There is a wide range of technical indicators and those who have the choice are spoilt for choice. New developments compete with long-established indicators for the favor of the traders. The Bollinger Bands tend to belong to the latter group, as they were first introduced in the 70’s and 80’s.

There is a wide range of technical indicators and those who have the choice are spoilt for choice. New developments compete with established indicators for the favor of the traders. The Bollinger Bands rather belong to the latter group, since they were already introduced in the 70’s and 80’s.

The Bollinger Bands belong to a whole group of trading bands with the goal of developing an indicator that follows the price trend on the one hand, but on the other hand also shows the fluctuation possibilities within it. With the help of such an indicator, not only would the fundamental direction of the underlying asset under consideration be recognizable, but the bands would also provide potential support and resistance lines. The big question was which trend is currently dominant in the underlying and when in this trend the underlying asset is cheap or expensive.

A noble endeavor, which Bollinger also pursued. However, in contrast to various other attempts like the envelopes, Bollinger did not want to construct “arbitrary” bands, but rather place them on a “statistical” foundation: volatility. He experimented with various concepts, but in the end decided on the standard deviation. The standard deviation is a measure that describes the distribution of data around its center. If a base value fluctuates only slightly around its mean value, the standard deviation will be relatively small. However, if the base value is subject to larger fluctuations, the standard deviation will also be larger. The standard deviation can be found in guidelines (see Fig. 1), there abbreviated as STDEV, also as a single indicator. As you can see in Figure 1, the current standard deviation in the DAX daily chart averaged 123.61 points over the last 10 trading days. The DAX thus fluctuates 123.61 points around its average price of the last 10 days. It should be noted that these fluctuations can be either up or down. The standard deviation is only a measure of volatility, but not of the direction of the market. In addition, we will explain some special assumptions regarding the standard deviation later, but at this point we would like to derive the Bollinger Bands first.

With the standard deviation we have a measure for the volatility in the market. What Bollinger still needed to construct its price bands was a measure of the mean and trend in the underlying. Here it was obvious to use a simple moving average. Not least because such a moving average is already necessary for determining the standard deviation. After all, this measures the fluctuation margin around an average value. Together, the Bollinger Bands thus consist of three elements:

- The moving average as a centerline
- The standard deviation as a measure of volatility
- The construction of the price bands above and below the centre line by removing the standard deviation up and down to the average

By default, guides and most other charting tools use a simple 20-sided moving average to construct the centerline. For this period, the standard deviation is now measured and twice the value of this is added up and down to the mean value. As shown in Figure 2, the current standard deviation is 174.02 points. Multiplied by a factor of 2, this results in a fluctuation range of 348.04 points. The mean value is 9,261.03 points. If we add 348.04 points to this, we get the upper band at 9,609.07 points. If we subtract twice the standard deviation from the mean value, we get the lower band at 8,912.99 points.

Consequently, when using the Bollinger Bands, the trader has two basic adjustment options. One is the length of the moving average and the other is the factor for the standard deviation. The parameters used in Figure 2 correspond to the values commonly used in most charting tools, but the trader is required to optimize them for the underlyings he is looking at.

According to Bollinger, this step begins with the choice of the length of the moving average. As a trend filter, this should show the basic direction of the underlying asset and at the same time serve as a support. Consequently, the moving average should be selected in such a way that it is broken as rarely as possible within the scope of the targeted trend movement. As an example, we look at an existing downtrend in which the market made a recovery. At the upper reversal point of the recovery, the bears return and try to resume the downward trend. In the course of the following wave of selling, however, the prices do not make it to a new low, but turn north again above it. The moving average could now be chosen in such a way that the resulting correction low lies within the range of the moving average. As an example, Figure 3 shows the trend reversal in the summer of 2012 in the DAX. As can be seen, the 50’s moving average acted as a support during the bottoming process and also during the following uptrend, prices will remain above the moving average.

The second step is to set the multiple of the standard deviation. It is no coincidence that a basic setting at twice the standard deviation has become established. There is a simple assumption behind this: The returns in the market are normally distributed. This means that a positive return around the average value of X% has the same probability as a negative one. The distribution function of the return is similar to a bell curve. This assumption is exciting in that under these conditions within the simple standard deviation about 70% of all prices will be within the simple standard deviation and within the double standard deviation already about 95%. If this assumption is correct and we draw a band around the moving average in the amount of twice the standard deviation, about 95% of all prices would lie within the band. In other words, there are seldom prices outside the band, which is mainly in response to our desire to obtain potential support and resistance from the price bands.

## Application of the Bollinger Bands

Within the framework of classic trend analysis, we can use the moving average to determine the current prevailing trend in the underlying instrument. If the average rises and prices tend to be above it, an upward trend prevails. In such a case, price losses should initially only be seen as corrections and should ideally end within the range of the moving average. At this point, you should not regard the average as a wall, but rather as an area in which the correction should ideally end. Temporarily falling below this is therefore not a major problem. Provided that the moving average can fulfill its function as a support and the prices start to move upwards again, the area of the upper Bollinger Band would be a potential target. Within this range, depending on the set multiple of the standard deviation, the “normal measure” for the buy wave would be exhausted and the price could enter into another correction.

If the underlying asset falls below the moving average for the first time on a sustained basis, this would provide the trader with an indication that the current upward trend threatens to reverse. The lower Bollinger Band could now serve as a target area where a recovery should begin. As prices are now below the average, this acts as a resistance and if the trend change is “real”, this area could be expected to generate new selling interest followed by a new low. This new low can be seen as confirmation of the trend change. The game now turns around and within the potential new downtrend there is a price fluctuation between the moving average and the lower Bollinger Band.

The principle of the Bollinger Bands has a clear logic in its classical application. The moving average as a trend filter combined with the standard deviation, which by definition hardly allows prices outside of it, sounds like a magic bullet. Figure 4 shows, however, that stock markets are not always logical. The development of the DAX over the last 12 months can be seen. In its standard setting and with the rules mentioned above, it quickly becomes obvious that a clear trend assessment in the DAX based on BB(20, 2) was more than difficult.

Far too often the price broke through the downward moving average from July onwards and touched the lower Bollinger Band several times, only to fail to reverse the trend. The volatile consolidation phase from the end of January onwards, when the market was very active, is especially noticeable. In retrospect, it is now easy to find the right settings for the Bollinger Bands. Thus, Fig. 5 shows the BB(50, 2). It is nice to see that the moving average now better reflects the trend.

The corrections within it usually end up within the range of the average as it should be. The upper Bollinger Band as a resistance looks differently. In fact, there were hardly any prices outside of the band during the rally, but at a resistance one actually expects that the price bounces off it significantly. Instead, the price moved up just below the band for a long time. In this respect, the interpretation of the bands could be limited to the fact that although they limit the movement in the respective direction (rarely prices outside), there need not necessarily be major counter-movements when the bands are reached. This can be observed again and again, especially with good trend movements.

### Conclusion:

The Bollinger Bands belong to the classic trend indicators, which can be used in many ways due to their construction. Basically, they are intended to capture the fluctuations of the underlying asset and if we look at various underlying assets including the associated Bollinger bands, this seems to work well in that there are hardly any prices outside the bands. As is often the case, however, the devil is in the details of the Bollinger bands. Especially when it comes to deriving concrete trading rules based on the Bollinger Bands that are also profitable, things get complicated. The simple argumentation as presented in this article is no longer sufficient. How good are the supports and resistances based on the bands really? How is a breakout from the band to be evaluated? Is it an overbought/oversold market or is it perhaps an impulse in the direction of the breakout? These are just a few questions that we will pursue in another article on the Bollinger Bands.