Target Maths
The Math Behind the Bollinger Bands – How Scary Is It?
Most traders have an intuitive idea of what Bollinger Bands and associated indicators like %b and Bollinger width show them. It’s not difficult to visually see the bands expand and contract with changing market activity, or to grasp that most of the trading action takes place between the upper and lower BBs. But many traders are a bit sketchy on how those upper and lower boundaries are calculated: what are they actually describing?
First, let’s quickly go over the math.
I haven’t met a trader who doesn’t get what a simple moving average is – the mean of the closing prices over any specified number of days (or whatever trading period defined on the chart). For use with the Bollinger indicator, this number of days typically used is 20. This average is the cornerstone of Bollinger Bands; the bands are drawn a certain amount above and below this simple moving average.
Figuring how far away from the moving average (MA) line to draw the upper and lower bands is where things become quite a bit more interesting. In the typical chart software, the bands are drawn two STANDARD DEVIATIONS above and below the MA. Don’t panic when I describe this: it’s a mouthful, but once I show the formula it will make much more sense.
ONE standard deviation is computed by combining the squares of the difference between each of the data points and their arithmatic average, then finding average of those differences, and deriving its square root. As I said: it’s a mouthful, so let’s see a real example to lend some clarity:
- Take a data set of 9, 8, 10, 7, 11, 6, 12, 6, 12. The average of this set is 9; that’s our corner stone.
- Next, we determine the difference of each data point from that average (ex. 9-9=0, 8-9=-1, 10-9=1, 7-9=-2, etc.) and square each difference (ex. 0^2=0, -1^2=1, 1^2=1, -2^2=4, etc.).
- The following step is to find the average of those squared differences. In this example, the average is 5.11.
- Finally, we find the square root of that number, which is 2.26. That number, 2.26 in this instance, is one standard deviation from the simple average of the data set.
“Great,” you say. “What does all that tell me?” A valid question. It’s a question more people should be asking before using the Bollinger indicators.
Here is the first part of how this number can be useful: in a random sample of data (which the closing prices on our chart are assumed to be), just about 68% of the data points will lie no further from the average than one standard deviation. By the same token, assuming the same normal distribution of data points, about 95% of them will be within TWO standard deviations of their average – which is the usual setting for this indicator in most charting software.
Note that this description contains nothing about the future action of stock prices! It doesn’t tell us about up or down action – it just graphically shows us the statistical range in which the past 20 days of price activity have taken place. In other words, how active or passive has recent price activity been?
I described several ways the astute trader might use this information to guide his trading strategy in the article “How to Use the Bollinger Indicator for Trading“, but we can capture the sense of things like this: when the bands are straining to catch up to price activity, and getting markedly wider, there has been a sizeable change in market sentiment. Or when the bands have contracted sharply, traders are standing pat, waiting for something to happen – and when something DOES happen, an extended move in the stock can be the result. Traders should have a plan for both contingencies.
Final reminder: as with all indicators, the Bollinger bands are just another way to describe what you can see already in price activity on the charts. It’s not magic. Spend some time watching the indicator and getting a feel for how the bands move with price action. With that experience in your head, you can use them skillfully to scan for opportunities or target the right spot to act in a chosen stock.
As always, stay timid!
Timothy McCready
About the Author
An avid trader of multiple financial markest, Timothy McCready (also known as Timorous on his website) is also very mindful of the dangers presented by trading without proper education or a definite plan. He shares his thoughts on the markets so that other traders can profit without putting their hard earned capital at risk. Readers can get access (without charge) to his workbook: “How to Make Your Own Trading Plan” at http://www.TimorousTrader.com/.
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