Explain Bollinger Bands?

Answer 1

The idea of Bollinger Bands is flawed mathematically, but the reason is complicated. I wouldn't use them, but here is the idea.

There are several measures of statistical distributions. The four primary ones are mean, standard deviation, skewness and kurtosis presuming your "residuals" are normally distributed.

Skew is the measure of shift of the median from the mean, or how squished to one side the actual distribution is. Kurtosis is the measure of the fatness of tails.

Bollinger Bands ignore skew and kurtosis, the result is, they do not work.

The mean is what is usually called the "average." Standard deviation is the square root of what is usually called the variance, or how wiggly the data is around the mean.

Stock prices vary, so Bollinger Bands look at the recent mean, say of the last twenty minutes and how wiggly the price has been. Each trade the mean and variance are calculated and recalculated. As the variance increases, the bands get wider, likewise, they shift around the mean as it moves.

The basic idea of the Bollinger Band is that when a stock moves strongly above a point several standard deviations up or down, it should revert back to the rolling mean. So if a stock falls dramatically below the bottom Band, you should buy and if it shoots way above a Band, you should sell.

The weakness of the Bands are three-fold:

1) It ignores kurtosis and skew, in doing so, it is actually ignoring the true data and placing a false model on it.

2)It assumes there is sufficient information in the stock prices to make choices without additional information, however a review of the "residuals," would show that significant and important information is being ignored, forcing faulty decisions to occur.

3) Equity prices are not normally distributed and are either Cauchy or Levy-Alpha Skew distributed making point estimates meaningless using normal calculation methods.