(14) Don’t Envelop Prices In A Manner Consistent With Gaussian Distribution
It is one of the most surprising problems or issues of using Bollinger Bands in technical charts. A normal distribution, also known as Gaussian distribution or Bell Curve, is a continuous probability distribution pattern that occurs naturally in many situations.
These distributions are significant in statistics. They are often used in natural & social sciences to represent real-valued random variables whose distributions are unknown. According to Gaussian distribution rule:
(a) 68.2% of prices should be found within one standard deviation of the sample mean.
(b) 95.4% of prices should be found within two standard deviation of the sample mean.
(c) 99.7% of prices should be found within three standard deviation of the sample mean.
This will be described as price/band ratio. Although, it could be debated whether daily price fluctuations are normally distributed as per this rule but Bollinger price/band ratio offer little to no information from probabilistic perspective.
Therefore, Gaussian distribution could not be a suitable model for variables that are inherently positive or suddenly changes direction such as stocks or bonds or even index.
These variables can be better described by other distributions such as log-normal distribution or Pareto distribution.
(15) Price/Band Ratio Is Not Scale Invariant
It is one of the most difficult issues of using Bollinger Bands in technical charts. The price/band ratio from a given standard deviation should remain constant as timescales increase.
But, it is not the case with Bollinger Bands. These bands don’t remain constant as timescales increases. For example, when we observe S&P 500 prices with 2xSD banding:
(a) 160-bar Bollinger bands:
Price/band ratio = 83.7%
(b) 80-bar Bollinger bands:
Price/band ratio = 86.2%
(c) 20-bar Bollinger bands:
Price/band ratio = 88.5%
Therefore, traders need to take this into consideration when analyzing Bollinger bands chart patterns.
- Bollinger Bands Limitations: Azureedge.net