The second reason why I have increasingly shifted toward trading volatility is lesser known but it’s actually the most important one: it is truly mean reverting in contrast to practically every price series which all in essence follow a random walk. And I’m not just making wild claims here – I have actually proven for this to be the case.

ADF TestYou can do this as well by simply (yes, I’m being a bit cynical here) running the VIX through an Augmented Dickey Fuller test to check for stationarity (fancy word for ‘is it mean reverting’?). Which is exactly what I did – and more:

p-value = 0.0321613338723 The series VIX is likely stationary. p-value = 0.103166277707 The series VXV is likely non-stationary. p-value = 5.73166440286e-06 The series VIX/VXV is likely stationary. p-value = 5.73166440286e-06 The series VIX/VXV is likely stationary.In general, a p-value of less than 5% means you can reject the null hypothesis that there is a unit root. SAY WHAT?? Yeah, that’s exactly how I felt when I first read this back when, so I went digging for an explanation that non-pocket-protector-wearing-mortals like us could understand. Fortunately I came across lovely Mr. Nystrom who’s not just a bonafide math-genius but also knows how to explain complex math related topics but also wears silly hats:

Okay, that was different but we get it. The null hypothesis assumes the ‘boring’ assumption that this series is like all the others, i.e. non-mean-reverting. So how about the root thingy? If you look up ‘unit root test‘ in the Wiki you’ll find this right at the top:

“In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.”

Ahaaa! Now we’re getting somewhere. So that p-value basically gives us the odds that there is a unit root, meaning that it is non-stationary. And 5% is our standard threshold, which the VIX seems to be satisfying. Which percentage you choose for the ADF and other statistical tests is always data dependent and there is not right or wrong. You as the human being have to consider the implications of being wrong, meaning how probability of being wrong you are willing to accept. For the ADF a 5% threshold is commonly accepted.

Interestingly the VIX on its own is considered stationary per the ADF, [...]]]>

The second reason why I have increasingly shifted toward trading volatility is lesser known but it’s actually the most important one: it is truly mean reverting in contrast to practically every price series which all in essence follow a random walk. And I’m not just making wild claims here – I have actually proven for this to be the case.

You can do this as well by *simply* (yes, I’m being a bit cynical here) running the VIX through an Augmented Dickey Fuller test to check for stationarity (fancy word for ‘is it mean reverting’?). Which is exactly what I did – and more:

p-value = 0.0321613338723 The series VIX is likely stationary. p-value = 0.103166277707 The series VXV is likely non-stationary. p-value = 5.73166440286e-06 The series VIX/VXV is likely stationary. p-value = 5.73166440286e-06 The series VIX/VXV is likely stationary.

In general, a p-value of less than 5% means you can reject the null hypothesis that there is a unit root. SAY WHAT?? Yeah, that’s exactly how I felt when I first read this back when, so I went digging for an explanation that non-pocket-protector-wearing-mortals like us could understand. Fortunately I came across lovely Mr. Nystrom who’s not just a bonafide math-genius but also knows how to explain complex math related topics but also wears silly hats:

Okay, that was different but we get it. The null hypothesis assumes the ‘boring’ assumption that this series is like all the others, i.e. non-mean-reverting. So how about the root thingy? If you look up ‘unit root test‘ in the Wiki you’ll find this right at the top:

“*In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.*”

Ahaaa! Now we’re getting somewhere. So that p-value basically gives us the odds that there is a unit root, meaning that it is non-stationary. And 5% is our standard threshold, which the VIX seems to be satisfying. Which percentage you choose for the ADF and other statistical tests is always data dependent and there is not right or wrong. You as the human being have to consider the implications of being wrong, meaning how probability of being wrong you are willing to accept. For the ADF a 5% threshold is commonly accepted.

Interestingly the VIX on its own is considered stationary per the ADF, but the VXV is not. More importantly however the VIX/VXV ratio, which I use a lot, is considered stationary. Here I’m plotting the past decade of the ratio and although this is very subjective I think it’s fair to say that it is mean reverting.

But why use those two as a ratio? Are they actually moving in relative tandem with each other? Well, there’s another statistical test called the Cointegration Test. In order to run it you need two price series of the same interval (i.e. weekly, daily, hourly, etc.) which it will test for the probability of cointegration. This is what it’s spitting out:

t-statistic: -10.0428682 p-value: 1.93501804248e-16 Critical Value 1%: -3.43305394343 Critical Value 5%: -2.86273457071 Critical Value 10%: -2.56740591915

Don’t worry about the t-statistic, what’re once again focusing on is the p-value which has a negative exponent of 16 and that means the value is tiny. In other words, yessirree, those two are cointegrating for sure.

Not to throw too much at you today but you probably also want to test for covariance and correlation. The latter is conveniently scaled between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two independent variables, to Var(X), in the case where the two sets of data are equal.

Covariance of VIX and VXV: 83.1724666524 Correlation of VIX and VXV: 0.980667242113

Correlation usually is more intuitive to most people and I think a value of 0.98 is pretty damn correlated.

The scatter plot makes it pretty clear although we’re also seeing a tad of heteroskedasticity at work. Hey, no reason to be insulting!! Okay, I’ll explain that one another day.

Now that we actually know what the heck we’re talking about and can back it up with proof let’s actually look at some recent IV charts:

So here we’ve got the VIX on top and the VIX:VXV ratio below as candles – the first is the ratio and the second the spread between the two on a percentage basis. I know – FANCY!!

But what does it tell us? For one the ratio seems to be plotting a pretty solid support zone which we recently touched and now seem to be bouncing from. Which probably means we’ll be seeing an increase in volatility in the coming weeks and months. Most likely after the Santa Rally in January though.

But it’s just getting interesting. Please step into my lair:

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Dr. Copper not surprisingly found its maker overnight. Commodities are clearly being affected by a strengthening Dollar and for now we’ll have to be careful when picking long candidates in this sector.

10-year bonds have however happily continued higher and our current trail remains intact until we hit 2R in MFE or a new spike low is in place.

Last but not least crude which has also ended but not before leaving us with another juicy 4R in profits. That was our 2nd crude campaign in the past 2 weeks and both turned out exceptionally profitable. Wish it was always that easy!

]]>Alright you market mutants, it’s time to pay attention. There is a pretty good chance that we’re going to see a bonafide confirmed VIX Buy Signal at the end of the session today. At this very moment we only have an issued signal and if you remember for a confirmed signal we need three specific events:

A close of the VIX outside of the 2.0 Bollinger Band (20-day SMA). check A close back inside the 2.0 BB. This issues the signal. check A close below the previous day inside the 2.0 BB. This confirms the signal.Once you get those three events a major reversal usually occurs within the next week, arguable there is already one in the works. Why is it called a VIX Buy Signal? Because the ‘buy’ part refers to equities and not to the VIX.

The E-Mini futures are looking pretty supportive right now, having extended their Friday gains overnight. The ES is in earshot of its 25-hour SMA, which will have to be taken today or tomorrow in order to set us up for another push higher. Should the ES fail to extend its gains and drop back below 2435 then the medium term bullish case starts to gain more credibility. For right now it’s an off-chance but let’s wait what happens in today’s session.

The Dollar bounced a little late last week and implicitly knocked down precious metals a peg or two. Here shown is the inverted USD/JPY which continues to be tightly correlated with gold.

Which incidentally was kicked out at 2.2R during a quick stab lower right through my trailing stop. I was a bit miffed last Friday but seeing it back below my trail this morning again is a bit of consolation. Now it’s a bit premature to consider a re-entry, first we need to get the lay of the land on the Dollar situation which at the current time remains unclear.

Our bond campaign is still in the running but only barely. The stop sitting at break/even was almost reeled in before the weekend but thus far appears to be well placed. This one is fifty/fifty right now – the daily looks very supportive but all those intra-day gyrations could easily kick us off the bus.

Finally a longer term chart I wanted you all to see – crude. Ignore the daily panel on the left, which admittedly looks very bullish, and instead focus on the weekly panel on the right. Note how almost two years of sideways churn have squeezed those 100-week BBs almost to the max. This may continue for a few more weeks, even months [...]]]>

Alright you market mutants, it’s time to pay attention. There is a pretty good chance that we’re going to see a bonafide *confirmed* VIX Buy Signal at the end of the session today. At this very moment we only have an *issued* signal and if you remember for a confirmed signal we need three specific events:

- A close of the VIX outside of the 2.0 Bollinger Band (20-day SMA).
*check* - A close back inside the 2.0 BB. This issues the signal.
*check* - A close below the previous day inside the 2.0 BB. This
*confirms*the signal.

Once you get those three events a major reversal usually occurs within the next week, arguable there is already one in the works. Why is it called a VIX Buy Signal? Because the ‘buy’ part refers to equities and not to the VIX.

The E-Mini futures are looking pretty supportive right now, having extended their Friday gains overnight. The ES is in earshot of its 25-hour SMA, which will have to be taken today or tomorrow in order to set us up for another push higher. Should the ES fail to extend its gains and drop back below 2435 then the medium term bullish case starts to gain more credibility. For right now it’s an off-chance but let’s wait what happens in today’s session.

The Dollar bounced a little late last week and implicitly knocked down precious metals a peg or two. Here shown is the inverted USD/JPY which continues to be tightly correlated with gold.

Which incidentally was kicked out at 2.2R during a quick stab lower right through my trailing stop. I was a bit miffed last Friday but seeing it back below my trail this morning again is a bit of consolation. Now it’s a bit premature to consider a re-entry, first we need to get the lay of the land on the Dollar situation which at the current time remains unclear.

Our bond campaign is still in the running but only barely. The stop sitting at break/even was almost reeled in before the weekend but thus far appears to be well placed. This one is fifty/fifty right now – the daily looks very supportive but all those intra-day gyrations could easily kick us off the bus.

Finally a longer term chart I wanted you all to see – crude. Ignore the daily panel on the left, which admittedly looks very bullish, and instead focus on the weekly panel on the right. Note how almost two years of sideways churn have squeezed those 100-week BBs almost to the max. This may continue for a few more weeks, even months but at some point there is going to be an explosion of epic proportions when crude finally breaks out and starts to burn all the shorts.

I hope I’ll be there riding the tip of that rocket when it happens. Preferably without the mushroom cloud at the end though ;-]

]]>By doing what we do best – beg, borrow, steal, and never ever trade against the Fed. Well, I promised to make this a special post which probably means it’ll suck completely, but let me give this my best shot. Plus as this is a special occasion I’ll make it all available for free – so you leeches can rejoice. You may however consider getting off the fence and signing up for either Gold or the Zero so that we’ll be able to celebrate 10 glorious years 12 months from now.

As you know volatility – both realized and implied, has been one of my obsessions over the past few years. Something you keep hearing over and over again is how the VIX is mean reverting and if you look at a regular chart then it’s easy to swallow that pill.

Well, allow me to disagree, and unlike many I’ll back up my claims with actual data. First up let’s define what we mean by ‘mean reverting’ – basically we are testing for stationarity and we’ll be doing this via the Augmented Dickey Fuller (ADF) test. This tests the null hypothesis that demand follows a unit root process. You usually reject the null when the p-value is less than or equal to a specified significance level, often 0.05 (5%), or 0.01 (1%) and even 0.1 (10%). Now what’s important to note is that a) you define your test threshold ahead of time (in most cases it’s 5%) and that b) that the p-value is interpreted as a binary value. Either it is < 0.5 (high confidence of mean reversion) or it is not (no confidence of mean reversion). And that means a p-value of 0.51 would still mean we do not accept the null hypothesis.

Anyway, enough of the math babble, let’s run this sucker, I’m going to test 10 years of the VIX as well as 10 years of the VXV, then I’m going to test a ratio of the two. Let’s start with a threshold of 0.1:

p-value = 0.0324767618187 – The series VIX is likely non-stationary.
p-value = 0.103166277707 – The series VXV is likely non-stationary.
p-value = 6.34799786578e-06 – The series VIX/VXV [...]]]>
*Boy have we learned a lot, and how the heck did we even manage to survive all that drama? *

By doing what we do best – beg, borrow, steal, and never ever trade against the Fed. Well, I promised to make this a special post which probably means it’ll suck completely, but let me give this my best shot. Plus as this is a special occasion I’ll make it all available for free – so you leeches can rejoice. You may however consider getting off the fence and signing up for either Gold or the Zero so that we’ll be able to celebrate 10 glorious years 12 months from now.

As you know *volatility* – both realized and implied, has been one of my obsessions over the past few years. Something you keep hearing over and over again is how the VIX is mean reverting and if you look at a regular chart then it’s easy to swallow that pill.

Well, allow me to disagree, and unlike many I’ll back up my claims with actual data. First up let’s define what we mean by ‘mean reverting’ – basically we are testing for stationarity and we’ll be doing this via the Augmented Dickey Fuller (ADF) test. This tests the *null hypothesis* that demand follows a unit root process. You usually reject the null when the p-value is less than or equal to a specified significance level, often 0.05 (5%), or 0.01 (1%) and even 0.1 (10%). Now what’s important to note is that a) you define your test threshold ahead of time (in most cases it’s 5%) and that b) that the p-value is interpreted as a binary value. Either it is < 0.5 (high confidence of mean reversion) or it is not (no confidence of mean reversion). And that means a p-value of 0.51 would still mean we do not accept the null hypothesis.

Anyway, enough of the math babble, let’s run this sucker, I’m going to test 10 years of the VIX as well as 10 years of the VXV, then I’m going to test a ratio of the two. Let’s start with a threshold of 0.1:

p-value = 0.0324767618187 – The series VIX is likely **non-stationary**.

p-value = 0.103166277707 – The series VXV is likely **non-stationary**.

p-value = 6.34799786578e-06 – The series VIX/VXV is likely **stationary**.

p-value = 3.37882429904e-29 – The series VIX/VXV % Change is likely **stationary**.

And there you have it, given 10 years of daily VIX data, it turns out that according to the ADF, both the VIX and the VXV are not stationary and most likely only median reverting and otherwise following a subtle random walk. However it turns out that the raw VIX/VXV as well as its % change series has a 95% chance of being stationary. Now let’s run the same test with a 0.5% threshold, which to my understanding is considered acceptable for a financial series:

p-value = 0.0321613338723 – The series VIX is likely **stationary**.

p-value = 0.103166277707 – The series VXV is likely **non-stationary**.

p-value = 5.73166440286e-06 – The series VIX/VXV is likely **stationary**.

p-value = 3.2970819598e-29 – The series VIX/VXV % Change is likely **stationary**.

The VXV is still non-stationary apparently but the VIX apparently does satisfy the zero hypothesis with a confidence level of 95%. What does all that mean for us?

It means that mean reversion strategies should not just focus on the VIX on its own but its relationship to the VXV as, according to the ADF, it is considered stationary at a 99% confidence level. Above I produced a plot of the VIX:VXV ratio as it gyrates around its actual mean, which is around 0.91 over the past 10 years. We could obviously use a smaller or wider window but I think the mean wouldn’t shift by much. I also added thresholds at plus and minus one standard deviation. As you can see there are quite a few long and short VIX entry opportunities (or long SPX or the SPY) with several long entry opportunities as well. The latter however would be a lot more difficult over the past year and we probably would have to push out another standard deviation.

Here we are looking at the cumulative of the same ratio’s delta from the mean. Basically deduct the mean from the actual value and then add up the result. Due to the current mean we are starting and ending at the zero mark, but this basically shows us the net aggregate of investor sentiment over the past decade. Draw your own conclusions – I know I will

The thresholds I am using on my old manual chart are mostly done by observation but seem to match the calculated standard deviations pretty well. One of my epiphanies on this chart was that breaches above the mean (which again I nailed almost perfectly – hum hum) seem to be the ones which precede medium term corrections. As you can see we are still light years away from any of that.

This view of the VIX:VXV ratio shows us reversal periods via two stacked Bollinger bands I slapped on it. You basically look for a signal push > the lower 2.0 BB for a long entry and a signal drop < the upper 1.0 for a short entry. Unfortunately stockcharts doesn’t allow me to hide the superfluous lines. Anyway, apparently the long entries are pure gold and the short entries are so-so – not surprising as we’re in a raging bull market. I expect this situation to reverse one day when equities embark on a long needed corrective phase.

Now here’s the VIX again all on its own on a regular chart plotted on top of the SPX for context. The red ranges show us when it was scraping the bottom of the barrel and when buying yourself some long term protection against six sigma events was available at a discount. If you’re holding equities right now then this is a good time to grab a handful of long term puts and simply forget about them – cost of doing business and tantamount to bringing an oxygen mask when climbing Mount Everest.

The VIX ‘Easy Rides’ chart shows us in a cyan period and that means pretty much anything can happen on a short term basis, but medium or long term don’t even try to short this bull market.

The notorious CBOE SKEW ratio is pretty useless on its own but the SKEW vs. the VXV has been manna from heaven when it comes to calling long reversals. Short reversals again – not so great and if they happen they usually come weeks later, so timing entries requires other measures and I usually just look at price near important inflection points. As you can see recent breaches of the lower BB have not led to meaningful corrections in equities. We’re most likely going to get another one soon but that doesn’t mean the market is about to turn on a dime.

Of course I also had to chart the SKEW vs. VIX and once again the smart money bets on market bottoms.

Finally we’ll be wrapping things up with market breadth courtesy of the SPX50 vs. the SPX200 (the R is the % change version). And once again we are nowhere near bearish territory and if you any plans to short this market then I humbly suggest you keep your powder dry for now and wait for further instructions.

It’s summer and this post took me quite a while to put together while everyone I know here in Spain is out and about enjoying a beautiful summer.

My poor wife is probably online right now browsing for divorce attorneys so I’ll better be taking Friday off and do my best to talk her out of it. All services will run as usual tomorrow – see you all bright eyed and bushy tailed Monday morning!

]]>Alright we pretend that we have a very simple trading system which has but one single rule: Be long AMZN without a stop or a target. Simple enough and it serves us well for demonstration purposes as our P&L now effectively becomes the price series of Amazon. We are going to buy Amazon on 1/1/2012 and hold it through 1/1/2015 – four years of continuous price action.

Sharpe RatioNow one statistic often used to describe the performance of an asset or a trading system is the Sharpe ratio. Actually there are two – a more simpler one that compares the mean of your returns to the standard deviation of your returns – and one that uses an additional ‘risk free’ baseline measure such as for example the return of a treasury bill. All we need to do is to calculate the difference between our system returns and the returns of the ‘risk free’ treasury bills – let’s call that our risk_only series. Then we divide the mean of the risk_only series by the standard deviation of the risk_only series, and we’re done.

Of course calculating a sharpe ratio for the entire four years or even an entire year doesn’t really give us an accurate view of how well our system performs on an ongoing basis. For our purposes we are going to use a running window of 90 days, which is shown in the chart above. Well, that Sharpe ratio is looking rather volatile isn’t it? Which teaches us that reporting just a single value isn’t very helpful for predicting future system returns.

To give us a better idea we’re going to calculate the mean and the standard deviation of our Sharpe Ratio. We are using a 1.0 range up and down and plot that on top as to get a better understanding how volatile returns can be. And what we are learning is that it varies hugely and thus calculating a Sharpe ratio at any moment in time only gives us a fraction of the information. I could be building a system and test it back a year or two and when calculating the annual Sharpe I may be getting a very positive value and then six months later get a negative one. Sure getting a very positive averaged annualized Sharpe throughout an extended testing period is a good thing. But it does not tell us anything about the volatility that got us to that point. SQN implicitly fixes that problem to some extent (as it considers standard [...]]]>

Alright we pretend that we have a very simple trading system which has but one single rule: *Be long AMZN without a stop or a target*. Simple enough and it serves us well for demonstration purposes as our P&L now effectively becomes the price series of Amazon. We are going to buy Amazon on 1/1/2012 and hold it through 1/1/2015 – four years of continuous price action.

Now one statistic often used to describe the performance of an asset or a trading system is the Sharpe ratio. Actually there are two – a more simpler one that compares the mean of your returns to the standard deviation of your returns – and one that uses an additional ‘risk free’ baseline measure such as for example the return of a treasury bill. All we need to do is to calculate the difference between our system returns and the returns of the ‘risk free’ treasury bills – let’s call that our risk_only series. Then we divide the mean of the risk_only series by the standard deviation of the risk_only series, and we’re done.

Of course calculating a sharpe ratio for the entire four years or even an entire year doesn’t really give us an accurate view of how well our system performs on an ongoing basis. For our purposes we are going to use a running window of 90 days, which is shown in the chart above. Well, that Sharpe ratio is looking rather volatile isn’t it? Which teaches us that reporting just a single value isn’t very helpful for predicting future system returns.

To give us a better idea we’re going to calculate the mean and the standard deviation of our Sharpe Ratio. We are using a 1.0 range up and down and plot that on top as to get a better understanding how volatile returns can be. And what we are learning is that it varies hugely and thus calculating a Sharpe ratio at any moment in time only gives us a fraction of the information. I could be building a system and test it back a year or two and when calculating the annual Sharpe I may be getting a very positive value and then six months later get a negative one. Sure getting a very positive averaged annualized Sharpe throughout an extended testing period is a good thing. But it does not tell us anything about the volatility that got us to that point. SQN implicitly fixes that problem to some extent (as it considers standard deviation and opportunity) but knowing what I know now I would still plot it a a rolling window.

Many of us are using moving averages on a daily basis but rarely consider what it really represents. Yes, just as its name suggests it is a price average measured within a forward sliding window. Let’s plot a 90 day average and then consider what it’s telling us:

Yes yes, I know what you’re thinking. Mean reversion and all but what if you’re shifting the mean by adjusting the window? What is the perfect moving average? Well, frankly there is none because like all derivatives of price it suffers from auto correlation and residuals, which are basically your errors.

The perfect moving average has a width of 1 as it tracks price perfectly – from there we are starting to average and thus we are amplifying the distribution of our errors (i.e. the distance between price and our moving average). Let that sink in for a moment and then take a look at the chart above which plots a rolling window measuring the standard deviation of our price series. Clearly we are seeing quiet periods and rather volatile ones. So how volatile is our price series or the returns of our trading system? Very tough to say – the less volatile the better, right? But auto correlated historical series which follow a random walk it is very difficult for us to establish one concise measure that is universally applicable.

Remember that the larger our moving average window the larger the average standard deviation but also the more skewed the distribution of errors. Shown above is the rolling 90-day standard deviation of our system (in this case the price returns of NFLX) as a histogram. Note that the peak values are below 40 here but that the majority of the values are distributed between 10 and 20.

And here for comparison is a histogram of the rolling 30-day standard deviation. As expected the peak values are less pronounced now fizzling out blow 25 while the majority of the values are clustered between 5 and 10. So our std dev profile narrowed and flattened a little but our distribution appears more platykurtic.

Of course both histograms are based on the very same return series (in this case a simple price series) and thus our perspective once again is based on whatever sliding window we are choosing. In other words both histograms show us the very same return profile but from a different perspective. No matter which perspective you choose however, anything is better than just one single value.

Whenever we compute a parameter for any data set we need to also compute its volatility. Otherwise we do not know how far future measures deviate from the summary value we have just computed. The general strategy is to divide the data into subsets or sliding windows and then calculate a series of parameters instead of just settling on just one.

]]>

Still here? Very well then. Take a look at the chart above and then grab a piece of paper and write down your thoughts about what you are seeing. Would you trade this chart? What are your general impressions about it? Do you see any entry opportunities? Are we perhaps counting waves or looking at specific cycles? When you’re done please follow me to exhibit B:

I tell you what I think. Not a bad chart at first sight I’d say but it has its periods of sideways volatility. But when it gets going it really ramps so a trend trading system here may just work fine. Playing the swings may also work if you slap a Bollinger on it. Do you agree? Disagree? Make not of all that and then follow me to exhibit C:

Ouch, not a chart I would want to be trading – that looks pretty nasty. That’s usually the type of tape I try to avoid. Although it has trending periods it seems to turn on a dime at a moment’s notice. Agree – disagree? Take note.

It’s All Just NoiseI’m sure your curiosity has peaked by now and you wonder what the purpose of today’s exercise may be. And the sad truth of the matter is that it’s all nothing but noise. All three charts above were produced purely by the power of a simple python script using a vanilla random function:

import numpy as np import pandas as pd

import statsmodels import statsmodels.api as sm from statsmodels.tsa.stattools import coint # just set the seed for the random number generator np.random.seed(107)

import matplotlib.pyplot as plt

X_returns = np.random.normal(0, 1, 10000) # Generate the daily returns # sum them and shift all the prices up into a reasonable range X = pd.Series(np.cumsum(X_returns), name=’X’) + 50 # so the chart starts at 50 X.plot();

Order And ChaosTrust me, I know how you feel – it’s like the floor just gave way underneath you and took with it all the technical trading knowledge you’ve accumulated over the years. The good news is that it’s not as bad as you think, if that makes you feel any better. Let me explain. Over the past few years I spent quite a bit of time investigating fractal patterns in financial data series. A major aspect of my work was the use of machine learning tools in combination with time series classification parsers to find recurrent patterns, also called ‘motifs’. Some may call them fractals although technically speaking fractals are self-recurring on larger intervals, so I usually prefer the term [...]]]>

Still here? Very well then. Take a look at the chart above and then grab a piece of paper and write down your thoughts about what you are seeing. Would you trade this chart? What are your general impressions about it? Do you see any entry opportunities? Are we perhaps counting waves or looking at specific cycles? When you’re done please follow me to exhibit B:

I tell you what I think. Not a bad chart at first sight I’d say but it has its periods of sideways volatility. But when it gets going it really ramps so a trend trading system here may just work fine. Playing the swings may also work if you slap a Bollinger on it. Do you agree? Disagree? Make not of all that and then follow me to exhibit C:

Ouch, not a chart I would want to be trading – that looks pretty nasty. That’s usually the type of tape I try to avoid. Although it has trending periods it seems to turn on a dime at a moment’s notice. Agree – disagree? Take note.

I’m sure your curiosity has peaked by now and you wonder what the purpose of today’s exercise may be. And the sad truth of the matter is that it’s all nothing but noise. All three charts above were produced purely by the power of a simple python script using a vanilla random function:

import numpy as np

import pandas as pd

import statsmodels

import statsmodels.api as sm

from statsmodels.tsa.stattools import coint

# just set the seed for the random number generator

np.random.seed(107)

import matplotlib.pyplot as plt

X_returns = np.random.normal(0, 1, 10000) # Generate the daily returns

# sum them and shift all the prices up into a reasonable range

X = pd.Series(np.cumsum(X_returns), name=’X’) + 50 # so the chart starts at 50

X.plot();

Trust me, I know how you feel – it’s like the floor just gave way underneath you and took with it all the technical trading knowledge you’ve accumulated over the years. The good news is that it’s not as bad as you think, if that makes you feel any better. Let me explain. Over the past few years I spent quite a bit of time investigating fractal patterns in financial data series. A major aspect of my work was the use of machine learning tools in combination with time series classification parsers to find recurrent patterns, also called ‘motifs’. Some may call them fractals although technically speaking fractals are self-recurring on larger intervals, so I usually prefer the term motif as we normally look for the same recurring pattern within the same time window.

Turns out that I actually wrote a multiple-dimension parser and parsed for the same motif on a series of time windows, so in the end a fractal it is. What I learned in months of testing is that there are in fact recurring fractals in financial time series. However, the type and frequency significantly differ from one symbol to the next, plus the number of recurring patterns/fractals/motifs only account for about 5% of the series. Which means that 95% of it is noise, or more correctly what is known as a ‘random walk’.

So is everything we have learned about the markets complete horse wash? Are there in fact no technical patterns and are we fooling ourselves? Well, yes but no. In the words of George Box (one of the great statistical minds of the 20th century): “*all models are wrong, but some are useful*.” In reality there is most definitely a significant amount of randomness to all financial markets. But I would call it ‘guided randomness’ because in between the noise are the actions of human traders who look at a chart and believe that buying or selling at a certain threshold makes a lot of sense. And as such it often becomes a self fulfilling prophecy, because just like water it seems that a random walk simply follows the path of least resistance and then finds its next level. Which of course may explain why ‘following the herd’ works so well until it doesn’t

But still two of those random charts I posted above look pretty tradeable, don’t they? Which makes one think of course whether or not the true key to profitability and success as a trader lies in picking entries. And of course we already know that it doesn’t because markets change all the time and so do the systems that operate successfully during any arbitrary trading period. Meaning you may be picking great entries like your nose one quarter and then lose it all back and then some doing the very same thing the next.

Van Tharp once stated that [*successful trading is 40% risk control and 60% self-control. In turn, the risk control portion is one half money management and one half market analysis. Thus, market analysis is only about 20% of successful trading. Yet most traders emphasize market analysis while avoiding self-control and de-emphasizing risk control. To become successful, traders need to invert their priorities*].

We’ve talked about self control many times here but let’s set that aside for now. Focusing on the remaining 40% only half (i.e. 20%) supposedly should be devoted to market analysis. I think that’s a vast over estimation and my own belief is that market analysis should account for not more than 5% of your trading. A lot more time should be devoted to campaign management, risk management, and capital commitment. Which are activities that are by definition a lot more analytical than technical. Instead of reading charts to find entries we should be spending a lot more time analyzing how to extract maximum returns on entries we have been taking. Of course as a financial blogger that would most likely reduce my audience by a significant margin.

]]>As you know I usually stay away from any contracts which are in the process of rolling. Which is why it is rather annoying to see such a juicy looking formation on the E-Mini this morning. Under normal circumstances I would be all over this like a fat kid on a Mars bar. But unfortunately I’ll have to sit tight on this one until tomorrow, assuming of course the setup remains intact. Which setup? Well, wouldn’t you like to know?

That however doesn’t mean that we’ve got nothing to do. A reader asked me about gold being a possible trend trading candidate, and I agree but with a caveat: First up traditional trend trading (i.e. buying high and selling low) hasn’t worked very well even for the pros during the past (QE infused) decade. Also, the odds of banking coin as a trend trader in general have never been great, not so much because of the low win rate (35% or less) but due to the fact that most retail participants don’t have the psychological make up to actually sit out both the losing streaks and the drawn out winning streaks. In short – it looks good on the surface of a chart but it’s a very tough racket and few can pull it off.

Trend Trading ReloadedOf course where there is a will there is always a way. My personal approach is a bit more involved but has the advantage of allowing you to slowly scale into trend entries as opposed to jumping in with both feet every single time. What I do is to first gauge the long term charts, e.g. the daily, the weekly, the monthly. if those suggest the potential of an inflection point preceding a trend move then I’ll look at my hourly panel for a plausible entry opportunity. Which is often tricky as preceding long candles often yield very little short term context.

On gold today for example we have been graced by a little spike low which could work for our purposes. What I just did is to deploy only 0.25R with a stop a very respectable distance away. BTW the entire entry range extends further down as shown on the chart but remember that you always want to see a spike low, a Net-Line, a moving average or anything else you can hang your hat on.

Silver is where I’ll deploy another 0.25R in order to decrease the odds of being thrown off the horse by a stop run. I actually like this chart a lot better as the 100-day has just been conquered and is already in the process [...]]]>

As you know I usually stay away from any contracts which are in the process of rolling. Which is why it is rather annoying to see such a juicy looking formation on the E-Mini this morning. Under normal circumstances I would be all over this like a fat kid on a Mars bar. But unfortunately I’ll have to sit tight on this one until tomorrow, assuming of course the setup remains intact. Which setup? Well, wouldn’t you like to know?

That however doesn’t mean that we’ve got nothing to do. A reader asked me about gold being a possible trend trading candidate, and I agree but with a caveat: First up traditional trend trading (i.e. buying high and selling low) hasn’t worked very well even for the pros during the past (QE infused) decade. Also, the odds of banking coin as a trend trader in general have never been great, not so much because of the low win rate (35% or less) but due to the fact that most retail participants don’t have the psychological make up to actually sit out both the losing streaks and the drawn out winning streaks. In short – it looks good on the surface of a chart but it’s a very tough racket and few can pull it off.

Of course where there is a will there is always a way. My personal approach is a bit more involved but has the advantage of allowing you to slowly scale into trend entries as opposed to jumping in with both feet every single time. What I do is to first gauge the long term charts, e.g. the daily, the weekly, the monthly. if those suggest the potential of an inflection point preceding a trend move then I’ll look at my hourly panel for a plausible entry opportunity. Which is often tricky as preceding long candles often yield very little short term context.

On gold today for example we have been graced by a little spike low which could work for our purposes. What I just did is to deploy only 0.25R with a stop a very respectable distance away. BTW the entire entry range extends further down as shown on the chart but remember that you always want to see a spike low, a Net-Line, a moving average or anything else you can hang your hat on.

Silver is where I’ll deploy another 0.25R in order to decrease the odds of being thrown off the horse by a stop run. I actually like this chart a lot better as the 100-day has just been conquered and is already in the process of trending. Officially this is not really a trend trade as we’re not anywhere near the upper Bollinger. But heck, if the preceding ramp doesn’t count as a trend then I don’t know what does.

Odds have we’ll most likely get shaken out. And if we do we’ve lost very little coin and will have to try again later. But if gold and silver decide to head higher then we can start adding more exposure slowly, perhaps on a little dip lower or even a retest of the original entry range, both of which often leads to continuation higher. This soft entry approach makes trend trading a lot more tolerable as you’re not betting a full R every single time. If also often leads to counter entry opportunities, e.g. when the market clearly hates your idea and is most likely to reverse back to a previous support range.

Alright, I trust you are sufficiently warmed up and caffeinated because we’re just getting started – very exciting setups below the fold:

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So it’s fair to say whenever you equities take off you can be sure that retail in particular is looking for the proverbial BTFD to enter, which of course may never materialize or may occur way too late when the meat of the advance becomes ancient history. Which bodes the question: should you wait for a dip or should you enter during an advance? Well, yes and yes.

As Yogi Berra once said: If you come to a fork in the road, take it! Look, it all depends on your trading style. A trend trader doesn’t think twice about buying high and selling low. His success rate is low but when it does catch a trend he rides it as far as possible. Things are a bit more complicated for me in these situations. For one I love to ride trends and my campaign management logic is designed to give them sufficient time/space to run.

On the other hand I don’t like chasing the tape higher unless I see a pressing reason. Late stage advances are definitely not part of the package and approaching roll-over dates are always a big red flag for me. As you may know CME equity futures (i.e. the ES, YM, NQ) roll into September on Thursday and it’s not just a bit early to grab the new front month but I also expect a bit of volatility as folks are rolling their existing positions.

Tape ReadingNow while we’re on the topic I need to point out once thing and make sure you pay close attention. See that Bollinger squeeze on the E-Mini followed by an FU shake out (which caught yours truly) followed by the ramp higher? I drew a little blue square around the moment when it touched the upper Bollinger. This is when you buy. Every. Single. Time. No excuses and no ifs and no buts.

I actually did screw up there last week as I had just been stopped out and for some reason didn’t read the chart properly. Clearly there are never any guarantees but a Bollinger touch after a squeeze has a very good risk to benefit ratio. The risk is what you see happened on the downside – big bear trap. It’s quite possible to you may have gone short on a touch of the lower BB – it’s not a bad setup. But often the first touch is the fake out followed by the inverse resolve. Which is why the second touch had much [...]]]>

So it’s fair to say whenever you equities take off you can be sure that retail in particular is looking for the proverbial BTFD to enter, which of course may never materialize or may occur way too late when the meat of the advance becomes ancient history. Which bodes the question: should you wait for a dip or should you enter during an advance? Well, yes and yes.

As Yogi Berra once said: If you come to a fork in the road, take it! Look, it all depends on your trading style. A trend trader doesn’t think twice about buying high and selling low. His success rate is low but when it does catch a trend he rides it as far as possible. Things are a bit more complicated for me in these situations. For one I love to ride trends and my campaign management logic is designed to give them sufficient time/space to run.

On the other hand I don’t like chasing the tape higher unless I see a pressing reason. Late stage advances are definitely not part of the package and approaching roll-over dates are always a big red flag for me. As you may know CME equity futures (i.e. the ES, YM, NQ) roll into September on Thursday and it’s not just a bit early to grab the new front month but I also expect a bit of volatility as folks are rolling their existing positions.

Now while we’re on the topic I need to point out once thing and make sure you pay close attention. See that Bollinger squeeze on the E-Mini followed by an FU shake out (which caught yours truly) followed by the ramp higher? I drew a little blue square around the moment when it touched the upper Bollinger. This is when you buy. Every. Single. Time. No excuses and no ifs and no buts.

I actually did screw up there last week as I had just been stopped out and for some reason didn’t read the chart properly. Clearly there are never any guarantees but a Bollinger touch after a squeeze has a very good risk to benefit ratio. The risk is what you see happened on the downside – big bear trap. It’s quite possible to you may have gone short on a touch of the lower BB – it’s not a bad setup. But often the first touch is the fake out followed by the inverse resolve. Which is why the second touch had much better odds and I’m pretty miffed I didn’t take it.

On the other hand, had I taken it then it’s quite possible that I would have been stopped out by now as advancing my stop to a major spike low is rather common after 3R in profits. Which would make it 2R at maximum at this point, but once again that’s part of the game plus we are in a volatile market period.

USD/CAD was actually my favorite setup yesterday but it decided to give me a good scare after hours. It has since been recovering so if it can push back above its 100-hour SMA then it may just be ready to get going.

A reader asked me about the 6C in comparison and although it doesn’t trade perfectly inverse the setup is basically a mirror of the USD/CAD. As you can see the USD/CAD seems to be leading a little, at least this morning. Either way once 6C breaches 0.7449 then we may see an inverse resolution, so put your stop a few ticks above that.

EUR/USD is looking solid – much to my chagrin as you can imagine. At least my setup is looking good thus far as it continues to paint higher highs and higher lows. Which however also means that it needs to hold the current spike low near my entry range.

GBP/USD was an entry yesterday and I’m posting it again as it’s back in the same range. Nothing much to add here as I don’t see cause for concern yet. Holding the 100-hour SMA would be highly desirable here as well. Anyway, cable is volatile as heck since the whole BREXIT thing started and I wouldn’t recommend dropping more than 0.5R max into this one – make it 0.25 and you probably sleep better.

]]>Suffice it to say that this list is obviously incomplete and should always be considered in the context of your own trading activities. If you are a short term momentum trader then you actually may choose to ignore or even invert some of these rules. As with everything in life your mileage will vary. Without further ado:

Pick your entries carefully/meticulously. For trend traders the highest probability for success appears to be around major inflection points where potentially large explosive moves are possible. For mean reversion traders this means waiting for extreme signals followed by price confirmation. Everyone has a different lens and we trade different types of systems. What we all share is that our entries need to occur when the odds are clearly on our side. Do not make excuses and be patient. Let the tape come to you. Stick with your initial stop loss – no exceptions. I think that’s a very basic one but it bodes repeating. Keep your stops wider than usual. I recommend > 1.2 x daily ATR(14). So if the daily ATR is 20 ticks then your stop should be at minimum 24 ticks away. Obviously this rule is meaningless if you’re a ST swing trader but at minimum multiply your previous system stop loss by 1.5 or more. Keep your position sizes smaller than usual. I recommend 0.5% of your assets per campaign or less. The advantage of volatile markets is that they can move fast and far, thus even a smaller position should pay off well. You should already understand how R works and that larger stops affect your position sizing [1][2]. For example if you see a crude entry and you have insufficient assets for a single contract then you may want to trade an ETF instead. Do not trail too early. This mostly affects trend traders or people who trade break out patterns. I could draft an entire article about this but in a nutshell you should under no circumstances start trailing until your campaign touches 2R+ MFE. If you want to know why then just look at the campaigns above and you’ll understand. The odds for a final whipsaw before take off are high and I am seeing stop runs ahead of trending moves all the time now. You should also not be too quick about moving your ISL to break-even. Personally I am skipping my b/e rule at this point and will keep my ISL until 2R MFE. If you insist on [...]]]>

Suffice it to say that this list is obviously incomplete and should always be considered in the context of your own trading activities. If you are a short term momentum trader then you actually may choose to ignore or even invert some of these rules. As with everything in life your mileage will vary. Without further ado:

**Pick your entries carefully/meticulously**. For trend traders the highest probability for success appears to be around major inflection points where potentially large explosive moves are possible. For mean reversion traders this means waiting for extreme signals followed by price confirmation. Everyone has a different lens and we trade different types of systems. What we all share is that our entries need to occur when the odds are clearly on our side. Do not make excuses and be patient.*Let the tape come to you*.**Stick with your initial stop loss – no exceptions**. I think that’s a very basic one but it bodes repeating.**Keep your stops wider than usual.**I recommend > 1.2 x daily ATR(14). So if the daily ATR is 20 ticks then your stop should be at minimum 24 ticks away. Obviously this rule is meaningless if you’re a ST swing trader but at minimum multiply your previous system stop loss by 1.5 or more.**Keep your position sizes smaller than usual**. I recommend 0.5% of your assets per campaign or less. The advantage of volatile markets is that they can move fast and far, thus even a smaller position should pay off well. You should already understand how R works and that larger stops affect your position sizing [1][2]. For example if you see a crude entry and you have insufficient assets for a single contract then you may want to trade an ETF instead.**Do not trail too early.**This mostly affects trend traders or people who trade break out patterns. I could draft an entire article about this but in a nutshell you should under no circumstances start trailing until your campaign touches 2R+ MFE. If you want to know why then just look at the campaigns above and you’ll understand. The odds for a final whipsaw before take off are high and I am seeing stop runs ahead of trending moves all the time now. You should also not be too quick about moving your ISL to break-even. Personally I am skipping my b/e rule at this point and will keep my ISL until 2R MFE. If you insist on locking in your entry wait at minimum until 1R MFE.**Take partial profits after 3R.**This is not something I usually enjoy doing this early. But in the current environment and until we see a reduction in intra-day volatility I believe that taking partial profits after 3R MFE is necessary. How much you take off the table is up to you but I personally cash out 50% of my positions now.**Take every single entry**. The other side of the coin. There is no problem in being extra picky with your entries. But write down your entry rules and stick to them. Taking one campaign which results in a loss should not keep you from entering again tomorrow if the same conditions represent themselves. Don’t fall for recency bias.**Keep a trading log and monitor your activity on a daily basis**. Part of that is to also maintain an equity curve which clearly delineates where your pain threshold is and when you should stop trading.- I
**f you stop trading keep trading on paper.**There is only one way to know whether your system is in a drawdown or if it is permanently broken. You need to keep trading it, even if it is on paper. So keep taking entries in your demo account and record the P&L. As soon as the system appears to pick up again continue trading it, even if it’s with reduced position sizing. It’s quite natural for systems to go through earning and losing periods. **Don’t have an opinion and don’t listen to anyone who offers you one**. I guarantee you that nobody knows more about the future than you do. We are all driving blind here. Besides, successful trading is not about predicting the future, it is about dealing what’s directly in front of you in the most productive manner. Meditate on that.

I would like to cover the concept of developing your personal information diet and turning your brain into one lean mean thinking machine. The basic idea behind reducing your intake of information is nothing new and I first encountered it way back during my trend trading years. However, it is one thing for a trend trader to say that the news doesn’t matter and to limit one’s consumption. It it is another to consciously develop a systematic approach for consuming information and to extract only what is needed for arriving at high quality conclusions in the shortest amount of time.

As you can tell I have given the subject matter much consideration and over time I have developed principles which have become core tenets of my trading career. I will try to share some of them with you today in the hopes that you may not only be able to incorporate some of my ideas into your own trading activities but to how you process any information you encounter in general.

Tenet #1: Cui BonoLatin for “To whose benefit?” – literally “as a benefit to whom?”. Over time I have learned one simple fact the hard way: Whenever anyone tells you anything it is for a reason. Either they want to impress you, manipulate you, extract information, or lead you a certain way (intellectually or emotionally). Whenever a person tells me anything it now has become my habit to immediately question the motive of the piece of information or inquiry I have received. Why is this person telling/asking me this and who benefits? Cui bono. By the way some of this is directly derived from Neuro Linguistic Programming (NLP)- once you understand how people or the media is trying to manipulate you it’s a lot easier to avoid mental traps. And even knowing how it works does not make your completely impervious.

Tenet #2: Less Is MoreFlash back to 100 years ago when people only had to learn what they needed to know to survive. Information that was irrelevant to a person’s work and lifestyle was not needed, or readily available. But as time progressed, those who had the opportunity to expand their knowledge base were presented with greater prospects – and thus the quest for knowledge became a means of getting ahead.

Today we are exposed to tens of thousands of pieces of information each waking hour. The amount of data we consume has steadily increased over the last century and can be thought as an exponential curve that keeps pushing up hard. I believe we have long crossed the human brain’s ability to properly process and analyze all this data. [...]]]>
*To make sure you guys aren’t getting bored I decided to repost some timeless favorites from our Evil Speculator archives. Clearly the fight against information overload never ceases and is becoming more prevalent as the world is becoming more connected every day. As traders we need to give special attention to not only what information we expose ourselves to but also how much of it (good or bad) we let in every day.*

I would like to cover the concept of developing your personal information diet and turning your brain into one lean mean thinking machine. The basic idea behind reducing your intake of information is nothing new and I first encountered it way back during my trend trading years. However, it is one thing for a trend trader to say that the news doesn’t matter and to limit one’s consumption. It it is another to consciously develop a systematic approach for consuming information and to extract only what is needed for arriving at high quality conclusions in the shortest amount of time.

As you can tell I have given the subject matter much consideration and over time I have developed principles which have become core tenets of my trading career. I will try to share some of them with you today in the hopes that you may not only be able to incorporate some of my ideas into your own trading activities but to how you process any information you encounter in general.

Latin for “To whose benefit?” – literally “as a benefit to whom?”. Over time I have learned one simple fact the hard way: Whenever anyone tells you anything *it is for a reason*. Either they want to impress you, manipulate you, extract information, or lead you a certain way (intellectually or emotionally). Whenever a person tells me anything it now has become my habit to immediately question the motive of the piece of information or inquiry I have received. Why is this person telling/asking me this and who benefits? Cui bono. By the way some of this is directly derived from Neuro Linguistic Programming (NLP)- once you understand how people or the media is trying to manipulate you it’s a lot easier to avoid mental traps. And even knowing how it works does not make your completely impervious.

Flash back to 100 years ago when people only had to learn what they needed to know to survive. Information that was irrelevant to a person’s work and lifestyle was not needed, or readily available. But as time progressed, those who had the opportunity to expand their knowledge base were presented with greater prospects – and thus the quest for knowledge became a means of getting ahead.

Today we are exposed to tens of thousands of pieces of information each waking hour. The amount of data we consume has steadily increased over the last century and can be thought as an exponential curve that keeps pushing up hard. I believe we have long crossed the human brain’s ability to properly process and analyze all this data. Do you experience brain fog every once in a while? It may be partially related to your eating habits but most likely your brain is simply overloaded with all those tidbits you are trying to squeeze through it every day. We are simply not built to process this much information on a daily basis and there is much research that shows that the way our brains are wired and the way we perceive things are vastly different from that of our grandparents. Whether that is a good or bad things is up for debate – I think there may be good aspects but yet we should be careful about the flood of information we expose ourselves to.

Not only has the amount of information we consume increased exponentially – in my estimate the vast majority (i.e. 95% +) of what you encounter is completely useless. It does not help you succeed, it does not help you survive, and it does not educate you in any meaningful fashion. Even worse – quite a lot of it is actually harmful to your ability to arrive at a decision. Imagine a menu with 1000 dishes and 200 deserts. We all like options but that would clearly be overkill. Once you embrace an aggressive approach to consuming information it is rather easy and actually enjoyable to reduce your intake. I guess this implicitly correlates with Cui Bono and Less Is More. And again some of this is actually a product of studying NLP.

Almost self explanatory I guess. If you really want to trade on information or then news then you obviously need to dig up something the rest of the schmucks are not privy of. And unless you work at Goldman odds are you are like the rest of us – out of the loop. That rule in itself will save you hours of reading every week. Why would any news item instantly accessible by hundreds of thousands of traders provide you with any trading advantage? Very doubtful and instead you should spend your time reading tutorials or books on trading.

I might as well have called this one ‘Most People Talk Out Of Their Asses’ – and unfortunately this is the sad truth. Just go to your neighborhood bar and listen to type of crap that comes out of most people’s mouth about things they have no clue about. When someone tells you something – anything – always question the quality of the source. For instance someone is trying to give you trading advice then ask how long they have been trading and if they are profitable on a consistent basis. I know this sounds pretty basic but you would be surprised about how many purported ‘experts’ have little or not background in the subject matter they are advising you on.

I probably could go on but these five principles are really all you need in order to slowly start reprogramming your mind. Next time you come across a headline in the financial media the first question you should be asking yourself is: *Why am I reading or hearing this?* And by that I mean ‘what is the source’s motive of providing me with this information?’ Chances are it is not for you to be more profitable, most likely it is the exact opposite. *Who is providing me with this information?* Does this guy know what he’s talking about? And most of all – *do I really need to waste my precious time absorbing this information? * Chances are you you can safely skip this one over and devote your time to more productive matters.

]]>

Alright Lucy (that’s her name), imagine you take your ball into the yard outside and start kicking it. Every time you kicked it you measure the distance. Warning: Since Lucy is a spoiled little American brat we’ll be talking about yards – which will cause European metric based children to experience instant cerebral hemorrhage. So you kicked it the first time and it went 10 yards. You write that number down and then kick it again. Unfortunately you tripped a little and so the ball only went 3 yards. It counts anyway so write it down. Next time you take a running start and the ball flies 20 yards. Excellent, that definitely gets recorded for posterity. Meanwhile your annoying little brother shows up and kicks the ball away from you. He’s half your size so it only went 6 yards but he kicks it again and scores 8. You run after the little bugger and kick it back about 12 yards. Who instantly starts bawling and just out of spite kicks that ball as far as he possibly can – 9 yards – through the kitchen window. Game over and of course you blame your brother for everything.

So let’s do the numbers – we have measured 7 kicks in yards:

10, 3, 20, 6, 8, 12, 9

First we need to figure out the average or mean of the distances, which we get by adding all those numbers together and dividing it by 7. So that would be 68 divided by 7 which yields us 9.71. Let’s draw a line on our chart:

Alright at this point it’s becoming clear that Lucy must have been feeding her ADD meds to her dog as she ran out to play about five minutes ago. Mental note to drop her from this year’s Christmas shopping list. So let’s explain the rest to that good-for-nothing brother of yours:

All we do from here is to deduct the mean (i.e. 9.71) from all the numbers:

0.29, -6.71, 10.29, -3.71, -1.71, 2.29, -0.71

Oh-ooooh – negative numbers. I don’t remember anyone kicking the ball backwards! What to do? Simple we square those numbers which gets us a positive series:

0.08, 45.08, 105.80, 13.80, 2.94, 5.22, 0.51

Now that’s weird. Seems like the negative numbers turned into very large exponents. Those are actually the relative ‘variances’ based on the mean and if we take the mean of all those numbers we get to… drum rolls… 24.78. That number represents the average variance from the mean.

So how about standard deviation? I got [...]]]>

Alright Lucy (that’s her name), imagine you take your ball into the yard outside and start kicking it. Every time you kicked it you measure the distance. *Warning: Since Lucy is a spoiled little American brat we’ll be talking about yards – which will cause European metric based children to experience instant cerebral hemorrhage*. So you kicked it the first time and it went 10 yards. You write that number down and then kick it again. Unfortunately you tripped a little and so the ball only went 3 yards. It counts anyway so write it down. Next time you take a running start and the ball flies 20 yards. Excellent, that definitely gets recorded for posterity. Meanwhile your annoying little brother shows up and kicks the ball away from you. He’s half your size so it only went 6 yards but he kicks it again and scores 8. You run after the little bugger and kick it back about 12 yards. Who instantly starts bawling and just out of spite kicks that ball as far as he possibly can – 9 yards – through the kitchen window. Game over and of course you blame your brother for everything.

So let’s do the numbers – we have measured 7 kicks in yards:

10, 3, 20, 6, 8, 12, 9

First we need to figure out the average or mean of the distances, which we get by adding all those numbers together and dividing it by 7. So that would be 68 divided by 7 which yields us 9.71. Let’s draw a line on our chart:

*Alright at this point it’s becoming clear that Lucy must have been feeding her ADD meds to her dog as she ran out to play about five minutes ago. Mental note to drop her from this year’s Christmas shopping list. So let’s explain the rest to that good-for-nothing brother of yours:*

All we do from here is to deduct the mean (i.e. 9.71) from all the numbers:

0.29, -6.71, 10.29, -3.71, -1.71, 2.29, -0.71

Oh-ooooh – negative numbers. I don’t remember anyone kicking the ball backwards! What to do? Simple we square those numbers which gets us a positive series:

0.08, 45.08, 105.80, 13.80, 2.94, 5.22, 0.51

Now that’s weird. Seems like the negative numbers turned into very large exponents. Those are actually the relative ‘variances’ based on the mean and if we take the mean of all those numbers we get to… drum rolls… 24.78. That number represents the average *variance* from the mean.

So how about standard deviation? I got you covered. All you need to do is to square that number and you get to 4.987, which is the standard deviation. Finally!

Of course one really annoying thing about that imbecile of a brother is that he never trusted you. So he whips out his mobile phone and goes to an online SD calculator. ‘Ha-haaa!’ he shouts ‘you were wrong!! See here, the real standard deviation is 5.376. I knew you always sucked in math’.

Ooops that’s embarrassing, what happened? Well, tell your brother that he calculated the ‘sample SD’ while you gave him the ‘population SD’. What’s the difference? If you take only a sample from a larger population of numbers then you need to actually deduct 1 from the number samples when calculating your variance. Instead of dividing the sum of the squared values by 7 we divide them by 6.

Here’s a spreadsheet I put together so you don’t get confused. On the bottom left you see our ‘control number’ which Excel’s built-in SD function. So we are spot on!

All that’s left to do for us now is to actually draw the SD value(s) to our chart, in this case a very simple bar graph. Just like with a Bollinger you take the mean and then add the SD of 5.37. For the negative SD you simply deduct the same SD. That gives us two lines shown above in green, one at 4.338 and another at 15.09 (for sample SD which is what everyone uses by default). If you count the numbers of bars (i.e. kicks) that fall within that standard deviation range you arrive at 5 out of 7 (the 2nd and 3rd are outside). That sounds about right as that is 71% within a very small sample of 7. Strangely when writing that little story for Lucy I just pulled those numbers out of my butt and it’s interesting that the numbers worked out so well. So there appears to be a natural and almost instinctive order to distribution patterns.

Now if Lucy raided her mom’s cookie jar and due to an epic sugar rush kept kicking that ball for hours on end whilst collecting the distances odds suggest that the final tally would settle around 68% – a little over 2/3 of the sample size. Another way of phrasing it is that 68% of all the kicks would most likely fall within a standard deviation range of 4.338′ to 15.09′. And that is called ‘normal’ distribution or ‘Gaussian’ data.

But wait there is more. We can actually keep adding SD intervals simply by adding the same distance (i.e. 5.37) once again and then again. Which is visualized in the graph shown above – I’m sure you’ve come across it in the past. In this specific case the kicking range spanning 2 standard deviations would be between 0.87′ to 18.558′ and encompass over 95% of all the samples. Each standard deviation interval is also often referred to as ‘confidence intervals’ and that is what the nerds mean by ‘sigma’.

Here’s a handy table that shows you each confidence interval, *assuming normal distribution* (a topic we have covered in the past but will revisit in the near future). If you click on the table it’ll get you to the page where you can play with the numbers or add your own.

Remember last time when you read some article over on ZeroEdge suggesting the possibility of a ‘six sigma’ event? Well, if you count the rows in that table above then you realize that this puts us in the top 0.001% of all trading days, which is 1/1000th of one percent, or one out of 100,000. Wait a minute. 100,000 / 365 comes out to 273 years? Almost three centuries? But we had several major market crashes in the past 100 years alone, not even counting recent flash crashes:

- Florida Real Estate Craze in 1926
- The Great Depression starting in 1929
- The Big Crash of 1987
- The Asian Crisis starting in 1989
- The Dotcom Crash in 2000
- The Housing Bubble Crash in 2007.

That comes out to at least 6 large ‘unforeseen’ market events in the past century. If you would average that out over 300 years that would be 24 out of 100,000 trading days, or 0.024%. Deduct that from 100 and you get to 99.976. For it to be a six sigma event it would have to be > 99.999 but it’s smaller. It’s not even > 99.99% which would have made it a five sigma event. It is however > 99.9% so perhaps they should call them Four Sigma events instead?

- Lucy loves kicking balls but apparently doesn’t like math very much. Then again she’s nine years old, what’s your excuse?
- Mole is a horrible uncle who tortures innocent children with math riddles (I charge per hour by the way).
- Standard deviation is a measure of how spread out numbers are.
- SD is the square root of the variance throughout all the samples.
- I should never listen to ZeroEdge, read Evil Speculator instead.
- Apparently financial risk is not being assessed correctly. Big surprise there!
- You should definitely buy Nassim Taleb’s new book (no I don’t earn any commissions from that link).