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? 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 Forward Prediction
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 trendines of the market. Once a break is done there is a high probability it either vigorously reverserses 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
This behaviour of staying outside of today’s band seems to be quite consistent. The screenshot below shows the result of a simulation using stock data over more than 10 years of history. The green column gives the probability of being outside todays bollinger band in 20 days from now if the market trades inside the band today; the red column gives the future outside probability if the market today is already outside the band. There is not a lot of variation in the data…
Importance of Volatility
The next question was, if these probabilities can be pushed up a little bit. A mere 60% is not the white cream of trading.
Volatility is reflected in the width of the bollinger band. Doing an oscillator which shows the relative volatility, compared to the previous 50 days, I can build another trick into the out-of-bollinger probability. I can ask he question on how current volatility relates to the future outside probability. Is is a probable to be outside the bands in 20 days from now if today’s relative volatility is high or low?
The results are quite clear. The tighter the band is today, the higher the probability of being outside of it in 20 days from now.
The chart above shows the probability of being outside of today’s band in 20 days from now (starting inside band) as a function of the level of relative volatility. The lower relative volatility is, the higher the probability of being outside in the future.
The same is true if we already start outside of today’s band chart below). The lines on the chart below calculating after at least 250 events.
The results are as expected if we test for a high volatility setup. On the chart below the indicators show the bollinger-outside-probability for these times.
Note: If your bollinger band is wider than 50% of it’s highest last 50 days volatility, you have got a higher than 50% chance to be within today’s band within 20 days from now. This would not qualify as my favourite setup for a trend following position….
A tight bollinger band seems to be the best setup for a breakout strategy. Although these tests did not say anything about direction, the charts make it quite obvious that bollinger bands can be used as a tool for detecting a no-go zone. There is a higher than 50% probability, that the market will not be within today’s band in 20 days from now.