The average move of a market

Markets have a high degree of randomness (and madness), but there are some things which hardly change over time. One is the width of an average market move before a counter-move can be observed.

The average move of a market

As shown on the screenshot above, the last major moves in Dow Jones all had about the same magnitude. I can not give a cause for this behaviour, it is just an observation.

Technical analysis has made use of this wisdom for the last 100 years, so let`s see if we can use this highly subjective measurement in a more standardised, algorithmic way.

Algorithmic test of wide of moves

To do an algorithmic test of the average width of an up or down move, the Zig-Zag indicator is a fabulous starting point. This indicator is always drawn from a swing high to a swing low, and it has a filter setting to filter minor counter moves.

The chart below shows the Dow Jones Index with the Zig-Zag indicator, filtering all moves less than 2%. Filtering all minor moves shows the market structure. But unfortunately this also adds a significant delay to this indicator. It looks good in history, but is hardly useful in real time. As an example, the low shown at the end of the chart is not fixed by now. Only if the market moved up more than 2% (on close to close basis), the low around 24500 would be fixed. But then it is most probably too late to enter into a long trade…

The average down move of Dow Jones Index

So instead of asking myself what the current market structure might be, I will use this indicator to calculate the average length of a market move. A later post will show the distribution of the length of market moves.

The screenshot above shows the average up and down move of the market, when the Zig-Zag noise filter is applied. The bottom line gives you the width of the average down move, if all moves less than 5% are removed.

On average, since 1897, the Dow Jones Index experienced a 13% down move, before an at least 5% up move could be expected.

If Dow Jones would be normal distributed, the average width of an up or down move would be equal. But as we had a strong up movement since 1897 (start of analysis) the average up moves are somewhat higher than the down moves.

Analysis of width of market moves

Knowing how far the market can travel without a significant reversal (the filter setting) helps in developing realistic scenarios for the future. Knowing these numbers for your market and time frame is key to placing appropriate stops and targets.

Below are the results for an average market move with a 3% noise filter applied for Dow, S&P, German Power, Emissions and WTI crude. I used 10 years of data for this analysis. Contact me for other market/counter move settings.

keep researching…

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Market crash or market correction?

Over the last days and weeks some traders have been worried if the currently ongoing correction in the markets will evolve into a crash, or if it is just a normal correction.

Crash or correction

The main difference between a correction and a crash is the panic level. But it is not the absolute level of .VIX, the CBOE implied volatility meter. It is the difference between realized and implied volatility that defines a crash which defines real panic.

If things are expected to go totally wrong, VIX will have a way higher level than realized volatility. But as you can see on the chart below, VIX and realized volatility are just in tune.  (Oct. 29th 2018)

So my conclusion is: business as usual, have a cup of tea…

Divergence in market breath indicator (stocks above 20 day average) might also suggest it is not a crash.

Still the majority of stocks (60%) of Dow Jones Industrial trade above their 200 day average. US market breath is still bullish…

And having a longer-term look at the market one can clearly see, that the movement of the last two weeks hardly has any significance when it comes to the real big moves we all are frightened or hope for…

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Bollingerband: The search for volatility

Usually it makes no sense to fight against normal distribution. But there are setups which have got a high probability of unexpected behavior.  Volatility can be the key to future market movements.

Bollinger bands width percentile

Bollinger Bands are a great tool to describe market volatility. And my favorite tool to measure the width of Bollinger Bands is Bollinger percentile.

Like the IV percentile indicator my Bollinger percentile indicator is a probabilistic indicator. It gives the probability of Bollinger Bands having a narrower upper band – lower band range than currently given.

A Bollinger percentile of 93% (screenshot) means, that in only 7% of the last 1000 trading days Bollinger bands have been wider than they are today.

A Volatility Prognosis

We already had some statistics on how likely the market will be within today’s Bollinger band in a given number of days from now.

This time I would like to find out if the market will be within a market neutral volatility prognosis cone in a given number of days from now.

Bollinger bands are somehow trend following. This comes due to the moving average they are based on. The volatility cone I am testing in this article is market neutral. It has no bullish or bearish offset. I am using Kahler`s volatility to calculate this fair bet vola cone.


  1. How likely is the market within the shown volatility cone within 20 days from now?
  2. Can Bollinger Percentile identify areas with a higher/lower probability of being inside/outside of the vola cone?

Outside Kahler`s volatility cone in 20 days from now

First let’s run a test on the probability of the market to be outside the shown fair bet vola cone within 20 daily bars from now.

Running on 10 years of daily data the test shows the expected result; In slightly more than 50% of time the stocks have been outside of the fair bet vola cone.

Bollinger percentile volatility prognosis

Old market wisdom says that after a volatile phase things will calm down. This is the basic idea behind the next tests.

I would like to see if the probability of being in or out of the projected vola cone can be determined by looking at the width of the current Bollinger band.

Running the same test as above, but calculating the results depending on the level of the Bollinger percentile indicator gives a new picture.

If Bollinger percentile is above 50, you got a higher probability of being outside the volatility prognosis in 20 days from now than you would have with a Bollinger percentile below 50. Bollinger percentile above 50 means, that the width of the Bollinger band has been below the current level in more than 50% of the last 250 bars.

The width of the volatility cone itself is not influenced by the width of the current Bollinger band. It’s width is calculated over  the last 1000 daily bars of historic data and does not change a lot over time. The Bollinger band is calculated over 20 days.

On the screenshot above you see the probability of the market of being outside the volatility cone in 20 days from now. The first row of results gives the probability of being outside if Bollinger percentile is above 75%, the second row gives the results for being outside the vola cone when Bollinger percentile is below 25%. As you can see, there is quite a difference.

The results behave opposite to what I would have expected.

A wide Bollinger band does not lead to a higher probability of the market being inside a market neutral vola prognosis. I would have assumed, that if we got a wide Bollinger band, the market would calm down and stay within a range for some days. But the opposite is true.


Depending on your trading style these findings can be used is several ways.

  • If you trade market neutral strategies, the vola projection gives the break even points of a fair priced at the money straddle, you can use these findings to decide if it is better to buy or sell a straddle.
  • If you are trading directional you can use these findings to look for probable breakout scenarios or for placing target/stop orders to make use/protect form unlikely events.

Research pays off, contact me for more details.


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Tradesignal Implied Volatility and IV Percentile Scanner

Implied Volatility and IV Percentile

Thanks to  implied volatility and IV percentile data is available. For free on a weekly basis. Using this data and the given code the data can be loaded into Tradesignal. This enables you to do your custom market scans, combining Tradesignal technical analysis and the implied volatility data from the optionstrategist website.

Free data

The first step to use the optionstrategist data would be to safe it into a text file. Just copy and paste the data, no additional formatting is required. The free data on the website is updated every Saturday.

Read the file in Tradesignal

After storing the data in the text file, you will have to open a scanner in Tradesignal and apply the given code. Set the scanner to load at least 250 data, as the long history is used to calculate the realized volatility.

Scanner code (indicator)

function code for kvol:

The code is build to run with the version 9 of Tradesignal online terminal

It will read the implied volatility and the IV percentile from the stored file. Additionally it will calculate the fair price for a straddle (realized vola) and compare implied volatility to the fair price volatility.

Scanning for promising stocks

I ran a scan on the S&P500 stocks, and to reduce the list of possible trades I applied some filters to the 500 results.

This reduced the 500 S&P stocks to a handful stocks. They all are traded with sufficient volume, have got a high IV percentile, the implied volatility is way higher than the fair price vola would be and they are all in a price range that fits my portfolio size.

Feel free to define your own scans. With this Tradesignal code and the given free data containing all US stocks it should be easy to find the right candidate for your next trade.


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IV Percentile – when to sell volatility

You got to know when to hold ’em,
Know when to fold ’em,
Know when to walk away,
And know when to run.
(Kenny Rogers)

When to sell implied volatility

Volatility is a nicely reverting time series. If it is high chances are good that it will come down again. The only problem is to find out when volatility is high, and when it is low. Unfortunately there are no absolute levels, you can’t say that 50% implied volatility is high, as this specific stock might have an implied volatility of 80% most of the time. So you can only compare the current volatility level to historic levels and so define if volatility is currently high or low.

Volatility rank

One simple measure to find out if volatility is high or low would be the volatility rank. It is calculated like the stochastic indicator used in technical analysis. Volatility rank (in %) = (current IV – Min IV)/(Max IV -Min IV). The maximum and minimum of volatility is usually calculated over one year.

But this calculation method has got some major drawdowns. Singular implied volatility spikes will affect the values of the year after, and it will seem that volatility is low, just because it is low relative to this one spike, but not in a broader sense. Also the absolute level has not meaning by itself. 50% would just mean that current IV is 50% of the last spike up.

IV Percentile – a probability based indicator

Unless IV rank, the stochastic like indicator, IV percentile is a probabilistic indicator. It does not give the position of current implied volatility relative to it’s historic levels, it give the probability of IV for being lower than today. So a IV percentile reading of 0 (zero) means, that there has been no IV lower than the current one. This would be a nice setup for buying volatility. It most probably will go up. On the other side, a volatility reading of 93% (as we have it on October 12th after the S&P sell-off means, that on 93% of all days in history volatility has been lower than the current one. You might want to go with the probabilities and sell volatility.

IV percentile does not only give you a level, it also gives you the probability of falling volatility.As soon as IV percentile is above 50 you have a better than 50% chance that volatility will be lower soon. Have a look at the VIX article I did, it comes to a similar conclusion. This is a key indicator when you plan to sell implied volatility.

Scan for IV Percentile

IV percentile is the perfect indicator for a market scan. Find all stocks with an IV percentile above 50 (look for 85% and higher…) and you will have an edge when selling volatility. As you can see on the chart above, a high IV percentile number also correlates with an implied volatility being above the fair bet volatility. So your edge actually has two legs: (1) current IF is high and will most probably revert down (IV percentile > 50%) and (2) implied volatility is overpriced according to historic measures.

If you add all the edges you can get the luck will be on your side.

Free IV percentile data is available at


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Implied vs. Realized Volatility for NASDAQ100 stocks

(1) You shall only trade when the chances are on your side

Comparing implied and realized volatility

Selling volatility can be a profitable game, but only if you sold a higher volatility than the market realizes later on. Comparing realized and current implied volatility gives you an idea if the chances are on your side.

We already had a look at realized volatility and what the fair price for a straddle might be. Have a look at the kvolfair bet articles. These articles present a way to calculate the historically correct price for a straddle. Whenever you sell a straddle (to sell volatility), implied volatility should be higher than the fair bet price. Only then you will win on a statistical basis.

VIX and fair bet volatility

The chart above shows the S&P500 implied volatility index VIX and the long term fair bet volatility. Right now VIX is below the 12.5% fair bet yearly volatility, suggesting that it might not be the right time to sell volatility in the S&P500 without further analysis. Statistically, selling such a low implied volatility will not be a profitable game.

NASDAQ 100 stocks implied vs. realized volatility

As it seems that current VIX is too low to sell, let`s have a look at the implied vs. realized volatility of the NASDAQ100 stocks. The table below gives the implied volatility (Sep. 30th.2018) and the long term fair bet price for volatility. To calculate this comparison I analyzed 10 years of daily data per single stock.

The higher the ratio of fair bet kvol vs implied volatility, the better the chances are that volatility selling is profitable. TSLA, XRAY, COST and CTAS are some of the stocks you might have a look on, CA, SIRI, FOX are some of the stocks I would not think about when setting up the next short straddle.

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Distribution of Returns

“Tomorrow never happens. It’s all the same fucking day, man. ”  Janis Joplin

Distribution of Returns

Analyzing history and hoping it will somehow repeat itself  is the big hope of all quantitative traders. This article is about the distribution of market returns, but not about normal distribution, Gauss and standard deviation. This article is about the visualization of market returns and what can be learned from it.

Probability distribution diagrams show the probability of a specific outcome. How likely is it that the market will be at a specific price sometimes in the future?  How does a specific bullish or bearish indicator signal affect the future market behavior on a statistical basis? An approaching visualization of the statistical probabilities are the best way to understand market behavior and find your chances in trading.

Distribution of returns

The chart below shows the distribution of returns of the American Express stock.

The probability of a specific future return is coded in shades of grey. The darker the distribution diagram, the higher the probability that the market will be there in the future. To generate this kind of chart all 1 to 50 day returns over the last 10 years have been analysed. A 50 day forward projection of expected returns is shown.

When changing the contrast settings of the distribution indicator, one gets a better impression on how likely specific events will be. As there are only 255 types of grey from white to black, a multiplication of the density by a contrast setting will overexpose the likely events. Everything that is not black, has hardly ever happened in history.

The shape of he probability distribution shown on the chart is somehow different than a normal distribution; and  the shape of this shown distribution will differ largely from market to market. This is the representation of different, inherent attributes of each market. The distribution of Nasdaq will look different than that of EURUSD. To see these differences helps when designing custom trading strategies, price targets and fair option prices.

The next chart is a returns projection for the VXX volatility ETF. We already had an article regarding the volatility of VIX ; this indicator offers a more intuitive representation of future returns than the classic distribution diagrams used back then. Data since 2011 has been used to generate this likelihood projection for the next 100 days.


Signal response and returns distribution

That different markets behave differently is nothing new to the experienced trader, this indicator just helps to visualize this fact.

An other interesting usage of this distribution indicator is to analyze the behavior of the market after a specific technical trading signal has occurred.  A path analysis  of the market.

The loop on the chart below shows the distribution of German power trading returns after a bullish-, neutral- and bearish signal. Significant differences between the distribution and probability of the realized returns after these 3 signals can be observed. These differences will finally lead to a trading strategy tailored to the specific signal-market response.

Also have a look at Demystifying the 200 day average for further ideas on how to analyze the quality of signals.

A picture says more than a thousand words..

Sorry Janis, it seems it`s not always the same f****** day. Tomorrow depends on today’s action.




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Bet on Bollinger

Ever since John Bollinger introduced his Bollinger Bands in the early 1980s they have been a favourite indicator to all technical trades. This article is about the probabilities of Bollinger bands.

How good are the chances to be outside or inside of the bands in the future? How do these probabilities relate to the current position of the market relative to the Bollinger bands? What impact has overall volatility on these statistics? These questions will be answered.

Bollinger Bands Breakout Probability

By definition of the indicator most of of the times the market will trade inside the Bollinger band. But what happens in the future? Where will the market be in some days from now. These are the questions which interest me from a truing point of view.

So I did some test on the forward prediction qualities of the Bollinger band indicator. For all tests I used the 20 day, 2 standard deviations setting, which is the standard setting for most charting packages. I then looked at the positioning of the market 20 days after relative to its current Bollinger band.


The first test was done on the S&P500 index, using data since 1983. The indicator shown on the screenshot below gives the probability of the market being outside today’s Bollinger band in 20 days from now.

The red line is the probability of being outside todays band if we are already out of the band today.  The green line shows the probability of being outside of today’s band in 20 days from now if we are trading inside of the band today.

The outside starters being outside the band in the future more likely than the inside starters, is most probably due to the trend lines of the market. Once a break is done there is a high probability it either vigorously reverses or that it carries on. Both events lead to an outside of today’s Bollinger band event.

100%-outside probability is the probability to be inside todays band in 20 days from now. It is less than 50%, regardless of today’s market relative to the band.

Stability of results

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Backtesting Market Volatility

If you want to predict volatility, you can place a bet on the option market. Just buy an at the money put and call, and at expiry day you will either win or lose, depending on the actual market move since you bought the straddle and the price you paid for the straddle. To put it simple, if the market moves more than you paid for the two options you will win, otherwise you will lose. This article is about a back test of volatility.

The fair price for volatility

When I look at the S&P500 I could buy or short a straddle with 16 business days until expiry right now for around 70$. That’s the implied volatility.

When I look at the standard deviation of 16 day returns, using the last 30 days to calculate it, it shows me a volatility of around 30$. That’s historical volatility.

When I use my own fair bet KVOL Volatility, it gives me a volatility of about 50$

Now I got three measures for volatility, but which one is the best prediction for future market volatility? And how big will the error (=wins and losses) be if we place this bet over and over again?

Backtesting volatility

Placing an perpetual bet on future volatility using the payback profile of a short straddle will give me an idea on how good historical volatility and Kahler’s volatility was able to predict future volatility. In a perfect world this virtual test strategy should be zero sum game; if not, future volatility is either over or underestimated by these 2 indicators.

If I know which indicator gives me the best volatility assumption, I can use this information to find out, if the current implied volatility of the market is too high or too low. Sell high, buy low…

The chart above gives you an idea on how I did the backtest. I place a weekly bet on volatility, based on a short straddle trade. So if I close outside the of the projected volatility, I have a loss. If the market closes inside the projection, I win. The maximum win will be the price of the volatility indicator at the beginning of the bet, the max loss is the point move within the week minus the price I got for volatility at the beginning of the bet.

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Demystifying the 200 day average

The 200 day average is usually considered as a key indicator to tell if markets are bullish or bearish. But can this be proved statistically, or is it just an urban legend handed down from one generation to the next?

Let’s do some studies and find out.

The 200 day moving average

Looking at the chart of the S&P500 index and it’s 200 day average let’s me think that the 200 day average is actually a useful indicator to separate the bull and bear phases of the market. But the eye tends to see what the brain is looking for, so you might have focused on the crash 2008 and the bull market afterwards, but have ignored all these little breaches below the 200 day moving average which happened in between. As a trader I can`t make any money with knowing that there has been a long period under the 200 day average, i need to make my decision as soon as the market drops below the 200 day average.

Distribution of returns above and below the 200 day moving average

The chart above (on the right side) shows the returns distribution of 10 day returns. The green distribution represents the 10 day returns if S&P500 is trading above it`s 200 day moving average, the red line represents the 10 day returns returns when the market is trading below its 200 day moving average. Data from 1980 up to now has been used.

What are the curves telling us?

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