution is normal (bell-shaped)."
In the mainstream description of Standard deviation above, readers will
hopefully notice a few points that will raise a few more questions about
much of the information we receive within the public domain. Foremost,
the explanation states, "Standard deviation is a widely used measure of
the variability or dispersion, being algebraically more tractable though
practically less robust than the expected deviation or average absolute
deviation. It shows how much variation there is from the "average"
(mean)."
What is critical to understand here is the above explanation tells us we are measuring "average deviation" from the mean... However, as we have already seen on our 30-year chart of the DJIA, movement away from the mean (to the upside for 19 years from the early 1980's to 2000 in our example) is actually indicative of expectations aligned and a possible bull market in place.
Thus, we really want to see variation from the mean, as the long-term
average or mean, is really the outlier. Moreover, nowhere in the above
statement is there any mention of a dynamic mean or the possibility that
distributions might just be dynamic in and of themselves. Clearly, the
common discussion of standard deviations assumes a static distribution
and an immobile mean, which is not true in markets. Though I have yet to
explain what's really happening within volatility and standard
deviations, what readers can note for now is... In the common explanation
of standard deviations, there appears to be no mention of the possibility
of DYNAMIC standard deviations - at least not upon first glance.
More on this in a moment...
Please continue reading the explanation of standard deviation from
Wikipedia.com.
"In addition to expressing the variability of a population, standard
deviation is commonly used to measure confidence in statistical
conclusions. For example, the margin of error in polling data is
determined by calculating the expected standard deviation in the results
if the same poll were to be conducted multiple times. The reported
margin of error is typically about twice the standard deviation – the
radius of a 95% confidence interval. In science, researchers commonly
report the standard deviation of experimental data, and only effects
that fall far outside the range of standard deviation are considered
statistically significant—normal random error or variation in the
measurements is in this way distinguished from causal variation.
Standard deviation is also important in finance, where the standard
deviation on the rate of return on an investment is a measure of the
volatility of the investment."
Taking a deeper look at the above passage, we are primarily focused on
the later part, which (again) reads, "In science, researchers commonly
report the standard deviation of experimental data, and only effects that
fall far outside the range of standard deviation are considered
statistically significant—normal random error or variation in the
measurements is in this way distinguished from causal variation. Standard
deviation is also important in finance, where the standard deviation on
the rate of return on an investment is a measure of the volatility of the
investment."
Again, hopefully readers have noticed the common perception of "outlier" (the unpredictable, devastating price movements within, or outside of a distribution) as, "effects that fall far outside the range of standard deviation."
However, as the data we've already seen in the DJIA presents... The
return to the mean after 19-years of ascending price action, was and will
continue to be based on catastrophic events, like 9/11 and the Financial
Crisis. When 9/11 hit and the Financial Crisis ensued, as we've already
seen in the long-term charts of the Dow, the data did NOT fall outside of
the range of standard deviations...
In fact, the 50-month mean is dead center inside the range of standard
deviations, which is where the major indices headed directly towards when
the Crash of 1987 took place, as the dot.com bomb unfolded, when 9/11
occurred and as the Financial Crisis ensued. Again, the outlier is the
mean.
We are conditioned to think of "statistically significant" as data
outside of the first, second and third standard deviations, not a return
to the mean, which in the case of markets over the past 30 years,
couldn't be any more wrong, or further from the truth.
What all of the above tells us is the common information (even within
statistics) presented to the common public often falls way short of
explaining, or even touching on in many cases, how distributions and
standard deviations apply to real - dynamic - markets and trading.
Furthermore, as I'm about to show, the final statement of the above
explanation of standard deviation, "the standard deviation on the rate of
return", completely misses the mark too...in-terms of real-time
application to markets, from the perspective of active traders and
investors.
Looking at Figure 4.1 again, standard deviations measure the "wingspan"
of a distribution, which are thought of (by most people) as static, much
like the larger concept of mean and distribution as immobile, having
infiltrated markets as well. However, neither the means or distributions
within markets are static; rather, both are dynamic. What's really
important to dig into though...is understanding the concept of standard
deviations as dynamic, organic, and mobile.
When applied to markets, the standard deviations of a distribution not
only move up and down with the distribution, but also expand and
compress, seemingly independently. What we're talking about is a "double
dynamic" distribution that not only ascends and declines, but also
expands and compresses, all at the same time. We are talking jelly fishy
almost.
Is the expansion and compression of the standard deviations significant?
You know it. We will cover volatility and the expansion and compression
of standard deviations (as applied to trading) in detail throughout the
following pages... For now though let us just understand some vital
theoretical concepts.
In terms of markets, when the formula for standard deviation is applied to prices, the actual standard deviations expand and contract... In other words, at moments, the standard deviations will be trading far from the mean, while at others; the statistical benchmarks will mysteriously pull in close towards the mean. Why does such occur and what is the significance?
The standard deviations expand and compress, not because of bullish or bearish sentiment, but because of the real time, relevant volatility displayed in prices. (In times of low volatility, the standard deviations will compress, however, during times of high volatility, standard deviations will expand.) Under the surface though, what's really happening is nothing more than a natural luxury of the formula for standard deviations providing markets with a "little something extra."
As John Bollinger stated in Chapter 6 (endnote #6) in his breakthrough book Bollinger on Bollinger Bands, "It is this squaring of the deviations from the average that makes Bollinger Bands so adaptive, especially to sudden changes in the price structure."
It is here, that I would like to start clarifying the larger concept of volatility for readers. Foremost, please understand that "volatility" is a broad general word used hurtfully within markets, by those who do not really understand the game in the first place...
Here's what I mean... have you ever sat there watching one of the mainstream financial media stations, when suddenly one of the anchors, or pundits states, "Volatility is high with markets right now."
Well what does that mean? Seriously. Stating, "Volatility is high" only
does one thing and one thing only for common investors: invoke fear.
Furthermore, when I hear a pundit state, "Volatility is high," the first
thing I think is, "that guy doesn't know jack, and probably doesn't trade
with real money."
Here's why... Stating, volatility is high, is about the same as saying, "cars perform well in the snow." Let me clarify... "Four-wheel drive SUV's perform well in the snow" would be a much more accurate statement, because we are describing what type of car generally has better traction in the winter months, over the entire category of automobiles.
Thus, we must be able to identify what type of volatility is, or is not,
high at particular moments within trading, otherwise we are just lumping
a blanket statement of nothingness over markets, thus showing the world
we do not know what the hell we're talking about in the first place.
Sadly, the only real people within markets who understand volatility are
options floor-traders, as they take on significant time-related
volatility risk when writing options. However, even in the world of
options, the common definitions of volatility are relatively worthless to
average investors.
Case in point, in the world of options we have implied volatility (how much the market expects price to move) and statistical volatility, better known as the historical measurement of price volatility, over a given period of time. Options traders also know about the "Greeks" (Delta, Gamma, Lambda, Rho, Theta and Vega), which are...well...Greek to the average Joe.
Furthermore, in the world of equities, most lump volatility into "historical volatility, implied volatility, the Volatility Index, and intraday volatility", showing again, even the expert news sources, pundits and educational writers don't know jack... At least, that they don't trade with real money...
To finally clarify volatility for regular investors and traders, we really have four types of volatility that affect all markets daily. (By the way, I would like to mention "the Greeks" - in options trading - are by far the most effective understanding of volatility, though because this work is not meant to focus on options pricing and valuation, we will not cover the aforementioned here. I recommend, Option Volatility & Pricing by Sheldon Natenberg, which is the floor-trader's bible, for those who would like to know more.)
The four types of volatility that affect common trading and markets are:
1. Market Volatility
2. Probability Volatility
3. Mean-period Volatility
4. Price Volatility
For a quick explanation of each type of volatility, we will first start with Market Volatility, which is part in parcel, what we must be on the lookout for, in relation to longer-term mean reversion trading, where expectations for higher, or lower ground are no longer aligned... When long-term mean reversion ensues, Market Volatility is likely high.
1. Market (Historical) Volatility
Foremost, many often separate Historical Volatility from Market Volatility, as measured by the Market Volatility Index (VIX). However, I would like to argue that for the purposes here, historical volatility and market volatility are the same. It may be said that historical volatility in energy companies is less than the historical volatility in technology companies, if we were to split hairs. However, I believe most investors have this much common sense and can distinguish the two. By merging historical volatility with market volatility here, I am saying: Historically, when larger market volatility kicks up, so does that of the broader market, which I believe readers can validate on their with two minutes of free time and access to historical chart on the Internet. In addition, I am merging the two terms here, as really, they are the same. If one wanted to know the historical volatility on their particular stock, they would be seeking out "stock specific volatility", which in my eyes, should not be encompassed in the broader category of "historical volatility". See what I'm saying? If you want specifics, than be specific, please do not lump a broad word like "historical" into what I believe most would refer to as a much more explicit category like stock, option, commodity, or currency-specific volatility. With the previous in mind, by definition, the CBOE defines the Market Volatility Index (VIX) as:
• "The CBOE Volatility Index® (VIX®) is a key measure of market
expectations of near-term volatility conveyed by S&P 500 stock index
option prices. Since its introduction in 1993, VIX has been considered
by many to be the world's premier barometer of investor sentiment and
market volatility."
Figure 4.2 | Market Volatility Index with S&P 500
Let
me break it down: When the writers of options (AKA sellers, or
those who are taking on the risk to give others the right to
purchase a put or call at a later date) believe volatility is
about to see (or is in the process of seeing) a reasonable uptick,
will increase premiums to be compensated for the additional
time-related risk taken on.
Thus, when the VIX rises, higher fear levels are beginning to surface within markets, and thus, expectations are no longer aligned.
If you remember our previous discussion of the mean as the true outlier, when uncertainty shows up in markets, the first place prices head to is: the long-term mean.
Perfectly in-line with what I am proposing here, we see that in 2008/2009, and in early June of 2010, when the VIX rallied, the S&P 500 declined.
Thus, we must understand that Market Volatility is a measurement of
larger market fear (uncertainty prompting mean reversion trading - on
a LONGER TERM basis), based on option premiums.
2. Probability Volatility
As we already know, when measuring probability of a distribution,
approximately 68% of the data should rest within one standard deviation
of the mean, 95% within two standard deviations and nearly 99% within
three standard deviations. However, while the above probabilities are
thought of as reliant only with a normal (bell shaped) distribution, we
know as time is skewed, so are distributions within markets. The common
argument or whether distributions are, or are not "bell shaped" in
markets is moot though, as regardless of the shape, because of the
squaring of the deviations in the formula for standard deviation, the
probability holds, which is all we care about.
As Figure 4.3 shows, regardless of trading action, because of the expanding and compressing nature of the standard deviations, as measured in our image here, the theory that three standard deviations should contain 99.7% of the data, holds true. I want to mention that the reason why I truly love the larger volatility/probability price mass paradigm is because not only do we have empirical reasoning to explain why what is happening...is happening, but we can also empirically validate the theory over and over - with our own eyes - on the charts we trade from. No other indicator within markets provides this type of validation.
Figure 4.3 | Probability Volatility
What
we then begin to understand is simply when probability volatility
(measured through the 20-period hourly 3.2 standard deviations in
Figure 4.3) expands, the probability of higher, or lower prices
increases, while at the same time, when probability volatility (the
standard deviations) compresses, the likelihood of lateral
consolidation increases. I would like to mention that we must use
common sense when understanding probability volatility in markets...
When prices are trending over a long period of time, while probability
volatility would have spiked when the trend first began, towards the
end of the trend, probability volatility will almost always compress,
even though prices are still moving upward, or downward...
Why?
Because on a common sense basis, we're talking about TWO SIDES of a distribution that cannot move away from one another forever. When prices begin trending, probability volatility will spike in both directions, however, as price continues trending, eventually, the probability volatility band opposite the trend, will roll over toward the direction of the trend...
Imagine you are standing at the foot of a mountain, and suddenly you decide to begin running up a trail... Initially you would fail your arms outward, as you start in motion; however, as you start running, you would pull your arms and legs inward to maintain a more stable core, as you continued onward. If you were to stop abruptly, your arms would likely flail outward again, to stabilize your body. Such is the same with a distribution ceasing a trend as well. When prices stop moving in one direction, the immediate halt of the trend (seen through prices reversing through the mean of the shorter-term distributions) causes probability volatility to spike again, and then begin compressing, as prices move laterally and consolidate. We're talking about understanding the COMMON SENSE of the cycles of probability volatility, as related to distributions within markets.
Probability Volatility can both be independent and a consequence of Market Volatility, as probability volatility is stock, currency, commodity (whatever) specific, while also (at times) influenced by larger market action, should all of the market begin rolling upward, or downward, based on larger fears (uncertainty), or moments of calm trending (expectations aligned.) Common sense is required.
3. Mean-period Volatility
Mean period volatility is simply the paradigm where shorter-term distributions will likely show greater volatility than that of their longer-term counterparts. In addition, the shorter the period measured, the greater the volatility of the same mean measured.
Figure 4.4 | Mean-Period Volatility
What I'm saying is that a 50-period mean on 15-minute chart will show
greater volatility than a 50-period mean on a 4-hour chart.
However, because the longer-term distribution does indeed take more data to move, the longer-term probability volatility will show a greater range, than that of the shorter-term distribution.
In the end, when shorter-term probability volatility is outside of longer-term probability volatility, prices are likely trending. Conversely, when shorter-term probability volatility is compressing underneath longer-term probability volatility (unless price is towards the end of a sustained trend, or has just ceased trending), prices will begin consolidating (moving laterally), with shorter-term mean-period volatility trading above and below longer-term mean-period volatility.
4. Price Volatility
Price volatility is a both a cause of, and derivative of market volatility, probability volatility and mean-period volatility. While price volatility is really nothing more than an extra description of the total low-to-high range of prices in any given period measured, the label is required to separate "price action" from the other three volatility descriptions...
If price volatility is high, prices are likely moving from the bottom to the top of shorter-term 3.2 standard deviation probability volatility, even though the total range can be either lateral, or trending. In the end, when probability volatility is collapsing, the less likely price is to put in new highs and lows, and thus, will stall when hitting the third standard deviation. Should price strike a third standard deviation and then commence trending in the direction of the third standard deviation tagged, we should also see shorter-term mean-period volatility start showing slope, while at the same time, short-term third standard deviation probability volatility would spike outside of longer-term third standard deviation probability, confirming that the smaller subset distribution was on the move. It is important to note that elevated price, probability and mean-period volatility can occur in the absence of market volatility, however, are also likely a consequence of market volatility, when fear levels rise. In essence, price, probability and mean-period volatility are both independent and a consequence of market volatility. At the same time, market volatility is really independent of price, probability and mean-period volatility of individual components of markets. Only when many components show similar extensively elevated price, probability, and mean-period volatility, do they influence market volatility.
What the above tells us, is when an instrument begins to display price action that breaks the relevant short, or long-term trend (up, down, or sideways) probability volatility initially expands, only to later compress as participants ease into expectations aligned. Furthermore, while a larger surprise move within markets may initially spike probability volatility outward, as prices 'consolidate' afterward, probability volatility may initially spike as the sustained trend suddenly stops, however, probability volatility eventually compresses towards the mean, as mean-period volatility begins to flatten out.
Here's what's pretty amazing though... While price volatility (price action) taking out highs or lows, initially triggers probability volatility to spike, at times, probability volatility itself, can be a massive leading indicator alerting us to the fact that prices are about to spike... Sounds a little weird right? The aforementioned would happen if the stock, currency, commodity, or whatever we're watching was consolidating for a long-period of time and short-term probability volatility had returned to its natural state, collapsing underneath long-term probability volatility, with both coming in very close to their means. In this example, the total distributions (measured through probability volatility) would have shed significant mass, and thus a small movement in price, would cause short-term probability volatility to spike outside of long-term probability volatility, alerting us ahead of time, that prices were likely about to move.
Please just note, when probability volatility increases, the standard
deviations move away from the mean, and when probability volatility
decreases, the standard deviations move toward the mean, all because of
the natural luxury of the squaring of the deviations in the formula.
To explain why the expansion and compression of standard deviations is so
incredibly significant, we must not only dump what we've traditionally
come to understand as statistically significant outliers of a
distribution, but also about how distributions and statistics apply to
trading and markets on the whole.
Again, what we're really getting at here is a larger, commonly misunderstood perception of what standard deviations are, how they interact with distributions in markets, what the data is truly presenting, and even, how, why and what amazing data standard deviations hold in terms of leading information, which traders can use in real markets, in real time.
By the way, I know that for many, the mere mention of statistics and standard deviations can instantly cause some to nod off into slumber-land; however, don't worry, we're not going to cover a bunch of boring math here. We are going to cover the theory behind why what is happening is indeed happening and then directly apply the concepts to markets. There are tons of resources available to double check the formula for standard deviation and the like, so I won't waste your time here... Readers will find a plethora of educational resources all over the Internet to learn how to calculate standard deviation, etc... If the information is coming from a mainstream portal though, I might recommend checking two sources, just to be on the safe side. :)
Anyway, we already have tools within markets to do the bulk of the work
for us, one of which you already know: Bollinger Bands.
I do have to mention that while John Bollinger is one of my personal
idols in markets, I really wish he had not named the application of
standard deviations to price data (electronically) within markets
'Bollinger Bands.' It is my understanding that the naming of his
incredible breakthrough was an accidental occurrence on CNBC, but the
fact remains, by taking one thing, and then naming it something
completely unrelated, we just make markets more difficult for average
investors to comprehend. Anyway, it is what it is...at the end of the
day, I'm incredibly grateful for Bollinger's genius in bringing forward
the "bands" (standard deviations, or probability volatility) to markets.
We've begun to touch on why and how some information within markets may not be making it the investing public correctly (like the long-term mean as the real outlier), while also scraping the surface on how and why distributions and their means are dynamic in markets, not static. Moreover, we've also just slightly introduced the concept of standard deviations as doubly dynamic, organic and nearly jelly fishy... I'm guessing the latter probably still needs a little clarification, which we will now make sure to cover in Chapter 5. In addition, we're also clarified volatility within markets, understanding that there are really four different types which affect traders on a regular basis: Market Volatility, Probability Volatility, Mean-period Volatility and Price Volatility.
Next, in Chapter 5, we will clarify probability, volatility and dynamic distributions within trading - even more...
