Bollinger bands

Bollinger Bands (or Bollinger Bands ) are a chart analysis method developed by John Bollinger in the 1980s . Based on the normal distribution , it is assumed that current prices of a security are more likely to be close to the mean value of past prices than far from it.

General

In order to identify price trends, three values are used for determination. First, the moving average method is used to calculate the average price, usually over the last 20 days. The course is then “circled” by two further “bands” calculated from the empirical standard deviation . The calculated standard deviation is multiplied by a previously determined factor (Bollinger recommends a value of 2), and this value is then added or subtracted from the previously calculated average.

Price trend as a bar chart (white), middle Bollinger band (green) and upper and lower Bollinger band (blue)

Bollinger bands BB at time t consist of:

a middle band from the arithmetic moving average ( simple moving average ) of the closing prices C (closing) the past is calculated daily, ${\ displaystyle n}$

{\ displaystyle BB_ {t} ^ {middle} = {\ overline {C}} _ ​​{t} = {\ frac {\ sum _ {i = 0} ^ {n-1} C_ {ti}} {n} }}

an upper band ( entry band ), which is calculated by multiplying the standard deviation of the closing prices C by a certain factor k and then adding the result to the mean. ${\ displaystyle \ sigma _ {t}}$

{\ displaystyle BB_ {t} ^ {top} = {\ overline {C}} _ ​​{t} + k \ sigma _ {t}}

a lower band ( exit band ), which is calculated by multiplying the standard deviation by a certain factor k and then subtracting this from the mean value. ${\ displaystyle \ sigma _ {t}}$

{\ displaystyle BB_ {t} ^ {below} = {\ overline {C}} _ ​​{t} -k \ sigma _ {t}}

The same time horizon (namely days) is often used for the calculations of both the mean and the standard deviation , but this is not a requirement. In addition, the width of the band is often used so that the Bollinger band has a width of 2σ. ${\ displaystyle n = 20}$ ${\ displaystyle k = 2}$

The width of the gap between the upper and lower band is controlled by the factor k in connection with the standard deviation . Assuming that the prices of the next time step (t + 1) are random and normally distributed, the price is found with a probability depending on k within the band gap between the upper and lower band. For example, this probability is with the factor ${\ displaystyle \ sigma _ {t}}$

k = 1 at 68.3%

k = 2 at 95.4%

k = 3 at 99.7%.

The percentage values result from the respective quantiles of the normal distribution.

interpretation

The most common interpretation is as follows: A price close to the upper or lower band is interpreted as a signal for a short-term move to the other band. However, if a plateau forms on one of the two bands and this repeats itself, a trend reversal can be expected. The convergence of the upper and lower bands in the direction of the moving average implies a larger price movement and the direction cannot be determined. However, if the course breaks out of the channel, the continuation of this movement is assumed.

John Bollinger says, however, that the tapes themselves only provide information about whether a title is currently trading relatively cheaply or relatively expensively. To generate a valid trading signals, also also developed by Bollinger Parameter% b and Bandwidth to note (bandwidth). However, since these additional parameters are very rarely available in standard applications (stock exchange software or websites with chart functions), Bollinger bands are mostly misinterpreted because important information is missing.

In practice, Bollinger bands are often used to make buying and selling decisions. So it is e.g. B. It is quite easy to check the course for extraordinary fluctuations on the basis of a long-term development (trend-following breakout systems). If the price exceeds the upper band, rising prices are expected. This so-called long position is closed again when the price falls below the upper, middle or lower band again. If the trend is reversed, falling prices are expected. However, in their theoretical approach, the Bollinger Bands are not designed to make buying or selling decisions. They are only intended to determine whether a price is overvalued or undervalued.

criticism

Contrary to what some proponents believe, the bands cannot make reliable statements about the likelihood that the price will be within a certain distance from the moving average. For example, the assumption that the price is within the Bollinger Bands 95% of the time would be as wrong as the assumption that the price follows the moving average. This is primarily due to the fact that the moving average does not actually meet the requirements for an expected value and the assumption of normal distribution for price movements on the stock exchange is not correct. As far as we know, stock market movements do not follow any known distribution function ( Benoît Mandelbrot observed a power law distribution in his work , which, however, eludes linear analysis). Furthermore, the Bollinger Bands assume that the standard deviation is known, which is not the case here. The standard deviation described above is an uncertain estimate of the true deviation.

Nevertheless, this analysis method has proven to be a reliable means of visualizing price volatilities in practice . Bollinger himself pointed out that no particular importance should be attached to the price's contact with the upper or lower band and that additional factors should be used in the investment decision.

Interestingly, the massively erroneous interpretation of the Bollinger Bands based on incorrect statistical assumptions has led some traders to view these movements as the sole trading signal. In this respect, one can speak of self-fulfilling prophecy here.

literature

John Bollinger: Bollinger Bands. The easy way to determine course trends. FinanzBook Verlag, 2004 (2nd edition), ISBN 3-898-79023-1
Edward D. Dobson: Understanding Bollinger Bands . Traders Press, 1994, ISBN 0-934-38025-2